Force and Sound Pressure Sensors Used for Modeling the Impact of the Firearm with a Suppressor

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Article Force and Sound Pressure Sensors Used for Modeling the Impact of the Firearm with a Suppressor

Jaroslaw Selech 1, Arturas¯ Kilikeviˇcius 2 , Kristina Kilikeviˇciene˙ 3 , Sergejus Borodinas 4, Jonas Matijošius 2,* , Darius Vainorius 2, Jacek Marcinkiewicz 1 and Zaneta Staszak 1 1 The Faculty of Civil and Transport Engineering, Poznan University of Technology, 5 M. Skłodowska-Curie Square PL-60-965 Poznan, Poland; [email protected] (J.S.); [email protected] (J.M.); [email protected] (Z.S.) 2 Institute of Mechanical Science, Vilnius Gediminas Technical University, J. Basanaviˇciausstr. 28, LT-03224 Vilnius, Lithuania; [email protected] (A.K.); [email protected] (D.V.) 3 Department of Mechanical and Material Engineering, Vilnius Gediminas Technical University, J. Basanaviˇciausstr. 28, LT-03224 Vilnius, Lithuania; [email protected] 4 Department of Applied Mechanics, Vilnius Gediminas Technical University, Sauletekio˙ av. 11, 10223 Vilnius, Lithuania; [email protected] * Correspondence: [email protected]; Tel.: +370-684-04-169

Received: 23 December 2019; Accepted: 30 January 2020; Published: 2 February 2020

Abstract: In this paper, a mathematical model for projectiles shooting in any direction based on sensors distributed stereoscopically is put forward. It is based on the characteristics of a shock wave around a supersonic projectile and acoustical localization. Wave equations for an acoustic monopole point source of a directed effect used for physical interpretation of pressure as an acoustic phenomenon. Simulation and measurements of novel versatile mechanical and acoustical damping system (silencer), which has both a muzzle break and silencer properties studied in this paper. The use of the proposed damping system can have great influence on the acoustic pressure field intensity from the shooter. A silencer regarded as an acoustic transducer and multi-holes waveguide with a chamber. Wave equations for an acoustic monopole point source of a directed effect used for the physical interpretation of pressure as an acoustic phenomenon. The numerical simulation results of the silencer with different configurations presented allow trends to be established. A measurement chain was used to compare the simulation results with the experimental ones. The modeling and experimental results showed an increase in silencer chamber volume results in a reduction of recorded pressure within the silencer chamber.

Keywords: force sensor; silencer; point wave source; dynamic impact; sound pressure

1. Introduction The results of acoustic and force sensors’ measurement and their use in shooting simulation are analyzed in a series of articles. Acoustic parameters and force measurement technology is widely used in the assessment of the characteristics of the shot. Parameters of firearms and their accessories (sights, silencer, etc.) are research objects of many studies worldwide, as the high precision and reliability of their evaluation is required by state authorities of weapon supervision. A modern silencer of the firearm is vastly superior to ear-level protection and the only available form of suppression capable of making certain sporting arms safe for hearing [1–8]. Forces show an increasing number of cases of hearing damage [9–15]. Many of the early developments of the silencer were mainly empirical in nature [16–25]. The basic purpose of the silencer is to mask the position of the weapon, which can be precisely determined similarly to locating the blasting source [26–31]. A silencer suppresses the firing sound in

Appl. Sci. 2020, 10, 961; doi:10.3390/app10030961 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 961 2 of 14 several ways: by reducing the inner energy of the powder gases coming out of the barrel, by reducing their output velocity and temperature, or by breaking the powder gas flow and by making it whirl. All firearm silencers offered significantly greater noise reduction than ear-level protection, which is usually greater than 50%. Noise reduction of all ear-level protectors is unable to reduce the impulse pressure below 140 dB for certain common firearms. The firing sound is a combination of a number of acoustic waves formed as a result of four main components: the gunpowder gas flow muzzle wave, the shock wave generated due to the supersonic projectile movement, the wave formed by the air column ejected from the gun barrel in front of the projectile, and the acoustic wave generated by collision of gun parts during the firing process. The US Army’s Ballistic Research Laboratory (BRL) has developed a prediction method for muzzle devices [32] based on gathered experimental data on muzzle devices for distances from 10 to 50 calibers from the muzzle [33–35]. Helliker and other scientists [16,27,36–42] investigated many different muzzle devices including a silencer. The outputs of the models were not verified against experimental test data from muzzle blasts, which differ to conventional blast waves [43–48]. Carson and Sahni [49] studied containment devices in more detail both theoretically and experimentally in three approaches: acoustic theory, blast theory, and quasi-one-dimensional flow theory. Blast attenuation increased rapidly with the number of baffles in a silencer before maximum attenuation was achieved and a gradual decline occurred [50–56]. It is well known that, while the projectile accelerates with a high temperature and high pressure, the explosion of propellant gases generates the muzzle blast wave [49,57–65]. Since the muzzle energy increases, the impulsive wave intensity is estimated accordingly. A shot, as an impulse shock wave coming from the weapon, has many negative effects on people and the environment. Unlike other sounds, shock wave has high energy, low frequency, and impulsiveness. It is strongly directed and has long-range propagation [66–74]. The muzzle blast is strongly directed. Kirby [75] noted that both the Boundary Element Method and Finite Element Analysis have been used as tools to model the gas flows in vehicle exhaust silencers. Cummings [36] suggests that computational methods require considerable effort and can be difficult to track and other mathematical models are also reliant on very low Mach number velocities, which limits their application within firearms. In this paper, authors used the acoustic-solid interaction COMSOL multi-physics interface for finding a solid domain reaction (barrel with/without silencer) to the acoustic explosion inside the barrel, which corresponds to the blasting effect [76]. The main advantage of this device is that the sound is suppressed mainly in the area of the shooter while, in the direction of the shot, the sound is suppressed by up to 30% (and this device does not belong to the mufflers) and can, therefore, be used in hunting because if, in the direction of the shot, sound is suppressed by more than 30%, hunting would not be possible. Thus, a blocking device imposed for use in hunting has been developed and its use significantly reduces the sound pressure in the shooter zone and, in addition, significantly reduces the kickback force. The newly developed suppression device is intended for use in the leisure and non-military industry. The newly developed silencer would be a mixture of the silencer and muzzle brake designed to reduce noise and kickback. The main advantage of this unit is that the sound is suppressed mainly in the shooter area and up to 30% in the firing direction (and this indicator does not count as suppressors). As a result, the damping device can be used in leisure activities, as if the sound was suppressed by more than 30% in the direction of the firing. The damping device would be classified as dampers, which are not legal in many European countries like Lithuania. The silencer muzzle brake is widely described in both scientific and patent materials. However, there is hardly any information on devices with the desired damping-braking properties. This type of device is not for sale. Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 14

