Equivalent Acoustic Impedance Research Articles

Mechanism of airborne sound absorption through triboelectric effect for noise mitigation

Mitigating broadband noise with passive airborne sound absorbers has been a long-lasting challenge, particularly for low-frequency anthropogenic sounds below kilohertz with long wavelengths, which require bulky materials for effective absorption. Here, we propose a strategy that utilizes local triboelectric effect and in-situ electrical energy dissipation mechanism for airborne sound absorption. This approach involves a fundamentally different mechanism that converts airborne sound into electricity for energy dissipation, in contrast to conventional mechano-thermal energy conversion mechanisms. We establish an equivalent acoustic impedance model to provide theoretical analysis of the underlying sound absorption mechanisms, with a theoretical maximum mechano-electro-thermal coupling efficiency approaching 100% under optimal conditions. We design fibrous triboelectric composite foam materials accordingly and show their substantially boosted acoustic absorption performance experimentally, where the adoption of diverse triboelectric material pairs validates that a larger difference in material charge affinities intensifies the local triboelectric effect and results in higher acoustic absorbing performance.

Atmospheric Sound Propagation over Rough Sea: Numerical Evaluation of Equivalent Acoustic Impedance of Varying Sea States

This work presents a numerical study on atmospheric sound propagation over rough water surfaces with the aim of improving predictions of sound propagation over long distances. A method for generating pseudorandom sea profiles consistent with sea wave spectra is presented. The proposed method is suited for capturing the logarithmic nature of the energy distribution of the waves. Sea profiles representing fully developed seas for sea states 2, 3, 4, and 5 are generated from the Elfouhaily et al. (ECKV) sea wave spectra. Excess attenuation caused by refraction and surface roughness is predicted with a parabolic equation (PE) solver. A novel method for estimating equivalent effective impedance based on PE predictions at different sea states is presented. Parametric expressions using acoustic frequency and significant wave height are developed for effective surface impedances. In this work, sea surface roughness is on a scale comparable with the acoustic wavelength. Under this condition, the acoustic scattering is primarily incoherent. This work shows the limitations of using an equivalent surface impedance in such incoherent scattering cases.

Modulating the Acoustic Vibration Performance of Wood by Introducing a Periodic Annular Groove Structure

The acoustic vibration performance of wood affects the quality of many musical instruments, and the variability of wood causes obvious differences between individual timber samples. To mitigate the variations among the individual timber samples intended for musical instruments, in this study, we combined finite element simulation with experimental testing to investigate the effect of the periodic annular groove structure on the comprehensive acoustic vibration characteristics of wood. The results revealed that there are discernible correlations between the structural parameters of the periodic annular groove and the key acoustic parameters of wood, including the resonant frequency, equivalent dynamic modulus of elasticity, equivalent specific dynamic modulus of elasticity, equivalent acoustic radiation quality constant, and equivalent acoustic impedance. These relationships can be used to fine-tune the overall acoustic vibration performance of wood and harmonize the acoustic vibration characteristics among different timber specimens. The effects of the periodic annular groove structure on the five acoustic vibration parameters obtained through finite element simulations exhibited minimal differences to the corresponding results from experimental tests. Furthermore, there was a remarkably strong correlation between the outcomes of the finite element simulations and the experimental test results, with the coefficient of determination exceeding 0.99.

Fabrication and characterization of hybrid bulk and surface acoustic wave resonators with Ag/patterned-AlN/Mo/diamond/Si layered structure

Hybrid bulk acoustic wave and surface acoustic wave (BAW/SAW) devices attract extensive interests due to their high electromechanical coupling coefficient and quality factor. In this study, longitudinal BAW coupled SAW resonators with piezoelectric AlN inter-digital transducers (IDT) were simulated and fabricated on diamond substrates to increase the working frequency as well. The simulated figure of merit value is 104, 123 % improved comparing with the corresponding metal IDT of 46.5. The frequency response spectrum of single port reflection (S11) shows dominant harmonic resonance at 913 MHz with electromechanical coupling coefficient of 2.16 % and quality factor of 913. These results indicate mutual transductions between BAW and SAW occur with sufficient efficiency in hybrid structures, which is analyzed and interpreted by equivalent acoustic impedance theory.

