Model Of Acoustic Wave Propagation Research Articles

A cell-centered implicit finite difference scheme to study wave propagation in acoustic media: A numerical modeling

In the present paper, we present a Cell-Centered Implicit Finite Difference (CCIFD) operator-based numerical scheme for the propagation of acoustic waves that is very effective, accurate, and small in size. This scheme requires fewer estimation points than the traditional central difference derivative operator. Any numerical simulation is significantly impacted by the precision of a numerical derivative. Long stencils can deliver excellent accuracy while also minimizing numerical anisotropy error. However, a long stencil requires a lot of computational resources, and as these derivatives get bigger, they could start to look physically unrealistic due to contributions from nodes located extremely far, wherein the derivative is local in nature. Furthermore, using such lengthy stencils at boundary nodes may result in errors. The present article investigates a cell-centered fourth order finite difference scheme to model acoustic wave propagation which utilizes a lesser number of nodes in comparison to the traditional Central Difference (CD) operator. However, in general the implicit derivative operator has high computational cost and therefore despite its significant advantages it is generally avoided to be implemented in applications. This serves as a motivation for the present paper to explore a technique called CCIFD that significantly decreases the computational expense by nearly fifty percent. Additionally, spectral characterization of the CCIFD derivative operator has been analyzed and discussed. Finally, the wave propagation has been numerically simulated in 2-dimensional homogeneous and Marmousi model using CCIFD scheme to validate the applicability and stability of the scheme.

Simulations and analysis of underwater acoustic wave propagation model based on Helmholtz equation

In this study, we explore the effectiveness of elliptic partial differential equations (PDEs) in two and three dimensional space based on Helmholtz equation for simulations of acoustic sound in a very complex environment of propagation. For this purpose, we use an advance and robust numerical technique by utilizing the properties of shifted Chebyshev spectral collocation method. This technique is an extension of the traditional Chebyshev polynomials, incorporating a shift in their argument to enhance flexibility across a wider domain, while retaining an extraordinary numerical characteristic such as orthogonality and spectral convergence making them exceptionally effective in finding the approximate solutions. The exponential order of convergence of the proposed approach is shown both through theoretical and numerical approaches. We provide a number of numerical experiments to verify the theoretical results. The spectral convergence has been substantially enhanced by these numerical examples. The exponential order is further validated by numerical error behaviour in both L 2 and L ∞ norms.

Improving acoustic wave propagation models in highly attenuating porous materials.

This article presents an improved and extended modeling approach for acoustic wave propagation in rigid porous materials, focusing on examples, such as plastic foams used for noise reduction in automotive applications. We demonstrate that the classical model (Johnson-Champoux-Allard) in the asymptotic high-frequency limit, widely employed in the literature, fails to accurately reconstruct the transmitted acoustic signal through high absorbent porous materials characterized by significant wave attenuation. The study focuses on the airborne ultrasonic frequency range (30-200 kHz). To address this limitation, we introduce new non-acoustic parameters Σ and V for viscous effects, and Σ' and V' for thermal effects, with surface and volumetric dimensions, respectively, allowing for the reconstruction of the transmitted signal and accurate modeling of the pronounced acoustic attenuation within the material. These parameters are incorporated into the expansion on skin depths of the dynamic tortuosity α(ω) and thermal tortuosity α' (ω) response functions, which describe the inertial-viscous and thermal interactions between the fluid and the solid, respectively. This novel modeling approach enables a more comprehensive study of high attenuating porous media, which are crucial for effective noise reduction. Additionally, it opens up new possibilities for characterization beyond the capabilities of current models.

Ultra-broad low-frequency forbidden bands in 1D solid–fluid acoustic superlattices with multiple solid constituents

In this paper, a theoretical model of underwater acoustic wave propagation, based on the transfer matrix method, is employed to calculate acoustic wave transmission through a 1D solid–fluid superlattice (SFSL) with multiple solid constituents. The band structure of infinite multi-element SFSL and the transmission coefficient of finite one are obtained, both of which reveal the existence of multiple separated ultra-broad low-frequency forbidden bands, even in the case of solid constituents with very close acoustic parameters. Simulations about the finite multi-element SFSL are carried out to verify the correctness of these findings. In addition, the influence of the acoustic parameters and the structural parameters on the low-frequency forbidden bands (LFBs) of SFSL with two solid constituents (m = 2) is also investigated. It is found that the required two separated LFBs can be achieved by choosing appropriate material parameters. For the situation of m ≥ 2, it is expected to provide more possibilities to engineer low-frequency bandgaps. Our results infer that multiple separated LFBs in multi-element SFSL can be quite useful for making highly performing low-frequency acoustic filters in selective angle ranges, which are useful for the elimination of the side lobes of low-frequency acoustic transducers.

