DOCSLIB.ORG

Circular Concentric Helmholtz Resonatorsa) A

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Circular Concentric Helmholtz Resonatorsa) A Circular concentric Helmholtz resonatorsa) A. Selamet and P. M. Radavich Department of Mechanical Engineering, The Ohio State University, Columbus, Ohio 43210 N. S. Dickey The University of Michigan, Ann Arbor, Michigan 48109 J. M. Novak Powertrain Operations, Ford Motor Company, Dearborn, Michigan 48121 ~Received 27 December 1995; accepted for publication 30 July 1996! The effect of specific cavity dimensions of circular concentric Helmholtz resonators is investigated theoretically, computationally, and experimentally. Three analytical models are employed in this study: ~1! A two-dimensional model developed to account for the nonplanar wave propagation in both the neck and the cavity; ~2! a one-dimensional solution developed for the limit of small cavity length-to-diameter ratio, l/d, representing a radial propagation in the cavity; and ~3! a one-dimensional closed-form solution for configurations with large l/d ratios which considers purely axial wave propagation in the neck and the cavity. For low and high l/d, the resonance frequencies determined from the two-dimensional approach are shown to match the one-dimensional predictions. For cavity volumes with l/d.0.1, the resonance frequencies predicted by combining Ingard’s end correction with one-dimensional axial wave propagation are also shown to agree closely with the results of the two-dimensional model. The results from the analytical methods are then compared with the numerical predictions from a three-dimensional boundary element method and with experiments. Finally, these approaches are employed to determine the wave suppression performance of circular Helmholtz resonators in the frequency domain. © 1997 Acoustical Society of America. @S0001-4966~97!05312-5# PACS numbers: 43.20.Ks, 43.20.Mv, 43.50.Gf @JEG# INTRODUCTION area discontinuity from the neck to the volume, but it is only effective for a limited range of geometries when used with Helmholtz resonators, which consist of a volume com- the classical model above. In their extensive work, Miles municating through an orifice or neck to some external exci- ~1971! and Miles and Lee ~1975! investigated the Helmholtz tation, produce narrow bands of high wave attenuation. The resonance behavior of harbors by employing the electrical classical approach in modeling these resonators is to neglect analogy; the former treats the simple shapes including circu- the spatial distribution leading to an equivalent spring–mass lar and rectangular harbors with constant depth, the latter system where the mass of air in the neck, m5r0Aclc ,is develops analytical approaches for irregular geometries with driven by an external force and the volume acts as a spring variable depth. Alster ~1972! extended the spring-mass anal- 2 2 with stiffness s5r0c0Ac /V, Ac and lc being the neck area ogy by including the mass of the spring and incorporating a and length, respectively, and V the resonator volume ~Ray- spring with varying stiffness. His experimental results for a leigh, 1945, Art. 303; Kinsler et al., 1982, Chap. 10!. For number of different resonator shapes showed a significant this one degree of freedom system, vr5As/m, leading to a improvement over the lumped model. Several other simple single resonance frequency of f r5(c0/2p)AAc /lcV, which end corrections are also listed by Chuka ~1973!. To predict is a function of the cavity volume, but independent of the the resonance frequency, Tang and Sirignano ~1973! as- volume dimensions. Experimental observations, however, sumed one-dimensional wave propagation in both the reso- have deviated from this frequency, which is attributed to the nator neck and cavity volume. Panton and Miller ~1975! de- motion of some additional mass on both sides of the neck. veloped a relationship for the resonance frequency which To improve the accuracy, the neck length is usually ‘‘cor- matched experimental results well when used with Ingard’s rected’’ by adding a term for each end in order to account for end correction. Their effort was based on a one-dimensional this fluid motion, thereby modifying lc in the foregoing ex- wave motion in the cavity alone and a spatially lumped short pression for f r by lc8 5 lc 1 dv 1 d p . A number of analytical neck length. Monkewitz and Nguyen-Vo ~1985! studied non- treatments based on somewhat simplified physics have been planar effects in two-dimensional resonators with a semicy- introduced to develop these end correction factors. Rayleigh lindrical cavity and three-dimensional resonators with a ~1945! derived a length correction for resonators mounted in hemispherical cavity. By asymptotically matching the solu- a baffle. Ingard ~1953! developed an end correction to ac- tions of the linearized inviscid equations in terms of low- count for multidimensional wave propagation excited at the frequency expansions in the exterior, neck, and cavity, they proposed volume and length corrections for these