Broadband low-frequency sound insulation performance of quasi-zero stiffness local resonant acoustic metamaterial plate

For realizing the effective broadband insulation of sound at low frequencies, a novel local resonant acoustic metamaterial plate having quasi-zero stiffness is proposed. Based on the classical mass-spring local resonance model, a metastructure is constructed by introducing additional inclined springs with negative stiffness. First, the normalized equivalent stiffness of the quasi-zero stiffness structure is derived from the perspective of dynamics. Then, by employing the method of equivalent medium, a sound insulation model of the metastructure is established theoretically. For validation, numerical simulations as well as experimental measurements are carried out. It is demonstrated that in the positive (equivalent) stiffness regime, increasing either the stiffness ratio or pre-compression can significantly reduce the local resonance frequency of the metastructure, which exhibits the great insulation performance around the local resonance frequency. For a typical example, the proposed metastructure can achieve a transmission loss of 30 dB around 10 Hz. In contrast, within the negative stiffness regime, the metastructure does not exhibit local resonance, thus avoiding sound insulation valley caused by the “coincidence effect”. Compared with traditional materials or similar metamaterials, the proposed metastructure has significant advantages in sound insulation (e.g. more than 30 dB drop over a wide frequency band of 53－1500 Hz). By analyzing the equivalent mass density, reflection coefficient, and acoustic impedance ratio of the metastructure, the physical mechanism behind its superior insulation performance is further explored. The equivalent mass density changes from positive to negative and tends to infinity at the insulation peak. The insulation peak is attributed to a nearly perfect total reflection of sound wave caused by impedance mismatch, while the insulation valley is caused by low-frequency “coincidence effect” originating from the local resonance band gap. The using of the quasi-zero stiffness local resonance to achieve low-frequency broadband sound insulation overcomes the disadvantages of traditional metamaterials such as reduced stiffness or additional mass, thus becoming vastly attractive for constructing low-frequency broad band sound insulation structures.

Finite-Element Method for Calculating the Sound Field in a Tank with Impedance Boundaries

In this paper, a finite-element method for calculating the sound field in a water tank with impedance boundaries is proposed based on the theory of standing waves in a tube. The equivalent acoustic impedance of the tank walls is calculated by establishing a three-dimensional axisymmetric virtual standing-wave tube in finite-element software, whereupon boundaries with that impedance are used as the tank boundaries. Since the impedance is the property of the material itself, the calculated impedance value can be used for the calculation of the three-dimensional sound field. The sound field due to a point source in a glass tank is calculated using the proposed method, the correctness of which is assessed experimentally. By comparing the experimental and numerical results, the proposed method is shown to be correct.

Dynamics of acoustic impedance matching layers in contactless ultrasonic power transfer systems

The acoustic impedance mismatch between transducer materials and medium in ultrasonic power transfer systems narrows the transduction bandwidth and causes losses through the back reflection of progressive pressure waves at the boundary between the transducers and medium. Capturing both resonances and losses due to impedance mismatch of interwoven elements is essential for advancing the development of these systems. We present a unified approach, based on the multiplication of a sequence of transfer matrices, to determine an equivalent acoustic impedance. The analytical model couples the properties of the transmitter and receiver with multiple matching layers and a single classical quarter-wave layer in controlled setups with the objective of minimizing reflections through acoustic impedance mismatch alleviation. Losses due to ultrasonic attenuation in the material layers and medium are also considered. The acoustic field at the receiver location constitutes the input to the coupled electro-elastic equations of the fluid-loaded and electrically-loaded piezoelectric receiver. Experiments are performed to identify the input acoustic pressure from a cylindrical transmitter to a receiver disk operating in the 33-mode of piezoelectricity. The results show significant enhancements in terms of the receiver’s electrical power output when implementing a two-layer matching structure. We present the results showing non-dimensional wave number variations versus characteristic impedance, which can be used to calculate the materials’ thicknesses for acoustically matching ultrasonic power transfer systems to an acoustic medium of interest at any desired resonant frequency while considering any type of glue or epoxy as the bonding layer. The derived physical models facilitate the development of high-fidelity matched systems with enhanced contactless power transmission.