94 The silencer muzzle brake is widely described in both scientific and patent materials. However, Appl. Sci. 2020, 10, 961 3 of 14 95 there is hardly any information on devices with the desired damping-braking properties. This type 96 of device is not for sale. 97 TheThe silencer silencer and and muzzle brake problemsproblems areare mostmost oftenoften addressed addressed in in the the scientific scientific literature: literature: impact 98 impacton bullet on trajectorybullet trajectory [77–79 [77–79]], effects, effects of sound of sound pressure pressure generated generated during during the the shot shot on on hearing hearing [80 –85], 99 [80–85],and reducing and reducing the sound the pressuresound pressure of firearms of fire byarms using by varioususing various types types of silencers of silencers [86–88 [86–88].]. However, 100 However,problems problems related to related the use to of the the use device of the for device recreational for recreational use are use not are addressed. not addressed. 101 AA prototype prototype is iscurrently currently being being developed developed at JSC at JSC Oksalis, Oksalis, and andthe determination the determination of the of properties the properties 102 (acoustic(acoustic parameters andand kickbackkickback force)force) of of this this prototype prototype would would allow allow for afor well-validated a well-validated theoretical 103 theoretical model based on the results obtained. With the right model and theoretical optimization model based on the results obtained. With the right model and theoretical optimization studies, 104 studies, it would be possible to retest and evaluate the performance of the damping-braking device. it would be possible to retest and evaluate the performance of the damping-braking device. The goal is 105 The goal is to achieve optimum damping-braking device characteristics and to evaluate the to achieve optimum damping-braking device characteristics and to evaluate the production capabilities. 106 production capabilities. 2. Materials and Methods 107 2. Materials and Methods The object of the investigation is a damping system used in a firearm. Explosive Weapon (Merkel 108 The object of the investigation is a damping system used in a firearm. Explosive Weapon (Merkel RX Helix Black 308 Win) is presented in Figure1a. The damping system is shown in Figure1a–c, 109 RX Helix Black 308 Win) is presented in Figure 1a. The damping system is shown in Figure 1a, 1b, 110 andrespectively. 1c, respectively. Images Images of a suppression of a suppression system system fitted fitted to the to weapon the weapon are shownare shown in Figure in Figure1a,c. 1a Assembly and 111 1c.of Assembly the damping of the system damping (silencer) system is (s presentedilencer) is inpresented Figure1 b.in Figure 1b.

(a)

(b) (c)

112 FigureFigure 1. 1. FirearmFirearm with with a fire a ﬁre damping damping system system (silencer): (silencer): a) explosive (a) explosive weapon weapon (Merkel (Merkel RX Helix RX HelixBlack Black 113 308308 Win); Win); b) ( bassembly) assembly of the of the damping damping system system (silencer (silencer);); c) a (suppressionc) a suppression system system fitted ﬁttedto the toweapon. the weapon.

114 InIn the designdesign process,process, computational computational simulations simulations are are used used toinvestigate to investigate how dihowfferent different geometries 115 geometriesand operational and operational parameters paramete affect optimizingrs affect optimizing the performance the perfor ofmance systems of (Figuresystems2 (Figure). Of the 2). available Of 116 thecomputational available computational tools, COMSOL tools, Multiphysics COMSOL Multiphy appliessics a finite applies element a finite method element to solvemethod diff toerent solve physics 117 differentand engineering physics problemsand engineering (e.g., acoustic problems propagation) (e.g., acoustic governed propagation) by partial di ffgovernederential equationsby partial (PDEs). 118 differentialThe acoustic-solid equations interaction, (PDEs). transientThe acoustic-solid multi-physics interaction, interface combinestransient themulti-physics pressure acoustics interface as well 119 combinesas transient the and pressure solid mechanicsacoustics as interfaces well as transi to connectent and the solid acoustic mechanics pressure interfaces variations to inconnect the air the domain 120 acoustic pressure variations in the air domain to the structural deformation in the solid domain. A to the structural deformation in the solid domain. A dedicated multi-physics coupling condition is 121 dedicated multi-physics coupling condition is readily defined for the air-solid boundary and sets up readily defined for the air-solid boundary and sets up the air loads on the solid domain and the effect

of the structural accelerations on the air. Each module is governed by its own equations that describe the speciﬁc physics. Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 14

122 the air loads on the solid domain and the effect of the structural accelerations on the air. Each module 123 is governed by its own equations that describe the specific physics.

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122 theAppl. air Sci. loads2020, 10on, 961 the solid domain and the effect of the structural accelerations on the air. Each mo4dule of 14 123 is governed by its own equations that describe the specific physics.

124

125 Figure 2. CAD assembly of 3D silencer model section view included chamber and internal holes.

126 The pressure acoustics model involves a monopole point source that considers the flow pulse at 127 the center of a barrel bottom (Figure 3) to illustrate some properties of time-dependent acoustic 128 problems [89]. The acoustic pressure field p(x,t), along the barrel is given by the scalar wave equation 129 shown below.

124 + ∇ ∙ − (∇ − = (, ), (1) Figure 2. CAD assembly of 3D silencer model section view included chamber and internal holes. 125 Figure 2. CAD assembly of 3D silencer model section view included chamber and internal holes. 130 where pt is the total acoustic pressure, ρ is air density, c is speed of sound, and qd is the dipole domain 131 source,The which pressure represents acoustics a domain model involvesvolumetric a monopole force and pointS(x,t) sourceis the thatmonopole considers point the source flow pulseterm 126 The pressure acoustics model involves a monopole point source that considers the flow pulse at 132 givenat the by center the equation of a barrel below. bottom (Figure3) to illustrate some properties of time-dependent acoustic 127 the center of a barrel bottom (Figure 3) to illustrate some properties of time-dependent acoustic problems [89]. The acoustic pressure field p(x,t), along the barrel is given by the scalar wave equation 128 problems [89]. The acoustic pressure field p(x,t), along the barrel is given by the scalar wave equation shown below. (, ) = ( − ), (2) ! 129 shown below. 1 ∂2p 1 133 where δ(x-x0) is the delta function in three+ dimensions( pt andqd adds= S( xthe, t) ,source at the point where x = x (1)0. ρc2∂t2 ∇· −ρ ∇ − + ∇ ∙ − (∇ − = (, ), (1) 134 whereThept ismonopole the total acousticamplitude pressure, S dependsρ is airon density,the source c is type speed and of, sound, in our andcalculationqd is the, dipoleis the volume domain 135130 flowwheresource, rate p whicht isout the from representstotal the acoustic source a domain pressure, (peak volumetric 4 m ρ3 i/s).s air All density, force external and c is Sboundaries( speedx,t) is theof sound, monopole of the andair domain pointqd is the source are dipole established term domain given 136131 assource,by a the spherical equation which waverepresents below. radiation. a domain This radiation volumetric condition force and allows S(x,t) an is outgoing the monopole spherical point wave source to leave term 4π 137132 thegiven modeling by the equation air domain below. with minimalS (reflections.x, t) = STheδ(x maximumx ), element size is closely related (2)to ρ − 0 138 the speed of sound in the air, frequency bandwidthc , and number of elements per wavelength (we (, ) = ( − ), (2) 139 uwheresed Nδ =(x 4). x0) is the delta function in three dimensions and adds the source at the point where x = x0. − 133 where δ(x-x0) is the delta function in three dimensions and adds the source at the point where x = x0. Silencer 134 The monopoleAir domain amplitude S dependsSolid domain on the ( barrelsource) type and, in our calculation, is the volume 135 flow rate out from the source (peak 4 m3/s). All external boundaries of the air domain are established 136 as a spherical wave radiation. This radiation condition allows an outgoing spherical wave to leave 137 the modeling air domain with minimal reflections. The maximum element size is closely related to 138 the speed of sound in the air, frequency bandwidth, and number of elements per wavelength (we Monopole point source 139 used N = 4). Boundary with added mass and spring foundation 140 Silencer Air domain Figure 3. CAD assembly ofSolid the 3D domain silencer (barrel with) barrel and some boundary condition. 141 Figure 3. CAD assembly of the 3D silencer with barrel and some boundary condition. The monopole amplitude S depends on the source type and, in our calculation, is the volume flow 142 rate outIn the from pressure the source acoustics (peak 4 and m3 /s). solid All mechanics external boundaries model simulation, of the air domain several areassumptions established were as a 143 made:spherical (1) only wave isotropic radiation. loss This factor radiation of the mechanical condition allows system an is outgoingtaken into spherical account, wave(2) the to monopole leave the Monopole point source 144 pointmodeling source air time domain duration with minimalis about 1, reflections. 2 ms (in real The rifle maximum barrel, elementthe shot sizeduration is closely vary relatedfrom 1 toto the60 145 msspeed), (3) of the sound holes in number the air, frequencyof the silencer bandwidth, are select anded from number 7 to of 9 elementsand used perin a wavelengthparametric sweep (we used of 146 Boundary with added mass and spring foundation 140 theN = time4). -dependent study, and (4) the monopole point source has a normal distribution waveform of In the pressure acoustics and solid mechanics model simulation, several assumptions were made: 141 (1) only isotropicFigure loss3. CAD factor assembly of the of mechanical the 3D silencer system with isbarrel taken and into some account, boundary (2) condition the monopole. point source time duration is about 1, 2 ms (in real rifle barrel, the shot duration vary from 1 to 60 ms), 142 (3) theIn holes the pressure number acoustics of the silencer and solid are selected mechanics from model 7 to 9 andsimulation, used in several a parametric assumptions sweep of were the 143 made:time-dependent (1) only isotropic study, and loss (4) factor the monopole of the mechanical point source system has is a normaltaken into distribution account, waveform(2) the monopole of flow 144 pointpulse insource modeling. time duration The default is about temperature 1, 2 ms and (in initialreal rifle pressure barrel estimated, the shot 20duration◦C and vary 0 Pa, from respectively. 1 to 60 145 msMoreover,), (3) the theholes bottom number of aof barrel the silencer has 90 are kg select of addeded from mass 7 to and 9 and a spring used foundation,in a parametric as shownsweep of in 146 theFigure time3.-dependent study, and (4) the monopole point source has a normal distribution waveform of