configura- a!A preliminary version of this study has been presented at the SAE Noise tions. Selamet et al. ~1993, 1995a! developed an expression and Vibration Conference as SAE 951263, Traverse City, MI. for the transmission loss of a Helmholtz resonator with wave 41 J. Acoust. Soc. Am. 101 (1), January 1997 0001-4966/97/101(1)/41/11/$10.00 © 1997 Acoustical Society of America 41 approach, Sec. III the boundary element method, and Sec. IV the experimental setup. The results from the analytical ap- proaches and the boundary element method are compared with experiments and used to evaluate the end corrections in Sec. V. The study is concluded with final remarks in Sec. VI. I. ONE-DIMENSIONAL ANALYTICAL APPROACHES The generation and propagation of multidimensional waves in the resonator volume is clearly dependent on the relative magnitudes of the wavelength, the neck and duct diameters and the volume dimensions. Provided that the in- cident wave from the neck to the volume is planar, there are two limiting configurations for which the wave propagation FIG. 1. Helmholtz resonator dimensions ~d p54.859 cm, dc54.044 cm, 3 in the volume can be considered one-dimensional, thereby lc58.5 cm, and V54500 cm !. allowing a relatively simple closed-form solution for trans- mission loss. This section presents the expressions for the motion. They also provided experimental results illustrating wave attenuation properties for these one-dimensional limits. that the relationship for resonance frequency given by Tang A. Radial propagation limit and Sirignano ~without end correction factors! worked well for volumes with large length-to-diameter ratio, while show- The discrepancy between the analytical results and the ing some deviation at low lv /dv ratios ~hereafter, l/d, for experiment is largest for l/d of the order 0.1 to 1.0. An brevity!. In a preliminary investigation, Selamet et al. accurate prediction of the transmission loss and resonance ~1994a! studied the effect of multidimensional propagation frequency in this region then requires a multidimensional and showed deviations in resonance frequency from the analysis. For smaller l/d ratios as the volume approaches a lumped parameter analysis, particularly at low l/d ratios. Re- ‘‘pancake’’ geometry, a one-dimensional solution in the ra- cently, Chanaud ~1994! developed a relationship for the reso- dial direction becomes possible as discussed next. nance frequency of configurations with a rectangular paral- Consider planar propagation in the main duct and con- lelepiped cavity volume. Finally, by curve fitting finite nector and purely radial wave motion in the cavity volume. element results, Sahasrabudhe et al. ~1995! provided polyno- For circularly symmetric propagation of acoustic waves in a mial expressions for the end correction as a function of ex- hollow disk of constant width, the linearized, inviscid wave pansion ratio and frequency. equation may be written as The present study considers the circular concentric 1 ] ]p 1 ]2p Helmholtz configurations with constant cavity volume and r 5 . ~1! r r r 2 t2 neck length, as shown in Fig. 1. The objective is to investi- ] S ] D c0 ] gate, as a function of the l/d ratio: ~1! the discrepancy in the Introducing the harmonic dependence resonance frequency from classical approaches, and ~2! the ivt acoustic attenuation behavior. To estimate the end correction p~r,t!5P~r!e , ~2! accurately at the neck–volume interface, a two-dimensional and using the separation of variables, the solution for com- axisymmetric analytical model is developed for these reso- plex pressure amplitude may be determined as nators. The study also employs two different one- P r 5C H~1! kr 1C H~2! kr , 3 dimensional analytical solutions based on ~1! radial propaga- ~ ! 1 0 ~ ! 2 0 ~ ! ~ ! tion for small l/d ratios, and ~2! axial propagation for large where C1 and C2 are complex constants related to the am- l/d ratios, to be referred hereafter as one-dimensional radial plitude of oscillation for the inward and outward traveling ~h! and axial solutions, respectively. Both closed-form solutions waves, respectively, and Hb is the Hankel function ~the are used in the study to examine their corresponding limits. Bessel function of the third kind! of order b and type h.As The pressure field inside the resonators is determined by the a function of the latter variable, h, Hankel functions may boundary element method and used to evaluate the degree of readily be expressed as H(1)5J1iY and H(2)5J2iY with J multidimensionality of the sound-pressure field at both ends and Y being the Bessel functions of the first and second kind, of the resonator neck. Experimental results are obtained by respectively. The momentum equation installing Helmholtz resonators in an impedance tube setup. ]u 1 Results from the boundary element method and experiments 52 “p ~4! are then compared with the resonance frequency relationship ]t r0 of the one-dimensional axial model modified by Ingard’s end combined with the harmonic relationship correction for multidimensional propagation.