Sound absorption performance of microperforated honeycomb metasurface panels with a combination of multiple orifice diameters

This study demonstrated a microperforated honeycomb metasurface panel (MHMP) with a micro-perforation on each honeycomb cell and designed an MHMP combining different orifice diameters. Based on two theoretical models (i.e., microperforated panel (MPP), and Helmholtz resonator (HR), models) and impedance tube testing, the sound absorption performance of MHMP was verified. Through impedance tube testing, the influences of orifice diameter and thickness of MPP on sound absorption performance of MHMP were assessed. The results demonstrate that the designed MHMP can absorb 99% of sound at its resonant frequency and conforms to the HR model. The MPP model proves that MHMP needs to be thinner to obtain better sound absorption effects at the same peak frequency of sound absorption compared with the MPP. With the increase of MPP thickness or decrease of orifice diameter, the resonant frequency of the MHMP decreases and the frequency band of sound absorption becomes narrower. The test results show that the sound absorption effects of MHMP with a combination of multiple orifice diameters being equivalent to those of MHMP with the mean value of the orifice diameters used in the combination. For example, sound absorption effects of MHMP combining orifice diameters of 0.5 and 0.7 mm are equivalent to those of MHMP with an orifice diameter of 0.6 mm. The HR model proves that the equivalent acoustic impedance of the combined MHMP is approximately equal to the mean value of acoustic impedances of an MHMP with different orifice diameters in the combination. In addition, the results show that such an equivalent phenomenon should be considered in the design of sound-absorption materials.

Modeling QCM-D Response to Deposition and Attachment of Microparticles and Living Cells.

Quartz crystal microbalance with dissipation monitoring (QCM-D) is a powerful tool for studying adhesion, yet its use for analyzing the deposition of microparticles and living cells on surfaces has been hampered by difficulties in interpretation. Here we report a new quantitative model of QCM-D response, presented as an equivalent acoustic impedance circuit. As an essential feature, the particle interaction with surrounding fluid is modeled by relations for a freely oscillating rotating and translating sphere in an unbounded fluid, which is a valid approximation for microparticles. This helps deduce from the measured reponse the parameters pertinent to the contact mechanics. We use the model to analyze deposition of different microparticles as well as Pseudomonas fluorescens bacteria on several substrates using QCM-D combined with real-time microscopy. The parameter space is increased by varying particle type and size, substrate surface chemistry and rigidity, and ionic strength of the solution, which allows observation of diverse responses and transition from inertial to elastic loading, including rarely observed resonant regimes. Ultimately, we find that the model describes reasonably well the observed response for different microparticles and substrates, as well as for bacteria, and enables extraction of the contact characteristics in elastic and mixed loading regimes. It also reveals discrepancies between measured and anticipated parameters for large particles. The new model can be a useful tool for interpreting and quantifying QCM-D data on the adhesion of particles and living cells to surfaces, including time-dependent adhesion phenomena.

Acoustic metamaterial panel for both fluid passage and broadband soundproofing in the audible frequency range

We present the design, including an experimental demonstration, of an acoustic metamaterial panel aimed at reducing incoming broadband noise in the audible frequency range while allowing an incoming fluid to pass through the holes formed in the panel. The noise reduction performance of the proposed acoustic metamaterial panel is attributed to an array of annular cavities enclosing the fluid passage holes. The acoustic behavior of the acoustic metamaterial panel is theoretically analyzed by the transfer matrix method, and an equivalent acoustic impedance of each annular cavity is included with its effective length in the derived transfer matrix. The effective bulk modulus for the acoustic metamaterial panel is then extracted from the transmission and reflection coefficients by using the retrieval method. It is shown that the frequency range of the negative effective bulk modulus coincides with the stop band of the acoustic metamaterial panel. The underlying physical mechanism for the negative effective bulk modulus is attributed to the out-of-phase motion of vibrating particles in adjacent annular cavities. A calculated transmission coefficient curve of the acoustic metamaterial panel is shown to be in good agreement with the measured one. The findings presented in this work should be useful in the design of a holey soundproof panel.

Acoustic behaviors of the microperforated panel absorber array in nonlinear regime under moderate acoustic pressure excitation.