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147 flow pulse in modeling. The default temperature and initial pressure estimated 20 °C and 0 Pa, Appl. Sci. 2020, 10, 961 5 of 14 148 respectively. Moreover, the bottom of a barrel has 90 kg of added mass and a spring foundation, as 149 shown in Figure 3. 150 DuringDuring the the research, research, the the dynamic dynamic eff ectseffects of aof bullet a bullet caused caused by by a silencer a silencer are are examined. examined. The The study study 151 usedused a bulleta bulle (180t (180 g). g). 152 TheThe main main object object of current of current research research in this inpaper this is paper the silencer’s is the silencer’s design. According design. According to the technical to the 153 requirements,technical requirements, the sound level the sound pressure level field pressure and rifle field delivery and rifle will delivery be minimized will be fromminimized the shooting from the 154 side,shooting but the side, sound but level the sound pressure level from pressure the target from is the not target necessary is not to necessary attenuation. to attenuation. 155 BrüelBrüel & Kjær & Kjær measuring measuring instruments instruments were used were to measure used to force measure and sound force pressure and sound parameters. pressure 156 Theparameters. mobile measurement The mobile resultsmeasurement processing results equipment processing “3660-D” equipment with "3660 DELL-D" computers with DELL (Figure computers4c). 157 The(Fig forceuresensor 4c). The 8320-002 force sensor (Figure 83204a)- were002 ( mountedFigure 4a) on were the gunmounted backrest. on the The gun apparatus backrest. for The measuring apparatus 158 thefor sound measuring pressure the is sound shown pressure in Figure is4d. shown Thispart in Fig depictsure 4d an. This audio part analyzer depicts with an audio a microphone analyzer 2250 with a 159 andmicrophone a hydrophone 2250 8103 and [a90 hydrophone,91]. 8103 [90–92].

(a)

(c)

(b) (d)

160 FigureFigure 4. Experimental4. Experimental setup setup for forcefor force and and sound sound pressure pressure measurements: measurements (a) the: a) force the sensorforce sensor 8320-002; 8320- 161 (b)002; the testing b) the bench;testing ( bench;c) the mobile c) the measurement mobile measurement results processing results processing equipment equipment “3660-D” "3660 with- DELLD" with 162 computers;DELL computers; (d) the apparatus d) the apparatus for measuring for measuring the sound the pressure sound press (Hydrophoneure (Hydrophone 8103). 8103).

163 TheThe received received measurement measurement signals signals from the from computer the computer were processed were usingprocessed static usingdata processing static data 164 packageprocessing Origin package 6 and Pulse Origin software 6 and Pulse packages. software Signal packages. spectra, Signal distributions, spectra, anddistributions statistical, and parameters statistical 165 wereparameters calculated. were calculated. Arithmetic mean: 166 Arithmetic mean: n 1 X x = x n, (3) n 1 i i=1 x   xi (3) n i1 Standard deviation: v , t n 1 X 2 167 Standard deviation: SX = (x x) , (4) n 1 i − i=1 − n 1 2 where n—the number of measurement results.S  xi—the ith measurementx  x result. (4) X n 1 i i1 ,

168 where n - the number of measurement results. xi - the ith measurement result.

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Appl. Sci. 2019, 9, x FOR PEER REVIEW 6 of 14 3. Results 169 3. Results 3.1. Measurements Results of the Firearm’s Backrest Force 170 3.1. Measurements Results Of The Firearm's Backrest Force Measurements of the firearm’s backrest force were carried out using a force-measuring device 171 (FigureMeasurements4a). of the firearm's backrest force were carried out using a force-measuring device 172 (FigureDuring 4a). the study, the dynamic effects caused by a different bullet on a rifle were examined. 173 The typicalDuring graphs the study, of the the backrest dynamic forces effects in thecaused end ofby thea different rifle’s back bullet (Figure on a4 riflea) are were shown examined. in Figure The5. 174 Thetypical statistical graphs parameters of the backrest of the forces results in arethe presentedend of the in rifle's Table back1. (Figure 4a) are shown in Figure 5. 175 The statistical parameters of the results are presented in Table 1.

Time(Signal 2) - Mark 1 (Real) \ FFT Time(Signal 2) - Mark 2 (Real) \ FFT [N]

1.6k

1.2k

800

400

1.4 1.45 1.5 1.55 1.6 1.65 176 [s] Figure 5. Typical time alteration graphs representing generated forces of the reaper of the rear barrel 177 Figure 5. Typical time alteration graphs representing generated forces of the reaper of the rear barrel directed at a human. Blue—when the silencer is used. Red—when the silencer is not used. 178 directed at a human. Blue - when the silencer is used. Red - when the silencer is not used. Table 1. Statistical characteristics of force measurement results. 179 The statistical characteristics of the results of the measurement of force in Table 1 show that the 180 damper reduces theSetup force * from 2,192,333 to 1,195,667 Force, N. NTherefore, it can be seen that the damping 181 device significantly reduces theMean amountStandard of force Deviationdirected at theMinimum person, whichMaximum is obtained during the 182 shooting. A 1195.667 10.841 1173 1214 183 The formula usedB to evaluate2192.333 the damping4.5056 force is shown 2185 below. 2200 * A—with silencer. B—without silencer. TN = (1-Fwith silencer/ Fwithout silencer)*100%. (5)

The statistical characteristics of the results of the measurement of force in Table1 show that the 184 damper reduces the forceTable from 1. Statistical 2,192,333 characteristics to 1,195,667 of N.force Therefore, measurement it can results be seen. that the damping device signiﬁcantlySetup* reduces the amount of force directedForce, N at the person, which is obtained during the shooting. Mean Standard Deviation Minimum Maximum The formulaA used to1195 evaluate.667 the damping10.841 force is shown below.1173 1214 B 2192.333 4.5056 2185 2200 TN = (1 Fwith silencer/Fwithout silencer) * 100%. (5) *A – with silencer. B− – without silencer. The damping evaluating the magnitude of force is given below. 185 The damping evaluating the magnitude of force is given below. T = (1 F /F ) * 100% = (1 1195.667/2192.333) * 100% = 45.46% N TN− = (1with- Fwith silencer silencer without/ Fwithout silencer silencer)*100% = (1-1195.667/2192.333)− * 100% = 45.46 % 186 The results showshow thatthat thethe dampingdamping devicedevice signiﬁcantlysignificantly reduces reduces the the amount amount of of force force directed directed at at a 187 persona person (reduction (reduction of of 45.46%). 45.46%).