How Ultrasonic Pulse-Echo Techniques and Numerical Simulations Can Work Together in the Evaluation of the Elastic Properties of Glasses

This paper presents the numerical simulation of the ultrasonic wave transmittance utilizing the elastodynamic finite integration technique (EFIT). With this methodology, it is possible to simulate the propagation of the ultrasound in a medium with a relatively low computational cost. The capability of this technique for determining the elastic properties of fluorophosphate and the aluminosilicate glasses is described in detail. The elastic constants of the glasses were calculated from the theoretically predicted longitudinal and transversal sound velocities and compared with the corresponding experimental data. Furthermore, the calculated and experimental elastic properties of the fluorophosphate and aluminosilicate glasses were correlated with the structural peculiarities of these glasses. This simulation technique is also suitable for unveiling the existence of possible defects in the glasses by comparing the experimental and simulation data. The EFIT technique is shown to be a very useful tool in order to provide fast and easy-to-acquire data regarding also the structural characteristics of various glassy systems. This can be used in conjunction with other spectroscopic techniques which can prove to be extremely useful for the non-destructive testing of vitreous materials. The latter can prove very important when vitreous materials used in optical or optoelectronic applications need continuous monitoring in order to ensure their optimum operation and functionality with limited intervention. The main contribution of this paper is the treatment of numerical time-domain modeling of 2D acoustic wave propagation in a viscoelastic medium by implementing the elastodynamic finite integration technique (EFIT).

Deriving Vocal Fold Oscillation Information from Recorded Voice Signals Using Models of Phonation.

During phonation, the vocal folds exhibit a self-sustained oscillatory motion, which is influenced by the physical properties of the speaker's vocal folds and driven by the balance of bio-mechanical and aerodynamic forces across the glottis. Subtle changes in the speaker's physical state can affect voice production and alter these oscillatory patterns. Measuring these can be valuable in developing computational tools that analyze voice to infer the speaker's state. Traditionally, vocal fold oscillations (VFOs) are measured directly using physical devices in clinical settings. In this paper, we propose a novel analysis-by-synthesis approach that allows us to infer the VFOs directly from recorded speech signals on an individualized, speaker-by-speaker basis. The approach, called the ADLES-VFT algorithm, is proposed in the context of a joint model that combines a phonation model (with a glottal flow waveform as the output) and a vocal tract acoustic wave propagation model such that the output of the joint model is an estimated waveform. The ADLES-VFT algorithm is a forward-backward algorithm which minimizes the error between the recorded waveform and the output of this joint model to estimate its parameters. Once estimated, these parameter values are used in conjunction with a phonation model to obtain its solutions. Since the parameters correlate with the physical properties of the vocal folds of the speaker, model solutions obtained using them represent the individualized VFOs for each speaker. The approach is flexible and can be applied to various phonation models. In addition to presenting the methodology, we show how the VFOs can be quantified from a dynamical systems perspective for classification purposes. Mathematical derivations are provided in an appendix for better readability.

Numerical analysis of Plastic Perforated Panel for Acoustic Protection

Acoustic protection is an important aspect in various industrial, commercial and residential applications. In order to reduce the transmission of noise, perforated panels are frequently used as a barrier. The present study aims to conduct a numerical analysis of plastic perforated panels for acoustic protection. The study employed a finite element method (FEM) approach and focused on the propagation of acoustic waves through perforations of varying diameters (30 mm, 40 mm, 50 mm, 60 mm, 70 mm and 90 mm) and at different frequencies (250 Hz, 500 Hz, 1000 Hz and 1500 Hz). The numerical analysis was conducted using the finite element software ANSYS. This work offers numerical analysis models of acoustic wave propagation, which can be used by those interested in similar problems, for different environments, in closed or open spaces. The results showed that the perforation diameter and frequency play a crucial role in the performance of the plastic perforated panels as an acoustic barrier. The results of the author�s research pointed out that the plastic materials can be used successfully in the construction of acoustic barriers. Next to it, the findings of this study can provide valuable insights for engineers and designers in the selection and optimization of plastic perforated panels for acoustic protection applications.