The acoustic performance of a microperforated panel (MPP) absorber array in the nonlinear regime is investigated both numerically and experimentally. The MPP absorber array is constructed by three parallel-arranged MPP absorbers with different cavity depths. A finite element model is used to simulate the acoustic response of the MPP absorber array by adopting the nonlinear impedance model. The results show that the absorption of the MPP absorber array is affected by the incident sound pressure when it is beyond around 100 dB. With appropriate structural and perforation property of MPP, the MPP absorber array in non-linear regime outperforms that in linear regime due to the improvement of equivalent acoustic impedance matching with ambient air over wide frequency range. However, when the sound pressure excitation is too high, the local resonance effect of the resonating component MPP absorber is diminished and the sound absorption is decreased. With the carefully chosen properties of MPP, the performance degradation induced by panel vibration can be avoided. An optimal set of MPP properties to avoid the performance degradation induced by panel vibration is determined. The measured normal absorption coefficients of a prototype MPP absorber array compare well with the numerical prediction in both linear and nonlinear regimes.

A framework for solving atomistic phonon-structure scattering problems in the frequency domain using perfectly matched layer boundaries

We present a numerical approach to the solution of elastic phonon-interface and phonon-nanostructure scattering problems based on a frequency-domain decomposition of the atomistic equations of motion and the use of perfectly matched layer (PML) boundaries. Unlike molecular dynamic wavepacket analysis, the current approach provides the ability to simulate scattering from individual phonon modes, including wavevectors in highly dispersive regimes. Like the atomistic Green's function method, the technique reduces scattering problems to a system of linear algebraic equations via a sparse, tightly banded matrix regardless of dimensionality. However, the use of PML boundaries enables rapid absorption of scattered wave energies at the boundaries and provides a simple and inexpensive interpretation of the scattered phonon energy flux calculated from the energy dissipation rate in the PML. The accuracy of the method is demonstrated on connected monoatomic chains, for which an analytic solution is known. The parameters defining the PML are found to affect the performance and guidelines for selecting optimal parameters are given. The method is used to study the energy transmission coefficient for connected diatomic chains over all available wavevectors for both optical and longitudinal phonons; it is found that when there is discontinuity between sublattices, even connected chains of equivalent acoustic impedance have near-zero transmission coefficient for short wavelengths. The phonon scattering cross section of an embedded nanocylinder is calculated in 2D for a wide range of frequencies to demonstrate the extension of the method to high dimensions. The calculations match continuum theory for long-wavelength phonons and large cylinder radii, but otherwise show complex physics associated with discreteness of the lattice. Examples include Mie oscillations which terminate when incident phonon frequencies exceed the maximum available frequency in the embedded nanocylinder, and scattering efficiencies larger than two near the Brillouin zone edge.

Oblique incidence sound absorption of parallel arrangement of multiple micro-perforated panel absorbers in a periodic pattern

The sound absorption performance of a micro-perforated panel (MPP) absorber array at oblique incidence and in diffuse field is investigated both numerically and experimentally. The basic module of the MPP absorber array consists of four parallel-arranged MPP absorbers with different cavity depths, and the whole MPP absorber array is created by arranging the basic modules in a periodically repeating pattern. Results show that the influence of incidence angle mainly lies in two aspects. First, the parallel absorption mechanism breaks down at lower frequencies at oblique incidence than at normal incidence due to the non-compactness of the resonating MPP absorber, which becomes non-compact if the time delay of incident wave across it is comparable to or larger than π/2. Second, the equivalent acoustic impedance of the MPP varies with respect to incidence angle which in turn changes the sound absorption performance of the MPP absorber array. Influence of the azimuthal angle is insignificant. Because of mutual influence among the member MPP absorbers, the normal incidence sound absorption of the MPP absorber array can be noticeably different from that of the basic module tested in impedance tube. The measured sound absorption coefficients of a prototype specimen in reverberation room compare well with the numerical predictions. The extra sound absorption due to diffraction of sound at the free edges of test specimen is the most efficient around 500Hz.

An experimental study of the acoustic impedance characteristics of human hair

Previous analytical and empirical studies of the human auditory system have shown that the cues used for localization are modified by the inclusion of nonrigid scattering surfaces (clothing, hair etc). This paper presents an investigation into the acoustic impedance properties of human hair. The legitimacy of a locally reactive surface assumption is investigated, and an appropriate boundary condition is formulated to account for the physiological composition of a human head with hair. This utilizes an equivalent impedance parameter to allow the scattering boundary to be defined at a reference plane coincident with the inner rigid surface of the head. Experimental examination of a representative synthetic hair material at oblique incidence is used to show that a locally reactive surface assumption is legitimate. Additional experimental analysis of a simple scattering problem illustrates that the equivalent impedance must be used in favor of the traditional surface impedance to yield physically correct pressure magnitudes. The equivalent acoustic impedance properties of a representative range of human hair samples are discussed, including trends with sample thickness, fiber diameter, bulk density, and mass.