188 3.2. Sound Pressure Measurement Results 189 Sound pressure measurements were carried out using the hydrophone 8103. Sound pressure 190 (Figure 4d), when the shot is being made, the time of change, and the spectral density graphs when

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3.2. Sound Pressure Measurement Results Appl.Sound Sci. 2019 pressure, 9, x FOR PEER measurements REVIEW were carried out using the hydrophone 8103. Sound pressure7 of 14 (Figure4d), when the shot is being made, the time of change, and the spectral density graphs when 191 shootingshooting with with and and without without the the silencer silencer is is shown shown in in Figure Figure6. 6. The The statistical statistical parameters parameters of of the the test test are are 192 presentedpresented in in Table Table2 as2 as well. well.

3,5 200 150 3,0

100 2,5 50 2,0 0 1,5 -50 -100 1,0 Sound Pa pressure, Sound Sound Sound pressure, Pa -150 0,5 -200 0,0 1,5 1,6 1,7 1,8 1,9 2,0 0 500 1000 1500 2000 2500 Time, s Frequency, Hz (a) (b)

193 FigureFigure 6. 6.Typical Typical sound sound pressure pressure graphs: graphs: (a )a) a a time time alteration alteration (b b)) a a spectral spectral density, density), when when a shot a shot with with a 194 barrela barrel is performed. is performed Blue—when. Blue - when the the silencer silencer is used.is used Red—when. Red - when the the silencer silencer is notis not used. used.

Table 2. Statistical characteristics of sound pressure measurement results. 195 Table 2. Statistical characteristics of sound pressure measurement results. Setup*Setup * SoundSound Pressure, Pressure Pa, Pa MeanMean StandardStandard Deviation Deviation MinimumMinimumMaximum Maximum A A92.517 92.517 1.5051.505 91.391.3 94.2 94.2 B B350.767 350.767 3.2873.287 347.8347.8 354.3 354.3 *A* A—with– with silencer silencer. B—without. B – without silencer. silencer.

196 TheThe statistical statistical characteristics characteristics of of the the sound sound pressure pressure measurement measurement results results in Table in Table2 show 2 show that the that 197 dampingthe damping device device (silencer) (silencer) reduces reduces the sound the sound pressure pressure from 350.767from 350.767 to 92.517 to 92.517 Pa. Thus, Pa. Thus, it can beit can seen be 198 thatseen the that silencer the silencer signiﬁcantly significantly reduces reduces the sound the sound pressure pressu obtainedre obtained during during the shooting. the shooting. 199 TheThe sound sound pressure pressure damping damping in in relation relation to to the the pressure pressure level level is is given given below. below.

T = (1 T(PP = (1 – (Pwith silencer+| maxP +| Pwith silencer| min)/(P |)/ (Pwithout silencer max+ +| |P Pwithout silencer min |))|)) * * 100%. 100%. (6)(6) P − with silencer max with silencer min without silencer max without silencer min 200 Damping evaluating the pressure level is given below. Damping evaluating the pressure level is given below.

TTP pressure Vulkan = (1 – (P(Pwith silencer max +|+ |P Pwith silencer min|)/|)/(P (Pwithout silencer max+ +| |P Pwithout silencer min|))|)) * 100%* 100% P pressure Vulkan − with silencer max with silencer min without silencer max without silencer min (7)(7) == (1(1 –92.517 92.517/350.767)/350.767) * 100% * 100= 73.6%. % =73.6 %. − 201 TheThe 73.6% results reduction show that in the sound silencer pressure significantly achieved re withduces the the use value of an of additional the sound silencer pressure during in the 202 firingshooter suggests zone during that the the silencer shooting used. T duringhe amount firing of significantlythe sound pressure increases value the soundcaused pressure by the firing in the in 203 shooterthe shooter area. area decreases by 71.26% using the additional silencer.

204 4.4. Discussion Discussion 205 FiguresFigures7 and7 and8 show 8 sho thew the backrest’s backrest’s (Figure (Figure4) rear 4) part.rear part When. W thehen shot the isshot executed, is executed, the forces the areforces 206 directedare directed to human to human time time and spectraland spectral density density graphs graphs during during the shootingthe shooting as well as well as when as when a damper a damper is 207 usedis used and and not not used. used. 208 TheThe instantaneous instantaneous local local acceleration acceleration in in the the air air domain’s domain’s point point is is reﬂected reflected to to the the sound sound pressure pressure 209 levellevel (SPL). (SPL) Time-dependent. Time-dependent numerical numerical simulation simulation results results in in the the local local point point of of the the barrel barrel bottom bottom is is 210 shown in Figure 7a. In four cases, only a barrel without the silencer and with 7-9 hole silencer types. 211 A normalized characteristic of local acceleration in the point of the air domain 1 m distance from the 212 bottom of the barrel in the first 10 periods of the shot are degreased using the silencer (all colors 213 instead of the dark blue in Figure 7a). We can assume that the acoustic sound pressure from this side

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214 is also degreasing when compared with the calculation of a standard rifle barrel (dark blue line in 215 Figure 7a). The acceleration in the far-field degrease faster using a silencer on the barrel exit.

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shown in Figure7a. In four cases, only a barrel without the silencer and with 7–9 hole silencer types. A normalized characteristic of local acceleration in the point of the air domain 1 m distance from the bottom of the barrel in the first 10 periods of the shot are degreased using the silencer (all colors instead Appl. Sci. 2019, 9, x FOR PEER REVIEW 8 of 14 of the dark blue in Figure7a). We can assume that the acoustic sound pressure from this side is also 214 is degreasingalso degreasing when when compared compared with with the calculationthe calculation of aof standard a standard rifle rifle barrel barrel (dark (dark blue blue line line in in Figure 7a). 215 FigureThe acceleration7a). The acceleration in the far-field in the far-field degrease degr fasterease usingfaster using a silencer a silencer on the on barrel the barrel exit. exit.

(a) (b)

216 Figure 7. Normalized local acceleration in the point 1 m from the barrel bottom by Z-axes (a) and total 217 acoustic pressure field along the yellow line inside the barrel (b): dark blue – only barrel, other colors 218 – with a 7-9-holes silencer.