Level set-based shape optimization of deformable structures for achieving desired sound transmission and reflective responses

In this paper, we propose a level set-based shape optimization method for acoustic wave propagation problems with a deformable structure. First, we propose a mathematical model for acoustic wave propagation with a deformed structure based on coordinate transformation and the Eulerian approach. Next, we formulate the shape optimization problem and perform sensitivity analysis based on the shape derivative concept. We then construct an optimization algorithm based on the framework of a level set-based shape and topology optimization method. Finally, we provide two-dimensional optimization examples that demonstrate the effectiveness of our proposed method in providing optimized designs with desired functionality, while considering the structural deformation.

Theoretically derived pore geometry in carbonates using the extended biot theory

Carbonates typically display a large scatter in velocity-porosity cross plots that is caused by the difference in stiffness that the highly variable pore geometry produces in carbonate rocks at a given porosity. In recent years, digital image analysis (DIA) made it possible to capture objective, quantifiable parameters of the pore geometry to explain the scatter in carbonate velocity-porosity cross plots. The geometrical parameters most influential for acoustic velocity are Perimeter over Area (measuring the complexity of the pore space) and Dominant Size (measuring pore sizes as equivalent diameter). Most theoretical models of acoustic wave propagation in porous media, however, do not incorporate those geometrical characteristics of the natural pore spaces? In contrast, the frame flexibility and coupling factors (fk and γk) embedded in the Extended Biot Theory capture the geometrical characteristics using poroelastic data. Here, these theoretically derived parameters are tested and validated with experimental data. In 95 limestone samples, Extended Biot Theory parameters fk and γk can be derived reliably from measured acoustic data. Both parameters correlate well to Perimeter over Area (r = 0.702, p < 0.0001), and Dominant Size (r = 0.792, p < 0.0001) derived using digital image analysis of thin section photographs. These correlations confirm the existence and the strength of the relationship between theoretical parameters from the Extended Biot Theory and quantitative pore geometry parameters. Thus, this study illustrates that: (1) estimating porosity from acoustic data can be substantially improved by incorporating information on quantitative pore space geometry; and (2) in cases where good estimates of porosity are available (e.g. from well-log data or seismic with extensive well control) quantitative pore geometric characteristics can be estimated directly from acoustic data. These quantitative pore geometry characteristics can be used to estimate permeability indirectly from acoustic data. For example, permeability estimates based on a Kozeny-Carman type function incorporating geometrical information derived from the topological Extended Biot Theory parameters fk and γk, yield a statistically significant, high Pearson correlation coefficient of r = 0.713 (p < 0.0001).

샘플링 기법에 따른 음향파 전파의 대리 모델 성능 비교

본 연구에서는 음향파 전파의 대리 모델을 일부 데이터만으로 학습함에 있어서 샘플링 방법에 따른 성능 차이를 비교 분석한다. Uniform sampling, farthest point sampling, Poisson disk sampling 기법을 활용해 소요 시간과 샘플 개수에 따른 대리 모델의 정확도 변화를 분석했다. 이전부터 음향파나 유체역학의 대리 모델링을 위해 여러 기계 학습 및 딥러닝 기반의 모델이 제안되었으나, 이러한 모델들은 데이터의 특성을 충분히 잘 반영하지 못했다. 본 연구에서는 각 샘플링 방법으로 데이터 세트를 생성하고, 심층 신경망 기반의 대리 모델을 학습했다. 조건별 성능을 비교하였을 때, 음향파 전파의 대리 모델 생성을 위해서는 정확도와 소요 시간 측면에서 Poisson disk sampling을 사용하는 것이 합리적임을 확인하였다. 본 연구를 통해 확인된 샘플링 기법에 따른 특성은 디지털 트윈과 같이 대리 모델의 생성이 실시간으로 빠르고 정확하게 이뤄져야 하는 상황에서 최적의 샘플링 기법을 선정하는 근거로 활용될 수 있다.br/

Computational Fluid Dynamic Simulation of Leakage Acoustic Waves Propagation Model for Gas Pipelines

When leakage occurs for natural gas pipelines, acoustic waves generated at the leakage point will propagate to both ends of the pipe, which will be measured and processed to detect and locate the leakage. When acoustic waves propagate in the gas, the amplitude will attenuate and the waveform will spread, which decides the installation distance of acoustic sensors. Therefore, computational fluid dynamic (CFD) simulation research on the acoustic wave propagation model is accomplished and verified by experiments to provide the foundation for the acoustic leak location method. The propagation model includes two parts: amplitude attenuation model and waveform spreading model. Both can be obtained by the established CFD simulation model. Additionally, the amplitude attenuation model can be verified by the experiments. Then, the simulation method is applied to conclude the propagation model under variable conditions, including different flow directions, Reynolds numbers, and diameters. Finally, the experimental demonstration of the leak location based on the propagation model is given. The results indicate that not only the gas viscosity but also the gas flow can influence the propagation model, and the leak location method based on the propagation model is effective. Conclusions can be drawn that CFD simulation on the propagation model for natural gas pipelines is an efficient way to carry out research and provide the theoretical basis for acoustic leak location method application.