Load more

Recommended publications
  • View a Copy of This Licence, Visit Iveco​ ​ Mmons.Org/​ Licen​ Ses/​ By/4.​ 0/​
    Hashimoto and Sumita Earth, Planets and Space (2021) 73:143 https://doi.org/10.1186/s40623-021-01472-7 FULL PAPER Open Access Excitation of airwaves by bubble bursting in suspensions : regime transitions and implications for basaltic volcanic eruptions Kana Hashimoto and Ikuro Sumita* Abstract Basaltic magma becomes more viscous, solid-like (elastic), and non-Newtonian (shear-thinning, non-zero yield stress) as its crystal content increases. However, the rheological efects on bubble bursting and airwave excitation are poorly understood. Here we conduct laboratory experiments to investigate these efects by injecting a bubble of volume V into a refractive index-matched suspension consisting of non-Brownian particles (volumetric fraction φ ) and a Newtonian liquid. We show that depending on φ and V, airwaves with diverse waveforms are excited, covering a frequency band of f = O(10 − 104) Hz. In a suspension of φ ≤ 0.3 or in a suspension of φ = 0.4 with a V smaller than critical, the bubble bursts after it forms a hemispherical cap at the surface and excites a high-frequency (HF) wave (f ∼ 1 − 2 × 104 Hz) with an irregular waveform, which likely originates from flm vibration. However, in a suspension of φ = 0.4 and with a V larger than critical, the bubble bursts as soon as it protrudes above the surface, and its aper- ture opens slowly, exciting Helmholtz resonance with f = O(103) Hz. Superimposed on the waveform are an HF wave component excited upon bursting and a low-frequency (f = O(10) Hz) air fow vented from the defating bubble, which becomes dominant at a large V.
    [Show full text]
  • Questions: Helmholtz Resonance
    Questions: Helmholtz resonance 1 Helmholtz resonance may occur when an enclosed volume of air is connected to the atmosphere by a short exit pipe when simple harmonic oscillations of air in the pipe are driven by pressure changes in the enclosed volume. The frequency of the resonance is given by … 1/2 f = v/2[Ax/VL] … where v is the velocity of sound in air, V is the volume of air enclosed air, Ax is the cross sectional area and L is the effective length of the pipe. a Explain, in physical terms, why the effective length L in the frequency relationship is a little longer than the actual length of the exit pipe. b Explain, in physical terms, why halving the volume of the enclosed air raises the resonant frequency. c A Helmholtz resonator is completely filled with carbon dioxide. Will the resonant frequency change and if so by how much? 2 A empty coffee container is shown. The round hole in the cap has a diameter of 1.45 cm. Short lengths of plastic pipe with an internal radius of 0.65 cm convert the container into a Helmholtz resonator. Measured resonant frequencies are plotted below against frequencies 1/2 calculated with the Helmholtz relationship f = v/2[Ax/VL] for four pipe lengths. a Are calculations less satisfactory for shorter or longer pipe lengths? b Increasing the effective length of the pipe by 1.3 cm, recalculating and plotting the revised data gives the graph below. c Which additional point on the graph represents the resonance when the pipe length is zero? d The sound box on a guitar is said to behave as Helmholtz resonator with an effective pipe length.