219 Total acoustic pressure field along the barrel (yellow line) is shown in Figure 7b. According to 220 the numerical calculation and the pressure field inside the barrel, using the 8holes silencer type 221 degreased almost twice. 222 Normalized sound pressure in the point 1 m from the barrel bottom in the time domain with 223 and without the silencer is shown in Figure 8a. Good enough acoustical damping performance is 224 represented using an 8-holes silencer. Another characteristic of analyzing vibration data is in the 225 frequency domain, which is(a )the most vibration analyzing type. Using a spectrogram,(b )we get a much 226 deeper understanding of the vibration profile and how it changes with time. The FFT (fast Fourier 216227 transform)FigureFigure 7.takes Normalized 7. Normalizeda block localof time-domain acceleration local acceleration indata the (Fig point inure the 1 m8a) point from and 1the returns m barrel from thebottom the frequency barrel by Z-axes bottom spectrum (a) byand Z-axes total of the ( a) and 217228 dataacoustic (Figuretotal acousticpressure 8b). The field pressuremain along data ﬁeldthe presents yellow along linethe the insidehigh yellowest the harmonics linebarrel inside (b): darkare the attenuated blue barrel – only (b by):barrel, darkthe othersilencer. blue—only colors Low barrel, 218229 frequency– withother aharmonics 7-9-holes colors—with silencer. has a 7–9-holeslower amplitude silencer. (blue line in Figure 8b).

230 FigureFigure 8. Normalized 8. Normalized sound soundpressure pressure in the point in 1 the m from point the 1 barrel m from bottom: the (time barrel alteration bottom: (a) (time and alteration 231 spectral(a) and density spectral (b)) density when a (shotb)) whenwith a a barrel shot withis performed. a barrel Blue is performed. - when the Blue—whensilencer is used. the Red silencer - is used. 232 whenRed—when the silencer the is silencernot used. is not used.

233 TheTotal SPL acoustic distribution pressure on the field frequency along of the 10 barrelHz both (yellow for the line)system is when shown the in silencer Figure 7isb. not According used to the 234 and used is shown in Figure 9. We can see than SPL from the “man” view is reduced (Figure 9b) numerical calculation and the pressure field inside the barrel, using the 8holes silencer type degreased almost twice. Normalized sound pressure in the point 1 m from the barrel bottom in the time domain with and without the silencer is shown in Figure8a. Good enough acoustical damping performance is represented using an 8-holes silencer. Another characteristic of analyzing vibration data is in the frequency domain, which(a) is the most vibration analyzing type. Using a spectrogram,(b) we get a much deeper understanding of the vibration profile and how it changes with time. The FFT (fast Fourier 230 Figure 8. Normalized sound pressure in the point 1 m from the barrel bottom: (time alteration (a) and transform) takes a block of time-domain data (Figure8a) and returns the frequency spectrum of 231 spectral density (b)) when a shot with a barrel is performed. Blue - when the silencer is used. Red - 232 thewhen data the (Figure silencer8b). is not The used. main data presents the highest harmonics are attenuated by the silencer. Low frequency harmonics has a lower amplitude (blue line in Figure8b). 233 The SPL distribution on the frequency of 10 Hz both for the system when the silencer is not used 234 and used is shown in Figure 9. We can see than SPL from the “man” view is reduced (Figure 9b)

Appl. Sci. 2020, 10, 961 9 of 14

Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 14 The SPL distribution on the frequency of 10 Hz both for the system when the silencer is not used 235 andwhen used compared is shown with in Figure the initial9. We can(standard) see than system SPL from (Figure the “man” 9a). Another view is reduced very famous (Figure and9b) whenuseful 236 Appl.comparedacoustic Sci. 2019 field with, 9, xis FOR thethe PEER initialpolar REVIEW (standard)plot diagram, system which (Figure represents9a). Another the SPL very distribution famous andof the useful exterior-field, acoustic9 of 14 237 fieldbased is on the far-field polar plot integral diagram, calculation which on represents the air surface the SPL in distributiona pressure acoustics of the exterior-field, model. Two polar based plot on 238238 diagramsfar-fielddiagrams integral forfor frequenciesfrequencies calculation 110110 on HzHz the andand air 1100 surface1100 HzHz in areare a pressurepresentedpresented acoustics inin FigureFigure model. 10a10a andand Two 1010b, polarb, respectively.respectively. plot diagrams WeWe 239239 canforcan frequencies assumeassume tthat,hat 110, usingusing Hz and thethe 1100 silencersilencer, Hz, are wewe presented cancan reducereduce in Figure oror slightlyslightly 10a,b, controlcontrol respectively. SPLsSPLs thatthat We can dependdepend assume onon that, ourour 240240 requirements.usingrequirements. the silencer, we can reduce or slightly control SPLs that depend on our requirements.

((aa)) ((bb))

241241 FigureFigureFigure 9. 9.9. (SPL)(SPL) (10 (10 Hz) Hz) iso iso-surface-surface of ofof the thethe initial initialinitial system systemsystem (a) ((a)a) and andand system systemsystem with withwith aa silencer silencersilencer (b) ((b).b)..

(a()a ) (b) (b)

Figure 10. Exterior-field SPL (far-field)—110 Hz (a) and 1100 Hz (b). 242242 FigureFigure 10. 10. Exterior Exterior-field-field SPLSPL (far (far-field)-field) –– 110110 HzHz (a)(a) andand 11001100 Hz Hz (b) (b).. Studies carried out to analyze the barrel of different characteristics show that the pressure is 243243 reducedStudiesStudies in part carriedcarried of the outout damper toto analyzeanalyze where thethe the barrelbarrel cavities ofof different arediff made.erent characteristicscharacteristics The pressure dropshowshow does thatthat notthethe exceedpressurepressure 15%. isis 244244 reducedAirflowreduced simulationsinin partpart ofof thethe have damperdamper shown wherewhere that thethe cavitiescavities airflow are rateare made.made. at the TheThe exit pressurepressure increased dropdrop by 8%. doesdoes In notnot assessing exceedexceed these15%.15%. 245245 Airflowresults,Airflow it simulationsimulations can be assumeds havehave thatshownshown this thatthat system thethe airflow directsairflow the raterate flow atat thethe along exitexit the increasedincreased shot and, byby thereby, 8%.8%. InIn assessingassessing suppresses thesethese the 246246 results,acousticresults, itit sound cancan bebe pressure assumedassumed (noise) thatthat thisthis in the systemsystem fire zone. directsdirects thethe flowflow alongalong thethe shotshot andand,, therebythereby,, suppressessuppresses 247247 thethe acousticacoustic soundsound pressurepressure (noise)(noise) inin thethe firefire zone.zone.

248248 5.5. ConclusionsConclusions 249 The research shows that, using force and sound pressure sensor measurement results of 250 modeling, can be accurately determined by modeling the impact of the muzzle brake to acoustic and 251 force parameters. 252 The research examined the effect of the newly created damper on the dynamic parameters 253 during the shooting.

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5. Conclusions The research shows that, using force and sound pressure sensor measurement results of modeling, can be accurately determined by modeling the impact of the muzzle brake to acoustic and force parameters. The research examined the effect of the newly created damper on the dynamic parameters during the shooting. The results show that the damping device significantly reduces the rebound force of a gun directed to a person, which appears during the shot. The force is caused by the use of a damper that decreases by 45.46%. The results show that the silencer significantly reduces the value of the sound pressure in the shooter zone during the shooting. The amount of the sound pressure value caused by the firing in the shooter area decreases by 73.6% using the additional silencer. According to the technical requirements, the sound level pressure field and rifle delivery will be minimized from the shooting side. According to a numerical calculation, the pressure field inside the barrel, using the 8-holes silencer type, degreased almost twice.