Mathematical modeling of acoustic wave propagation in elastic materials with multi-periodic hierarchical structure of heterogeneities

An asymptotic homogenization procedure is applied for acoustic waves' propagation in heterogeneous elastic medium with multi-periodic hierarchical structure of heterogeneities. We assume the existence of two periodic cells with characteristic sizes l_2 and l_1 respectfully. The ratio ε=l_2/l_1 is considered to be small and of the same order of magnitude as the ratio l_1/L, where L is the macroscopic characteristic size of a system. The solution of the problem will be largely determined by the relation between the wavelength λ and the characteristic sizes of the system. For the case when λ/l_1 ~1 we derive homogenized macroscopic equation for the displacement and obtain approximations to the displacement and frequency. Several illustrative examples are considered to show the effect of peculiarities of the structure on two different spacial scales on energy distribution in propagating wave.

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

Computational models of acoustic wave propagation are frequently used in transcranial ultrasound therapy, for example, to calculate the intracranial pressure field or to calculate phase delays to correct for skull distortions. To allow intercomparison between the different modeling tools and techniques used by the community, an international working group was convened to formulate a set of numerical benchmarks. Here, these benchmarks are presented, along with intercomparison results. Nine different benchmarks of increasing geometric complexity are defined. These include a single-layer planar bone immersed in water, a multi-layer bone, and a whole skull. Two transducer configurations are considered (a focused bowl and a plane piston operating at 500 kHz), giving a total of 18 permutations of the benchmarks. Eleven different modeling tools are used to compute the benchmark results. The models span a wide range of numerical techniques, including the finite-difference time-domain method, angular spectrum method, pseudospectral method, boundary-element method, and spectral-element method. Good agreement is found between the models, particularly for the position, size, and magnitude of the acoustic focus within the skull. When comparing results for each model with every other model in a cross-comparison, the median values for each benchmark for the difference in focal pressure and position are less than 10% and 1 mm, respectively. The benchmark definitions, model results, and intercomparison codes are freely available to facilitate further comparisons.

Underwater acoustic localization using a modular differentiable model for acoustic wave propagation

Model-based algorithms for underwater acoustic localization are highly dependent upon environmental knowledge that is rarely available. Moreover, model-based localization usually involves optimization in high-dimensional spaces to find the best candidate for source localization. On the other hand, data-driven methods deliver poor generalization performance in data starved scenarios. Therefore, in order to improve generalization, we propose a modular, deep learning-based architecture that inherently learns the multipath structure, while learning the environmental properties from the training data. Furthermore, since ReLU-based fully connected networks cannot capture the high-frequency contents of the signals of interest properly, we use sinusoidal activations. Although the model needs an estimate of the carrier frequency as a hyper-parameter, it is observed that it can tolerate deviations about the true frequency. This model maps the source and receiver locations to received signals and is then used in a gradient descent manner exploiting the automatic differentiation toolbox in PyTorch, to find the source location. To evaluate the performance of the algorithm, we use Bellhop to generate data for a given set of environmental parameters. We show that our method outperforms matched-field processing and a deep fully connected network without a modular structure.

A Semianalytical Approach for the Solution of Nonlinear Modified Camassa–Holm Equation with Fractional Order

This paper presents the approximate solution of the nonlinear acoustic wave propagation model is known as the modified Camassa–Holm (mCH) equation with the Caputo fractional derivative. We examine this study utilizing the Laplace transform (ℒ T) coupled with the homotopy perturbation method (HPM) to construct the strategy of the Laplace transform homotopy perturbation method (ℒ T‐HPM). Since the Laplace transform is suitable only for a linear differential equation, therefore ℒ T‐HPM is the suitable approach to decompose the nonlinear problems. This scheme produces an iterative formula for finding the approximate solution of illustrated problems that leads to a convergent series without any small perturbation and restriction. Graphical results demonstrate that ℒ T‐HPM is simple, straightforward, and suitable for other nonlinear problems of fractional order in science and engineering.