    [Show full text]
  • The Science of String Instruments
    The Science of String Instruments Thomas D. Rossing Editor The Science of String Instruments Editor Thomas D. Rossing Stanford University Center for Computer Research in Music and Acoustics (CCRMA) Stanford, CA 94302-8180, USA [email protected] ISBN 978-1-4419-7109-8 e-ISBN 978-1-4419-7110-4 DOI 10.1007/978-1-4419-7110-4 Springer New York Dordrecht Heidelberg London # Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer ScienceþBusiness Media (www.springer.com) Contents 1 Introduction............................................................... 1 Thomas D. Rossing 2 Plucked Strings ........................................................... 11 Thomas D. Rossing 3 Guitars and Lutes ........................................................ 19 Thomas D. Rossing and Graham Caldersmith 4 Portuguese Guitar ........................................................ 47 Octavio Inacio 5 Banjo ...................................................................... 59 James Rae 6 Mandolin Family Instruments........................................... 77 David J. Cohen and Thomas D. Rossing 7 Psalteries and Zithers .................................................... 99 Andres Peekna and Thomas D.
    [Show full text]
  • Advances in Aquatic Target Localization with Passive Sonar
    Portland State University PDXScholar Dissertations and Theses Dissertations and Theses Summer 7-14-2014 Advances in Aquatic Target Localization with Passive Sonar John Thomas Gebbie Portland State University Let us know how access to this document benefits ouy . Follow this and additional works at: http://pdxscholar.library.pdx.edu/open_access_etds Part of the Electrical and Computer Engineering Commons Recommended Citation Gebbie, John Thomas, "Advances in Aquatic Target Localization with Passive Sonar" (2014). Dissertations and Theses. Paper 1932. 10.15760/etd.1931 This Dissertation is brought to you for free and open access. It has been accepted for inclusion in Dissertations and Theses by an authorized administrator of PDXScholar. For more information, please contact [email protected]. Advances in Aquatic Target Localization with Passive Sonar by John Thomas Gebbie A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical and Computer Engineering Dissertation Committee: T. Martin Siderius, Chair Lisa M. Zurk Richard L. Campbell John S. Allen, III Mark D. Sytsma Portland State University 2014 c 2014 John Gebbie Abstract New underwater passive sonar techniques are developed for enhancing target local- ization capabilities in shallow ocean environments. The ocean surface and the seabed act as acoustic mirrors that reflect sound created by boats or subsurface vehicles, which gives rise to echoes that can be heard by hydrophone receivers (underwater microphones). The goal of this work is to leverage this \multipath" phenomenon in new ways to determine the origin of the sound, and thus the location of the tar- get. However, this is difficult for propeller driven vehicles because the noise they produce is both random and continuous in time, which complicates its measurement and analysis.
    [Show full text]
  • Chamber Music: an Unusual Helmholtz Resonator for Song Amplification in a Neotropical Bush-Cricket (Orthoptera, Tettigoniidae) Thorin Jonsson1,*, Benedict D
    © 2017. Published by The Company of Biologists Ltd | Journal of Experimental Biology (2017) 220, 2900-2907 doi:10.1242/jeb.160234 RESEARCH ARTICLE Chamber music: an unusual Helmholtz resonator for song amplification in a Neotropical bush-cricket (Orthoptera, Tettigoniidae) Thorin Jonsson1,*, Benedict D. Chivers1, Kate Robson Brown2, Fabio A. Sarria-S1, Matthew Walker1 and Fernando Montealegre-Z1,* ABSTRACT often a morphological challenge owing to the power and size of their Animals use sound for communication, with high-amplitude signals sound production mechanisms (Bennet-Clark, 1998; Prestwich, being selected for attracting mates or deterring rivals. High 1994). Many animals therefore produce sounds by coupling the amplitudes are attained by employing primary resonators in sound- initial sound-producing structures to mechanical resonators that producing structures to amplify the signal (e.g. avian syrinx). Some increase the amplitude of the generated sound at and around their species actively exploit acoustic properties of natural structures to resonant frequencies (Fletcher, 2007). This also serves to increase enhance signal transmission by using these as secondary resonators the sound radiating area, which increases impedance matching (e.g. tree-hole frogs). Male bush-crickets produce sound by tegminal between the structure and the surrounding medium (Bennet-Clark, stridulation and often use specialised wing areas as primary 2001). Common examples of these kinds of primary resonators are resonators. Interestingly, Acanthacara acuta, a Neotropical bush- the avian syrinx (Fletcher and Tarnopolsky, 1999) or the cicada cricket, exhibits an unusual pronotal inflation, forming a chamber tymbal (Bennet-Clark, 1999). In addition to primary resonators, covering the wings. It has been suggested that such pronotal some animals have developed morphological or behavioural chambers enhance amplitude and tuning of the signal by adaptations that act as secondary resonators, further amplifying constituting a (secondary) Helmholtz resonator.
