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A Multi-Tone Sound Absorber Based on an Array of Shunted Loudspeakers

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A Multi-Tone Sound Absorber Based on an Array of Shunted Loudspeakers applied sciences Article A Multi-Tone Sound Absorber Based on an Array of Shunted Loudspeakers Chaonan Cong 1, Jiancheng Tao 1,* and Xiaojun Qiu 2 1 Key Laboratory of Modern Acoustics (MOE), Institute of Acoustics, Nanjing University, Nanjing 210093, China; [email protected] 2 Centre for Audio, Acoustics and Vibration, Faculty of Engineering and IT, University of Technology, Sydney, NSW 2007, Australia; [email protected] * Correspondence: [email protected] Received: 1 November 2018; Accepted: 23 November 2018; Published: 4 December 2018 Abstract: It has been demonstrated that a single shunted loudspeaker can be used as an effective low frequency sound absorber in a duct, but many shunted loudspeakers have to be used in practice for noise reduction or reverberation control in rooms, thus it is necessary to understand the performance of an array of shunted loudspeakers. In this paper, a model for the parallel shunted loudspeaker array for multi-tone sound absorption is proposed based on a modal solution, and then the acoustic properties of a shunted loudspeaker array under normal incidence are investigated using both the modal solution and the finite element method. It was found that each shunted loudspeaker can work almost independently where each unit resonates. Based on the interaction analysis, multi-tone absorbers in low frequency can be achieved by designing multiple shunted loudspeakers with different shunt circuits respectively. The simulation and experimental results show that the normal incidence sound absorption coefficient of the designed absorber has four absorption peaks with values of 0.42, 0.58, 0.80, and 0.84 around 100 Hz, 200 Hz, 300 Hz, and 400 Hz respectively. Keywords: shunted loudspeaker array; modal solution; multi-tone sound absorption 1. Introduction The shunted loudspeaker, which consists of a closed-box loudspeaker and a shunt circuit, was first proposed for resonant acoustic field control in 2007 [1]. The acoustic impedance at the loudspeaker diaphragm and the resulting sound absorption coefficient can be adjusted by alternating the electric parameters in the shunt circuit, so the shunted loudspeaker can be implemented for noise control especially at low frequencies [2–4]. Early studies on the shunted loudspeaker mainly focus on normal sound absorption performance. Cernˇ ík et al. studied the effect of the shunt circuit on the sound reflecting performance of a shunted loudspeaker in an impedance duct [2]. Zhang et al. employed the negative impedance converter to counter the D.C. resistance and voice coil inductance of the loudspeaker to broaden the sound absorption bandwidth [5]. Tao et al. proposed constituting a thin compound broadband absorber by placing the shunted loudspeaker at the back of a micro-perforated panel [6]. Jing et al. designed a shunt speaker with a sound absorption coefficient above 0.9 at both 100 Hz and 200 Hz to control the noise of the power transformer [7]. Cho et al. replaced the closed box with a vented enclosure to enhance the sound absorption performance at low frequency [8]. Boulandet et al. adopted the response surface method to optimize the parameters of the shunted loudspeaker (such as the moving mass, the enclosure volume, the filling density of mineral fiber, and the electrical load value) [9]. In the studies above, analog components were used in the shunt circuit, and it was difficult to adjust the electrical impedance precisely. Boulandet et al. employed the real-time field programmable gate array Appl. Sci. 2018, 8, 2484; doi:10.3390/app8122484 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, x FOR PEER REVIEW 2 of 12 to adjust the electrical impedance precisely. Boulandet et al. employed the real-time field programmable gate array module and the voltage-controlled current source to constitute the shunt Appl. Sci. 2018, 8, 2484 2 of 12 circuits [10]. Rivet et al. proposed a hybrid impedance control architecture for an electroacoustic absorber that combines a microphone-based feedforward control with a current driven electro moduledynamic and loudspeaker the voltage-controlled system [11]. currentConsidering source the to constituteresonance thecharacteristics shunt circuits of [the10]. mechanical Rivet et al. proposedsystem of athe hybrid loudspeaker, impedance the control shunted architecture loudspeaker for anis electroacoustica typical resonant absorber sound that absorber combines with a microphone-basedadjustable feedback feedforward impedance control[12–14]. with a current driven electro dynamic loudspeaker system [11]. ConsideringFor implementation, the resonance the characteristics performance of of the the mechanical array of shunted system loudspeakers