Author Contributions: Conceptualization, J.S., K.K., and J.M. (Jonas Matijošius). Methodology, A.K. and J.M. (Jacek Marcinkiewicz). Software, S.B. and Z.S. Validation, J.S. and J.M. (Jacek Marcinkiewicz). Formal analysis, K.K. and Z.S. Investigation, J.M. (Jonas Matijošius). Resources, A.K. Data curation, S.B. and D.V. Writing—original draft preparation, J.S., A.K., and J.M. (Jonas Matijošius). Writing—review and editing, A.K. Visualization, K.K. and D.V. Supervision, S.B. Project administration, J.M. (Jonas Matijošius). All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Branch, M.P. Comparison of Muzzle Suppression and Ear-Level Hearing Protection in Firearm Use. Otolaryngol. Head Neck Surg. 2011, 144, 950–953. [CrossRef][PubMed] 2. Arslan, H.; Ranjbar, M.; Secgin, E.; Celik, V.Theoretical and experimental investigation of acoustic performance of multi-chamber reactive silencers. Appl. Acoust. 2020, 157, 106987. [CrossRef] 3. Strong, B.L.; Ballard, S.-B.; Braund, W. The American College of Preventive Medicine Policy Recommendations on Reducing and Preventing Firearm-Related Injuries and Deaths. Am. J. Prev. Med. 2016, 51, 1084–1089. [CrossRef][PubMed] 4. Itabashi, H.H.; Andrews, J.M.; Tomiyasu, U.; Erlich, S.S.; Sathyavagiswaran, L. Injuries due to firearms and other missile-launching devices. In Forensic Neuropathology; Elsevier: Amsterdam, The Netherlands, 2007; pp. 211–254, ISBN 978-0-12-058527-4. 5. Hamilton, D.; Lemeshow, S.; Saleska, J.L.; Brewer, B.; Strobino, K. Who owns guns and how do they keep them? The influence of household characteristics on firearms ownership and storage practices in the United States. Prev. Med. 2018, 116, 134–142. [CrossRef] 6. Fisher, H.; Drummond, A. A call to arms: The emergency physician, international perspectives on firearm injury prevention and the canadian gun control debate. J. Emerg. Med. 1999, 17, 529–537. [CrossRef] 7. Jain, S.K.; Singh, B.P.; Singh, R.P. Indian homemade firearm—A technical review. Forensic Sci. Int. 2004, 144, 11–18. [CrossRef] 8. Adams, R.J. Retailer–manufacturer responsibility in the marketing of firearms: Exploring the concept of negligent distribution. J. Retail. Consum. Serv. 2004, 11, 161–169. [CrossRef] 9. Breeze, J.; Cooper, H.; Pearson, C.R.; Henney, S.; Reid, A. Ear injuries sustained by British service personnel subjected to blast trauma. J. Laryngol. Otol. 2011, 125, 13–17. [CrossRef] 10. Guida, H.L.; Diniz, T.H.; Kinoshita, S.K. Acoustic and psychoacoustic analysis of the noise produced by the police force firearms. Braz. J. Otorhinolaryngol. 2011, 77, 163–170. [CrossRef] 11. Junuzovic, M.; Midlöv, P.; Lönn, S.L.; Eriksson, A. Swedish hunters’ safety behaviour and experience of firearm incidents. Accid. Anal. Prev. 2013, 60, 64–70. [CrossRef] Appl. Sci. 2020, 10, 961 11 of 14

12. Jones, H.G.; Greene, N.T.; Ahroon, W.A. Human middle-ear muscles rarely contract in anticipation of acoustic impulses: Implications for hearing risk assessments. Hear. Res. 2019, 378, 53–62. [CrossRef][PubMed] 13. Chau, J.K.; Cho, J.J.W.; Fritz, D.K. Evidence-Based Practice. Otolaryngol. Clin. N. Am. 2012, 45, 941–958. [CrossRef][PubMed] 14. Guida, H.L.; Taxini, C.L.; de Oliveira Gonçalves, C.G.; Valenti, V.E. Evaluation of hearing protection used by police officers in the shooting range. Braz. J. Otorhinolaryngol. 2014, 80, 515–521. [CrossRef][PubMed] 15. Yankaskas, K. Prelude: Noise-induced tinnitus and hearing loss in the military. Hear. Res. 2013, 295, 3–8. [CrossRef] 16. Kim, D.; Cheong, C.; Jeong, W.B. The use of a hybrid model to compute the nonlinear acoustic performance of silencers for the finite amplitude acoustic wave. J. Sound Vib. 2010, 329, 2158–2176. [CrossRef] 17. Lou, G.; Wu, T.W.; Cheng, C.Y.R. Boundary element analysis of packed silencers with a substructuring technique. Eng. Anal. Bound. Elem. 2003, 27, 643–653. [CrossRef] 18. Kirby, R.; Amott, K.; Williams, P.T.; Duan, W. On the acoustic performance of rectangular splitter silencers in the presence of mean flow. J. Sound Vib. 2014, 333, 6295–6311. [CrossRef] 19. Bilawchuk, S.; Fyfe, K.R. Comparison and implementation of the various numerical methods used for calculating transmission loss in silencer systems. Appl. Acoust. 2003, 64, 903–916. [CrossRef] 20. Ming Wong, L.; Gary Wang, G. Development of an automatic design and optimization system for industrial silencers. J. Manuf. Syst. 2003, 22, 327–339. [CrossRef] 21. Pollak, S.; Saukko, P. Gunshot Wounds. In Encyclopedia of Forensic Sciences; Elsevier: Amsterdam, The Netherlands, 2013; pp. 70–82, ISBN 978-0-12-382166-9. 22. Haag, M.G.; Haag, L.C. Sound Levels of Gunshots, Supersonic Bullets, and Other Impulse Sounds. In Shooting Incident Reconstruction; Elsevier: Amsterdam, The Netherlands, 2011; pp. 295–329, ISBN 978-0-12-382241-3. 23. Davis, R.R.; Clavier, O. Impulsive noise: A brief review. Hear. Res. 2017, 349, 34–36. [CrossRef] 24. Miller, M.T. Crime Scene Reconstruction. In Crime Scene Investigation Laboratory Manual; Elsevier: Amsterdam, The Netherlands, 2018; pp. 191–200, ISBN 978-0-12-812845-9. 25. Pääkkönen, R.; Anttonen, H.; Niskanen, J. Noise control on military shooting ranges for rifles. Appl. Acoust. 1991, 32, 49–60. [CrossRef] 26. Meng, X.; Wang, Z.; Zhang, Z.; Wang, F. A Method for Monitoring the Underground Mining Position Based on the Blasting Source Location. Meas. Sci. Rev. 2013, 13, 45–49. [CrossRef] 27. Hristov, N.; Kari, A.; Jerković,D.; Savić,S.; Sirovatka, R. Simulation and Measurements of Small Arms Blast Wave Overpressure in the Process of Designing a Silencer. Meas. Sci. Rev. 2015, 15, 27–34. [CrossRef] 28. Sallai, J.; Hedgecock, W.; Volgyesi, P.; Nadas, A.; Balogh, G.; Ledeczi, A. Weapon classification and shooter localization using distributed multichannel acoustic sensors. J. Syst. Archit. 2011, 57, 869–885. [CrossRef] 29. Vogel, H.; Dootz, B. Wounds and weapons. Eur. J. Radiol. 2007, 63, 151–166. [CrossRef] 30. Bro˙zek-Mucha,Z. A study of gunshot residue distribution for close-range shots with a silenced gun using optical and scanning electron microscopy, X-ray microanalysis and infrared spectroscopy. Sci. Justice 2017, 57, 87–94. [CrossRef] 31. Monturo, C. Ammunition. In Forensic Firearm Examination; Elsevier: Amsterdam, The Netherlands, 2019; pp. 21–71, ISBN 978-0-12-814539-5. 32. Liu, N.; Alexander, A.A.; Li, X.; Wang, S.; Lu, W.F.; Sulaimee, N.H.B.; Chew, C.-M. Modelling of abrasive blasting process from viewpoint of energy exchange. In Proceedings of the 2018 IEEE 23rd International Conference on Emerging Technologies and Factory Automation (ETFA), Turin, Italy, 4–7 September 2018; pp. 488–492. 33. Carson, R.A.; Sahni, O. Scaling Laws for the Peak Overpressure of a Cannon Blast. J. Fluids Eng. 2016, 139, 021204. [CrossRef] 34. Kong, B.; Lee, K.; Park, S.-R.; Jang, S.; Lee, S. Prediction of sound field from recoilless rifles in terms of source decomposition. Appl. Acoust. 2015, 88, 137–145. [CrossRef] 35. Costa, E.; Lagasco, F. Development of a 3D numerical methodology for fast prediction of gun blast induced loading. Shock Waves 2014, 24, 257–265. [CrossRef] 36. Cummings, A. High Frequency Ray Acoustics Models for Duct Silencers. J. Sound Vib. 1999, 221, 681–708. [CrossRef] 37. Fang, Z.; Liu, C.Y. Semi-weak-form mesh-free method for acoustic attenuation analysis of silencers with arbitrary but axially uniform transversal sections. J. Sound Vib. 2019, 442, 752–769. [CrossRef] Appl. Sci. 2020, 10, 961 12 of 14