    [Show full text]
  • Investigation of Divided Helmholtz Resonator by Perforated Plate
    INVESTIGATION OF DIVIDED HELMHOLTZ RESONATOR BY PERFORATED PLATE Assist.Prof. S. S. Patil1, Mr. Mithil Chavan2, Mr. Rahul Borude3, 4 5 Mr. Tejas Borate , Mr. Nilesh Giram 1,2,3,4,5Mechanical engineering, G. S.Moze college of engineering, Savitri BaiPhule Pune University, (India) ABSTRACT Now-a-days we have witnessed a great growth in noise in our surrounding .In this project we are going to investigate the performance of a Helmholtz resonator using a perforated panel. The current resonator has a drawback of low frequency bandwidth, it has simple geometry. In the proposed resonator we have attached a perforated panel in its geometry. In our new modified resonator it is expected an increase in frequency bandwidth and increase in transmission loss. In this project we have first analytically transformed the resonator into mathematical model in single degree and two degree of freedom and obtained the dimensions. We have made a CAD model from the theoretical dimensions and also programmed it in matlab for easy calculations. Theoretically the sound reduces by 2dB and experimental analysis will we done after construction of the physical model in the next semester. I.INTRODUCTION Sound is all around. Sometimes it is experienced as pleasant, sometimes as unpleasant. Unwanted sound is generally referred to as noise. Noise is a frequently encountered problem in modern society. One of the environments where the presence of noise causes a deterioration in people’s comfort is in aircraft cabins. Noise encountered in daily life can, for example, be caused by domestic appliances such as vacuum cleaners and washing machines, vehicles such as cars and aeroplanes.
    [Show full text]
  • Resonance in a Cone-Topped Tube
    ISB Journal of Physics, Vol. 5, Iss. 2 June 2011 http://www.isjos.org Resonance in a Cone-Topped Tube Angus Cheng-Huan Chia and Alex Chun-Hao Fann Abstract The relationship between ratio of the upper opening diameter of a cone-topped cylinder to the cylinder diameter, and the ratio of the length of the air column to resonant period was examined. Plastic cones with upper openings ranging from 1.3 cm to 3.6 cm and tuning forks with frequencies ranging from 261.6 Hz to 523.3 Hz were used. The transition from a standing wave in a cylindrical column to a Helmholtz-type resonance in a resonant cavity with a narrow opening was observed. Introduction Tuning Fork In this investigation, a tuning fork was held over a cylindrical pipe to create resonance in Water Level the air column as shown in figure 1. Plastic cones with varying upper openings were placed on top of the pipe and tuning forks PVC Pipe with four different frequencies were used. The nature of the resonance under various situations was studied. For the situation with no cone or short cones, a quarter-wavelength standing wave may be formed in a cylindrical column of air with Figure 1 The range of situations that was investigated: one open end. Given that frequency is the from a cylindrical air column, to a cone topped tube inverse of the period and wavelength equals with a small opening. 4(L + c) (end correction) as shown in figure 2, the equation can be derived as c ! = ! ×! − ! [Equation 1] ! ! L = λ ! For situations with long cones and small upper openings, it is expected that a Figure 3 A classic Helmholtz resonance may form in the air Helmholtz resonator[1].