A method to measure the equivalent acoustic impedance of a scatterer

The procedures of simplifying scatterers’ geometry and finding its equivalent acoustic impedance are proposed by using scattering holography and multiple multipole expansions. The scattered sound field depends on the incident field, the geometry, and the physical property of the scatterer, which can be measured by using tools such as a set of microphones and a 3‐D scanner. Once the sound field over a surface is measured, the whole sound field of 3‐D space can be reconstructed by acoustic holography. However, predicting near‐field sound by holography is inefficient in practice, because huge numbers of measurement points are required to describe the complex sound field in the vicinity of a scatterer. With this regard, multiple multipole expansions are employed to reduce the number and the size of elements of a scatterer necessary to express the measured scattered field. Therefore it is equivalent to simplifying the geometry of a scatterer, and enables us to predict the sound pressure and velocity, as well as acoustic impedance, on the scatterers’ surface. Using the proposed method, it is demonstrated that the equivalent acoustic impedance can be obtained. [Work supported by the BK21 project initiated by the Ministry of Education and Human Resources Development of Korea.]

Equivalent acoustic impedance model. Part 1: experiments and semi-physical model

The context of this research is devoted to the construction of an equivalent acoustic impedance model for a soundproofing scheme consisting of a three-dimensional porous medium inserted between two thin plates. Part 1 of this paper presents the experiments performed and a probabilistic algebraic model of the wall acoustic impedance constructed using the experimental data basis for the medium- and high-frequency ranges. The probabilistic algebraic model is constructed by using the general mathematical properties of wall acoustic impedance operators (symmetry, odd and even functions with respect to the frequency, decreasing functions when frequency goes to infinity, behaviour when frequency goes to zero and so on). The parameters introduced in this probabilistic algebraic model are fitted with the experimental data basis. Finally, this probabilistic algebraic model summarizes all the experimental data bases and consequently can be reused for other researches.

Equivalent acoustic impedance model. Part 2: analytical approximation

In the context of the prediction of noise levels in vibroacoustic systems, numerical models or analytical models can be developed. Generally, numerical models are adapted to the low and medium frequency ranges and analytical models to the medium and high frequency ranges. For analytical models, a classical approximation consists of modelling the multilayer system by an equivalent acoustic impedance. This paper deals with a multilayer system consisting of a porous medium inserted between two thin plates. Part 1 of this paper is devoted to the experiments performed and to the development of a probabilistic algebraic model for the equivalent acoustic impedance. In the present Part 2, an analytical method is constructed for this multilayer system. This method consists of introducing the unbounded medium in the plane directions x 1 and x 2 while the medium is bounded in the x 3-direction. A two-dimensional space Fourier transform introducing the wave vector co-ordinates k 1 and k 2 is used. For a given frequency and for k 1 and k 2 fixed, the boundary value problem in x 3 consists of 12 differential equations in x 3 whose coefficients depend on k 1 and k 2, with boundary conditions. This system of equations is solved by using adapted algebraic calculations. By inverse Fourier transform with respect to k 1 and k 2, the equivalent acoustic impedance is deduced. The method which is proposed is not usual. Finally, a comparison of this analytical approach is compared with the experimental results.

Application of the finite-element method for modeling backed transducers

To model backed transducers by the finite-element method, the main drawback is generally the large size of the numerical problem. Thus, the aim of this paper is to show how the backing mesh can be quite limited. For this purpose, the backing is considered as a lossy transmission line. Then, the equivalent acoustic impedance of the backing is expressed in terms of its thickness TB and the tangent of the phase angle (tan δ). It will be shown that the characteristics of a backed transducer (electrical impedance, acoustic radiated power, etc., ...) can stay unchanged if the thickness TB is scaled down and tan δ is scaled up, keeping the product TB tan δ constant. Finally, finite-element results are successfully compared with measurements results using lithium niobate backed transducer.