of the loudspeaker, needs to the be shunted further loudspeakerinvestigated. isA a linear typical array resonant of 10 soundshunted absorber loudspeakers with adjustable was placed feedback in the reverberant impedance [chamber,12–14]. and a soundFor pressure implementation, attenuation the of performance 14 dB was achieved of the array at 34.9 of shunted Hz [15]. loudspeakersFour shunted needsloudspeakers to be further with investigated.surface area of A 0.05 linear m2 array were of placed 10 shunted in the loudspeakerscorners of the was rectangular placed in room the reverberant with dimensions chamber, of 3 and × 5.6 a sound× 3.53 m pressure3 to reduce attenuation the sound of14 pressure dB was level achieved between at 34.9 70 HzHz [ 15and]. Four100 Hz shunted [16]. Thirty loudspeakers 50 × 50 withmm surfaceshunted area loudspeaker of 0.05 m2 cellswere were placed assembled in the corners as liners of the inside rectangular a pipeline room with with air dimensions flow, and the of 3obtained× 5.6 × 3.53insertion m3 to loss reduce was the 16 sounddB at the pressure target level frequency between [17]. 70 A Hz surface and 100 array Hz [ 16of ].shunted Thirty 50loudspeakers× 50 mm shunted could loudspeakercontrol the refracted cells were direction assembled of as the liners inci insidedent sound a pipeline around with 350 air flow,Hz [18]. and theHowever, obtained the insertion sound lossabsorption was 16 performance dB at the target of the frequency surface array [17]. Aof surfaceshunted array loudspeakers of shunted has loudspeakers not been investigated. could control the refractedIn this paper, direction a modal of the expansion incident method sound aroundis proposed 350 Hzto calculate [18]. However, the normal the soundsound absorptionabsorption performancecoefficient of of the the array surface of arrayshunted of shunted loudspeakers loudspeakers with different has not been acoustic investigated. impedances. The finite elementIn this model paper, is further a modal employed expansion to method validate is the proposed accuracy to calculateof the proposed the normal method. sound Simulations absorption coefficientshow that each of the shunted array of loudspeaker shunted loudspeakers can work almost with different independently. acoustic impedances.An experiment The was finite conducted element modelin the isimpedance further employed duct with to validatefour different the accuracy shunted of theloudspeakers proposed method. to validate Simulations the feasibility show that of eachachieving shunted multi loudspeaker-tone sound can absorption. work almost independently. An experiment was conducted in the impedance duct with four different shunted loudspeakers to validate the feasibility of achieving multi-tone2. Theory sound absorption. 2. TheoryThe schematic of the shunted loudspeaker array is presented in Figure 1a, where four shunted loudspeakers with equal areas are installed at the left terminal z = 0 of a square impedance duct. A planeThe wave schematic is incident of the normally shunted on loudspeaker the right terminal array isat presentedz = L with ina constant Figure1a, particle where velocity four shunted v0(ω). loudspeakersEach shunt loudspeaker with equal (named areas areas SL installed1 to SL4) atconsists the left of terminala closed-boxz = loudspeaker 0 of a square and impedance a shunt circuit duct. Aconnected plane wave to the is incident loudspeaker’s normally terminals. on the right The terminallength of at thez = ductL with cross a constant section particleis a, and velocity the lengthv0(w of). Eachthe front shunt face loudspeaker of each shunted (named loudspeaker as SL1 to SL4 )unit consists is a/2 of respectively. a closed-box loudspeakerThe shunt circuit and a shuntis show circuitn in connectedFigure 1b, where to the loudspeaker’sthe negative resistance terminals. −R Thee and length negative of the inductance duct cross section−Le are isuseda, and to counteract the length ofthe the D.C. front resistance face of each RE shunted and voice loudspeaker coil inductance unit is a/2 LE respectively. of the loudspeaker The shunt respectively. circuit is shown The in Figurecapacitance1b, where Cs and the inductance negative resistance Ls can be− Rswitchede and negative according inductance to the −designLe are targets. used to counteract the D.C. resistance RE and voice coil inductance LE of the loudspeaker respectively. The capacitance Cs and inductance Ls can be switched according to the design targets. y 0 a r r a 3 SL r e SL4 k a a e p s SL1 d v0() u x o l a d e t SL2 n u h y S z 0 L (a) Figure 1. Cont. Appl. Sci. 2018, 8, 2484 3 of 12 Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 12 air cavity Zs Cs −Re −Le Ls (b) FigureFigure 1. (a) A schematic of the shunted loudspeaker array set at the end of an impedance duct;duct; (b) thethe equivalentequivalent circuitcircuit ofof aa shuntshunt
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