    [Show full text]
  • THE FUNCTION of F-HOLES in the VIOLIN (Revised and Corrected)
    THE FUNCTION of F-HOLES in the VIOLIN (revised and corrected) The most noticeable thing apart from the difference in pitch, about the paper in the STRAD (April 2001, 408) was the similarity between the plots for the harmonic content of the notes played on the G and E strings respectively. This is not surprising since both sides of the central area of the top plate on which the bridge stands, are active; the centre of rotation is variable and not necessarily unique, somewhere between the two feet of the bridge and not exclusively at the right foot as many body and plate modes are activated simultaneously and to varying extents by the fundamental and harmonics of the note being played. The f-holes perform a function more complex which the paper attempted to point out, than the opening needed for the Helmholtz resonance. To consider this function first. The frequency of the Helmoltz resonance depends on the volume of air in the body of the violin and the total area of any openings. If the volume is 1945, increased the frequency goes down, 10% reduces it by about a semitone; if the f-hole area is enlarged the frequency goes up, 20% raises it about a semitone, and vice versa. So small variations in volume and f- hole area are not going to have a large effect. The area of an f-hole can be expressed in terms of an equivalent ellipse for the purpose of calculation (J.W.Strutt (Lord Rayleigh). The Theory of Sound, Dover, Vol 2, 176) as used by Helmholtz (On the Sensations of Tone, Dover, 1954 86).
    [Show full text]
  • A Model to Predict Acoustic Resonant Frequencies of Distributed Helmholtz Resonators on Gas Turbine Engines
    applied sciences Article A Model to Predict Acoustic Resonant Frequencies of Distributed Helmholtz Resonators on Gas Turbine Engines Jianguo Wang * , Philip Rubini *, Qin Qin and Brian Houston School of Engineering and Computer Science, University of Hull, Hull HU6 7RX, UK; [email protected] (Q.Q.); [email protected] (B.H.) * Correspondence: [email protected] (J.W.); [email protected] (P.R.); Tel.: +44(0)1482-465818 (P.R.) Received: 27 February 2019; Accepted: 2 April 2019; Published: 4 April 2019 Featured Application: Passive control devices for combustion instability and combustion noise in gas turbine engines. Abstract: Helmholtz resonators, traditionally designed as a narrow neck backed by a cavity, are widely applied to attenuate combustion instabilities in gas turbine engines. The use of multiple small holes with an equivalent open area to that of a single neck has been found to be able to significantly improve the noise damping bandwidth. This type of resonator is often referred to as “distributed Helmholtz resonator”. When multiple holes are employed, interactions between acoustic radiations from neighboring holes changes the resonance frequency of the resonator. In this work, the resonance frequencies from a series of distributed Helmholtz resonators were obtained via a series of highly resolved computational fluid dynamics simulations. A regression analysis of the resulting response surface was undertaken and validated by comparison with experimental results for a series of eighteen absorbers with geometries typically employed in gas turbine combustors. The resulting model demonstrates that the acoustic end correction length for perforations is closely related to the effective porosity of the perforated plate and will be obviously enhanced by acoustic radiation effect from the perforation area as a whole.
    [Show full text]
  • Helmholtz Resonators – Piezoelectric Effect • Harvester Design
    HARVESTING ENERGY USING PIEZOELECTRICS EXCITED BY HELMHOLTZ RESONANCE Tyler Van Buren -with- Prof. Alexander Smits, Lindsay Graff, Zachary McCourt, Emile Oshima, and Jason Mulderrig SMITS’ LAB: ENVIRONMENTAL RESEARCH Alexander Smits Eugene Higgins Professor of MAE Artificial atmospheric boundary layer Stratified flows Vertical axis wind turbines • Development of artificial atmospheric boundary layer • Turbulent boundary • generator for wind layers with temperature Many potential benefits tunnel testing gradients • Some drawbacks (e.g., • Occurs during dynamic stall, scaling to • How do model large sizes) buildings/structures transitions between day and night • Better understanding interact with of dynamic stall and atmospheric flows? • On off shore breezes performance ARE THERE OTHER VIABLE WAYS TO COLLECT WIND ENERGY? Helmholtz harvester • Fundamentals: – Helmholtz resonators – Piezoelectric effect • Harvester design Applications • Urban environments – Tall buildings, personal houses • Powering remote sensors Wind tunnel studies • Feasibility tests – Does it produce meaningful energy? • Better resonance – Can we improve it? • Effect of geometry THE CONCEPT HELMHOLTZ HARVESTER Turn a surrounding wind into a vibrating pressure field to be converted to electricity and collected Helmholtz Resonator Piezoelectric Effect HELMHOLTZ RESONATOR • Consider a container full of air with a small opening at MASS OF AIR IN NECK the top m • The air in the neck acts as a COMPRESSION OF AIR IN CAVITY mass • The air inside the container acts as a spring. • Apply a disturbance of pressure This results in a characteristic frequency based on container geometry and fluid properties A: Orifice Area V: Cavity Volume L: Orifice Neck Length c: speed of sound in air HELMHOLTZ RESONATOR • Consider a container full of air MASS OF AIR IN NECK with a small opening at the top m COMPRESSION • The air in the neck acts as a mass OF AIR IN CAVITY • The air inside the container acts as a spring.