38. Kilikevicius, A.; Skeivalas, J.; Jurevicius, M.; Turla, V.; Kilikeviciene, K.; Bureika, G.; Jakstas, A. Experimental investigation of dynamic impact of firearm with suppressor. Indian J. Phys. 2017, 91, 1077–1087. [CrossRef] 39. Lu, Y.; Zhou, K.; He, L.; Li, J.; Huang, X. Research on the floating performance of a novel large caliber machine gun based on the floating principle with complicated boundary conditions. Def. Technol. 2019, 15, 607–614. [CrossRef] 40. Libal, U.; Spyra, K. Wavelet based shock wave and muzzle blast classification for different supersonic projectiles. Expert Syst. Appl. 2014, 41, 5097–5104. [CrossRef] 41. Carson, R.A.; Sahni, O. Study of the relevant geometric parameters of the channel leak method for blast overpressure attenuation for a large caliber cannon. Comput. Fluids 2015, 115, 211–225. [CrossRef] 42. Mäkinen, T.; Pertilä, P. Shooter localization and bullet trajectory, caliber, and speed estimation based on detected firing sounds. Appl. Acoust. 2010, 71, 902–913. [CrossRef] 43. Qin, Q.; Zhang, X. Numerical investigation on combustion in muzzle flows using an inert gas labeling method. Int. J. Heat Mass Transf. 2016, 101, 91–103. [CrossRef] 44. Guo, Z.X.; Pan, Y.T.; Li, K.W.; Zhang, H.Y. Numerical Simulation of Overpressure about Muzzle Blast Flowfield. Adv. Mater. Res. 2012, 605–607, 2506–2509. [CrossRef] 45. Xiao, W.; Andrae, M.; Gebbeken, N. Experimental and numerical investigations on the shock wave attenuation performance of blast walls with a canopy on top. Int. J. Impact Eng. 2019, 131, 123–139. [CrossRef] 46. Mouritz, A.P. Advances in understanding the response of fibre-based polymer composites to shock waves and explosive blasts. Compos. Part A Appl. Sci. Manuf. 2019, 125, 105502. [CrossRef] 47. Hu, X.-D.; Zhao, G.-F.; Deng, X.-F.; Hao, Y.-F.; Fan, L.-F.; Ma, G.-W.; Zhao, J. Application of the four-dimensional lattice spring model for blasting wave propagation around the underground rock cavern. Tunn. Undergr. Space Technol. 2018, 82, 135–147. [CrossRef] 48. Lu, G.; Fall, M. Modelling blast wave propagation in a subsurfacegeotechnical structure made of an evolutive porous material. Mech. Mater. 2017, 108, 21–39. [CrossRef] 49. Carson, R.A.; Sahni, O. Numerical Investigation of Channel Leak Geometry for Blast Overpressure Attenuation in a Muzzle Loaded Large Caliber Cannon. J. Fluids Eng. 2014, 137, 021102. [CrossRef] 50. Lee, H.-S.; Kang, T.-Y.; Hong, J.-H. Development of a Muffler for 40 mm Medium Caliber Gun: Numerical Analysis and Validation. Int. J. Precis. Eng. Manuf. 2018, 19, 245–250. [CrossRef] 51. Yuanjuan, Z. Study on Attenuation Law of Open-pit Bench Blasting Vibration. Procedia Eng. 2014, 84, 868–872. [CrossRef] 52. Lee, J.S.; Ahn, S.K.; Sagong, M. Attenuation of blast vibration in tunneling using a pre-cut discontinuity. Tunn. Undergr. Space Technol. 2016, 52, 30–37. [CrossRef] 53. Sugiyama, Y.; Homae, T.; Wakabayashi, K.; Matsumura, T.; Nakayama, Y. Numerical simulations on the attenuation effect of a barrier material on a blast wave. J. Loss Prev. Process Ind. 2014, 32, 135–143. [CrossRef] 54. Wierschem, N.E.; Hubbard, S.A.; Luo, J.; Fahnestock, L.A.; Spencer, B.F.; McFarland, D.M.; Quinn, D.D.; Vakakis, A.F.; Bergman, L.A. Response attenuation in a large-scale structure subjected to blast excitation utilizing a system of essentially nonlinear vibration absorbers. J. Sound Vib. 2017, 389, 52–72. [CrossRef] 55. Igra, O.; Falcovitz, J.; Houas, L.; Jourdan, G. Review of methods to attenuate shock/blast waves. Prog. Aerosp. Sci. 2013, 58, 1–35. [CrossRef] 56. Girin, A. Attenuation of a point blast shock wave in the dusty air. J. Loss Prev. Process Ind. 2013, 26, 1569–1573. [CrossRef] 57. Huang, Z.; Wessam, M.E.; Chen, Z. Numerical investigation of the three-dimensional dynamic process of sabot discard. J. Mech. Sci. Technol. 2014, 28, 2637–2649. [CrossRef] 58. Carson, R.A.; Sahni, O. Numerical investigation of propellant leak methods in large-caliber cannons for blast overpressure attenuation. Shock Waves 2014, 24, 625–638. [CrossRef] 59. Kang, K.-J.; Ko, S.-H.; Lee, D.-S. A study on impulsive sound attenuation for a high-pressure blast flowfield. J. Mech. Sci. Technol. 2008, 22, 190–200. [CrossRef] 60. Rehman, H.; Chung, H.; Joung, T.; Suwono, A.; Jeong, H. CFD analysis of sound pressure in tank gun muzzle silencer. J. Cent. South Univ. Technol. 2011, 18, 2015–2020. [CrossRef] 61. Scaling of Air Blast Waves. In Fundamental Studies in Engineering; Elsevier: Amsterdam, The Netherlands, 1991; Volume 12, pp. 49–69, ISBN 978-0-444-88156-4. 62. Explosions and Pressure Waves. In Industrial Safety Series; Elsevier: Amsterdam, The Netherlands, 1994; Volume 3, pp. 445–462, ISBN 978-0-444-89863-0. Appl. Sci. 2020, 10, 961 13 of 14