Modelling of low-frequency acoustic wave propagation in dilute gas-bubbly liquids

A numerical modelling method for the low-frequency (∼102 Hz) acoustic wave propagation in a bubbly fluid with a low gas fraction is developed in this paper. Based on the digital image analysis of the bubbly fluid, the geometrical model of polydisperse bubble populations is created. The developed method is first verified by the Wood's (1955) equation and the Commander & Prosperetti (1989) model. Then the influence of gas fraction, excitation frequency and bubble radius on the acoustic properties of the bubbly fluid is systematically examined. The obtained results confirmed that the velocities and attenuations for different bubble radius distributions are close to those obtained for the monodisperse models. The gas fraction is the key controlling factor of the acoustic velocity, while the influence of the bubble size at low frequencies can be neglected. The velocity dispersion with frequency is about 5% even in Wood's regime and the attenuation increases with a higher gas fraction and excitation frequency, while it decreases with a smaller bubble radius. By estimation of bubble expansion during the migration of gas kick, variation trends of acoustic velocity and attenuation along the wellbore are discussed. This implies that variations of the velocity and attenuation of drilling fluid at low-frequencies during the gas migration can be used for an accurate and earlier gas kick detection than currently used methods.

Physically intuitive continuum mechanics model for quartz crystal microbalance: Viscoelasticity of rubbery polymers at MHz frequencies

AbstractEmploying a quartz crystal microbalance (QCM) as a MHz‐viscoelastic sensor requires extracting information from higher harmonics beyond the Sauerbrey limit, which can be problematic for rubbery polymer films that are highly dissipative because of the onset of anharmonic side bands and film resonance. Data analysis for QCM can frequently obscure the underlying physics or involve approximations that tend to break down at higher harmonics. In this study, modern computational tools are leveraged to solve a continuum physics model for the QCM's acoustic shear wave propagation through a polymer film with zero approximations, retaining the physical intuition of how the experimental signal connects to the shear modulus of the material. The resulting set of three coupled equations are solved numerically to fit experimental data for the resonance frequency Δfn and dissipation ΔΓn shifts as a function of harmonic number n, over an extended harmonic range approaching film resonance. This allows the frequency‐dependent modulus of polymer films at MHz frequencies, modeled as linear on a log–log scale, to be determined for rubbery polybutadiene (PB) and polydimethylsiloxane (PDMS) films, showing excellent agreement with time–temperature shifted rheometry data from the literature.

Quality inspection of micro solder joints in laser spot welding by laser ultrasonic method

The quality inspection of micro solder joints in laser spot welding (LSW) is a problem of great concern in industrial application. In this paper, a laser ultrasonic technology (LUT) was proposed to inspect the quality of micro solder joints in LSW. Firstly, based on the thermoelastic model of acoustic wave propagation in solid, a theoretical model was built and used to analyze the propagation properties of the Lamb wave in the whole field by finite element method (FEM), the transmitting properties of the excited Lamb wave via solder joint were affected by the effective contacted area of solder joint. Secondly, LUT was used to inspect the 1.2 mm/0.4 mm welding spot of standard/false 304 stainless steel welded components. By comparing the propagating properties of excited ultrasonic wave in different samples with different weld quality, the standard and false welding can be visually distinguished. Finally, a industrial CT was used to check the quality of the samples used in our experiment. Inclusions and pores have been found in the false solder joints, which will reduce the effective contacted area of solder joint, and then affected the propagation of ultrasonic wave. By combining the CT results and the experimental analysis, the experimental results detected by LUT are in good agreement with the simulation results. So, the LUT is a potential method in field of the quality inspection of micro solder joints in LSW.

Acoustic Wave Propagation Modeling using High-order Cell-based Finite-difference Methods

Acoustic Wave Propagation Modeling using High-order Cell-based Finite-difference Methods

Circuit model for thermoviscous propagation in annular waveguides.

This paper presents a circuit model of the thermoviscous acoustic wave propagation in waveguides with annular cross section. The model, validated against finite element method simulations of the input acoustic impedance, captures the annular waveguide behavior with good accuracy within a frequency bandwidth consistent with the lumped-element approximation. The cascading of multiple circuit models easily allows extending the bandwidth while preserving the same accuracy. The circuit model was derived from the low reduced frequency (LRF) wave propagation model in rectangular layers, representing a valid approximation of the complex LRF solution in annular waveguides. The simplified analytical description allows for the formulation of a compact T-network model comprised of standard circuit elements. This circuit model can be implemented in circuit simulators to accelerate both the analysis and engineering of devices having elements with annular cross section, such as micro-electro-mechanical systems devices or microphones.