    [Show full text]
  • Arxiv:2001.09353V1 [Physics.Flu-Dyn]
    Asymptotic modeling of Helmholtz resonators including thermoviscous effects Rodolfo Brand˜ao and Ory Schnitzer Department of Mathematics, Imperial College London, London SW7 2AZ, UK Abstract We systematically employ the method of matched asymptotic expansions to model Helmholtz resonators, with thermoviscous effects incorporated starting from first principles and with the lumped parameters characterizing the neck and cavity geometries precisely defined and provided explicitly for a wide range of geometries. With an eye towards modeling acoustic metasurfaces, we consider resonators embedded in a rigid surface, each resonator consisting of an arbitrarily shaped cavity connected to the external half-space by a small cylindrical neck. The bulk of the analysis is devoted to the problem where a single resonator is subjected to a normally incident plane wave; the model is then extended using “Foldy’s method” to the case of multiple resonators subjected to an arbitrary incident field. As an illustration, we derive critical-coupling conditions for optimal and perfect absorption by a single resonator and a model metasurface, respectively. arXiv:2001.09353v1 [physics.flu-dyn] 25 Jan 2020 1 I. INTRODUCTION Determining the acoustical response of a Helmholtz resonator, namely a hollow cavity con- nected to an exterior region through a small neck, is a long-standing problem in theoretical acoustics [1–4]. The Helmholtz resonance refers specifically to the fundamental “breathing” mode of the cavity, which occurs at a wavelength many times larger than the cavity. This is in contrast to all higher-order modes, which are related to the formation of standing waves. Helmholtz resonators have long been employed in acoustic devices such as perforated panel absorbers [5], mufflers [6] and acoustical dampers [7].
    [Show full text]
  • The Pennsylvania State University
    The Pennsylvania State University The Graduate School Department of Mechanical and Nuclear Engineering ACOUSTIC CONTROL IN ENCLOSURES USING OPTIMALLY DESIGNED HELMHOLTZ RESONATORS A Thesis in Mechanical Engineering by Patricia L. Driesch 2002 Patricia L. Driesch Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December, 2002 We approve the thesis of Patricia L. Driesch. Date of Signature Gary H. Koopmann Distinguished Professor of Mechanical Engineering Chair of Committee Martin Trethewey Professor of Mechanical Engineering Victor Sparrow Associate Professor of Acoustics Mary Frecker Assistant Professor of Mechanical Engineering Richard C. Benson Professor of Mechanical Engineering Head of the Department of Mechanical Engineering ABSTRACT A virtual design methodology is developed to minimize the noise in enclosures with optimally designed, passive, acoustic absorbers (Helmholtz resonators). A series expansion of eigen functions is used to represent the acoustic absorbers as external volume velocities, eliminating the need for a solution of large matrix eigen value problems. A determination of this type (efficient model/reevaluation approach) significantly increases the design possibilities when optimization techniques are implemented. As a benchmarking exercise, this novel methodology was experimentally validated for a narrowband acoustic assessment of two optimally designed Helmholtz resonators coupled to a 2D enclosure. The resonators were tuned to the two lowest resonance frequencies of a 30.5 by 40.6 by 2.5 cm (12 x 16 x 1 inch) cavity with the resonator volume occupying only 2% of the enclosure volume. A maximum potential energy reduction of 12.4 dB was obtained at the second resonance of the cavity. As a full-scale demonstration of the efficacy of the proposed design method, the acoustic response from 90-190 Hz of a John Deere 7000 Ten series tractor cabin was investigated.
    [Show full text]