63. Krehl, P. History of Shock Waves. In Handbook of Shock Waves; Elsevier: Amsterdam, The Netherlands, 2001; pp. 1–142, ISBN 978-0-12-086430-0. 64. Phadnis, V.A.; Silberschmidt, V.V. 8.14 Composites Under Dynamic Loads at High Velocities. In Comprehensive Composite Materials II; Elsevier: Amsterdam, The Netherlands, 2018; pp. 262–285, ISBN 978-0-08-100534-7. 65. Phadnis, V.A.; Roy, A.; Silberschmidt, V.V. Dynamic damage in FRPs. In Dynamic Deformation, Damage and Fracture in Composite Materials and Structures; Elsevier: Amsterdam, The Netherlands, 2016; pp. 193–222, ISBN 978-0-08-100870-6. 66. Guo, Z. Numerical Simulation of Muzzle Blast Overpressure in Antiaircraft Gun Muzzle Brake. J. Inf. Comput. Sci. 2013, 10, 3013–3019. [CrossRef] 67. Cheng, L.; Ji, C.; Zhong, M.; Long, Y.; Gao, F. Full-scale experimental investigation on the shock-wave characteristics of high-pressure natural gas pipeline physical explosions. Int. J. Hydrog. Energy 2019, 44, 20587–20597. [CrossRef] 68. Fang, B.; Wang, Y.-G.; Zhao, Q. On multi-dimensional linear stability of planar shock waves for Chaplygin gases. Appl. Math. Lett. 2020, 102, 106085. [CrossRef] 69. Yazdandoost, F.; Sadeghi, O.; Bakhtiari-Nejad, M.; Elnahhas, A.; Shahab, S.; Mirzaeifar, R. Energy dissipation of shock-generated stress waves through phase transformation and plastic deformation in NiTi alloys. Mech. Mater. 2019, 137, 103090. [CrossRef] 70. Hokamoto, K.; Fujita, M. Shock-wave research on condensed matter at the High-Energy Rate Laboratory of Kumamoto University—An introduction. Phys. B Condens. Matter 1997, 239, 187–190. [CrossRef] 71. Wu, J.; Liu, X.; Zhao, J.; Qiao, H.; Zhang, Y.; Zhang, H. The online monitoring method research of laser shock processing based on plasma acoustic wave signal energy. Optik 2019, 183, 1151–1159. [CrossRef] 72. Otsuka, F.; Matsukiyo, S.; Hada, T. PIC Simulation of a quasi-parallel collisionless shock: Interaction between upstream waves and backstreaming ions. High Energy Density Phys. 2019, 33, 100709. [CrossRef] 73. Xu, H.; Gao, J.; Yao, A.; Yao, C. The relief of energy convergence of shock waves by using the concave combustion chamber under severe knock. Energy Convers. Manag. 2018, 162, 293–306. [CrossRef] 74. Tonicello, N.; Lodato, G.; Vervisch, L. Entropy preserving low dissipative shock capturing with wave-characteristic based sensor for high-order methods. Comput. Fluids 2020, 197, 104357. [CrossRef] 75. Kirby, R. Simplified Techniques for Predicting the Transmission Loss of A Circular Dissipative Silencer. J. Sound Vib. 2001, 243, 403–426. [CrossRef] 76. Wei, Z.; Weavers, L.K. Combining COMSOL modeling with acoustic pressure maps to design sono-reactors. Ultrason. Sonochem. 2016, 31, 490–498. [CrossRef] 77. Carlucci, D.E.; Decker, R.; Vega, J.; Ray, D. Measurement of in-bore side loads and comparison to first maximum yaw. Def. Technol. 2016, 12, 106–112. [CrossRef] 78. Courtney, E.; Couvillion, R.; Courtney, A.; Courtney, M. Effects of Sound Suppressors on Muzzle Velocity, Bullet Yaw and Drag. In Proceedings of the 30th International Symposium on Ballistics, Long Beach, CA, USA, 11–15 September 2017; DEStech Publications, Inc.: Lancaster, Pennsylvania, 2017. 79. Lobarinas, E.; Scott, R.; Spankovich, C.; Le Prell, C.G. Differential effects of suppressors on hazardous sound pressure levels generated by AR-15 rifles: Considerations for recreational shooters, law enforcement, and the military. Int. J. Audiol. 2016, 55, S59–S71. [CrossRef] 80. Lankford, J.E.; Meinke, D.K.; Flamme, G.A.; Finan, D.S.; Stewart, M.; Tasko, S.; Murphy, W.J. Auditory risk of air rifles. Int. J. Audiol. 2016, 55, S51–S58. [CrossRef] 81. Meinke, D.K.; Murphy, W.J.; Finan, D.S.; Lankford, J.E.; Flamme, G.A.; Stewart, M.; Soendergaard, J.; Jerome, T.W. Auditory risk estimates for youth target shooting. Int. J. Audiol. 2014, 53, S16–S25. [CrossRef] 82. Mlynski, R.; Kozlowski, E. Selection of Level-Dependent Hearing Protectors for Use in An Indoor Shooting Range. Int. J. Environ. Res. Public Health 2019, 16, 2266. [CrossRef] 83. Murphy, W.J.; Tasko, S.M.; Finan, D.; Meinke, D.K.; Stewart, M.; Lankford, J.E.; Campbell, A.R.; Flamme, G. Referee whistles Part II—Outdoor sound power assessment. J. Acoust. Soc. Am. 2019, 145, 1816. [CrossRef] 84. Skrodzka, E.; Wicher, A.; Gołe¸biewski, R. A Review of Gunshot Noise as Factor in Hearing Disorders. Acta Acust. United Acust. 2019, 105, 904–911. [CrossRef] 85. Stewart, M. What to Know about Firearm Suppressors and Hearing Loss: Does a firearm suppressor always do enough to protect hearing? No. Should firearm users also wear hearing protection? Yes. ASHA Lead. 2018, 23, 18–20. [CrossRef] Appl. Sci. 2020, 10, 961 14 of 14

86. Murphy, W.J.; Campbell, A.R.; Flamme, G.A.; Tasko, S.M.; Lankford, J.E.; Meinke, D.K.; Finan, D.S.; Stewart, M.; Zechmann, E.L. Developing a method to assess noise reduction of firearm suppressors for small-caliber weapons. Proc. Meet. Acoust. 2018, 33, 040004. 87. Murphy, W.J.; Campbell, A.R.; Flamme, G.A.; Tasko, S.M.; Lankford, J.E.; Meinke, D.K.; Finan, D.S.; Zechmann, E.L.; Stewart, M. The attenuation of firearm suppressors as a function of angle and bullet velocity. In Proceedings of the National Hearing Conservation Association, Orlando, FL, USA, 15–17 February 2018. 88. Murphy, W.J.; Flamme, G.A.; Campbell, A.R.; Zechmann, E.L.; Tasko, S.M.; Lankford, J.E.; Meinke, D.K.; Finan, D.S.; Stewart, M. The reduction of gunshot noise and auditory risk through the use of firearm suppressors and low-velocity ammunition. Int. J. Audiol. 2018, 57, S28–S41. [CrossRef] 89. Yue, B.; Guddati, M.N. Dispersion-reducing finite elements for transient acoustics. J. Acoust. Soc. Am. 2005, 118, 2132–2141. [CrossRef] 90. Kilikeviˇciene,˙ K.; Matijošius, J.; Fursenko, A.; Kilikeviˇcius,A. Tests of hail simulation and research of the resulting impact on the structural reliability of solar cells. Ekspolatacja Niezawodn. Maint. Reliab. 2019, 21, 275–281. [CrossRef] 91. Kilikeviˇcius,A.; Skeivalas, J.; Kilikeviˇciene,˙ K.; Matijošius, J. Analysis of Dynamic Parameters of a Railway Bridge. Appl. Sci. 2019, 9, 2545. [CrossRef]

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