Acoustic Problems Research Articles

A generalized isogeometric boundary element method for the uncertain analysis of infinite domain two-dimensional acoustic problems

The key aim of this paper is to provide a new nth generalized order perturbed isogeometric fast multistage technique of boundary elements to compute the propagation of time harmonics in an infinite region. Structural geometry and boundary integral equations are constructed by using non-uniform rational B-splines. The source of system uncertainty is believed to be the incident plane wave number’s unpredictability. The actual field, depending on the input random variables, is simulated using the extended nth-order perturbation method. The field and kernel values for boundary integral formulas are generated via the nth-order generalized series of Taylor expansions using perturbation parameters. The fast multipole method (FMM) is utilized to speed up the process. The effectiveness and correctness of the proposed algorithm are verified by Monte Carlo simulations (MCs) with numerical examples.

Discontinuous Galerkin methods for the acoustic vibration problem

In two and three dimension we analyze discontinuous Galerkin methods (DG) for the acoustic vibration problem. Through all our study we consider an inviscid fluid, leading to a linear eigenvalue problem. The acoustic problem is written, in first place, in terms of the displacement. Under the approach of the non-compact operators theory, we prove convergence and error estimates for the method when the displacement formulation is considered. We analyze the influence of the stabilization parameter on the computation of the spectrum, where spurious eigenmodes arise when this parameter is not correctly chosen. Alternatively we present the formulation depending only on the pressure, comparing the performance of the DG methods with the pure displacement formulation. Computationally, we study the influence of the stabilization parameter on the arising of spurious eigenvalues when the spectrum is computed. Also, we report tests in two and three dimensions where convergence rates are reported, together with a comparison between the displacement and pressure formulations for the proposed DG methods.

Novel and efficient implementation of multi-level fast multipole indirect BEM for industrial Helmholtz problems

Fast multipole boundary element methods (FMBEM) have been successfully applied to solve ultra-large acoustic problems. In practice, there are still a large number of industrial applications where model sizes are well below a million Degrees of freedom. Thus, it is of practical importance to further improve the solver’s efficiency for such applications. This paper presents a novel formulation of the multi-level fast multipole indirect BEM, which relies on redesigning a conventional FMBEM with considerations from several aspects. A new flexible partition algorithm is proposed to generate a flexible and efficient multi-level structure for fast multipole calculations, which also allows the explicit calculation of the far field contributions. A hybrid and efficient regularization approach for hypersingular integral is investigated and implemented, which significantly reduces the iterative solving time. The use of efficient sparse approximate inverse preconditioners is key for fast convergence. Two strategies for constructing the sparsity pattern are implemented and evaluated. Numerical results show that by bringing the aforementioned techniques all together in one package, the new flexible multi-level fast multipole indirect BEM (f-FMBEM) provides significant improvements on actual simulation time over the conventional BEM and FMBEM solvers for industrial size problems (with a non-dimensional Helmholtz number up to kA∼323) on a modern workstation. To efficiently address larger problems, a more efficient multipole translation should be considered.

Multiphysical numerical analysis for acoustic metamaterials in ventilated ducts

In recent decades, metamaterials have shown interesting properties in the acoustic, mechanical, and aerospace engineering fields. The characteristic tunability on targeted bandwidth and the freedom of design have lately extended the metamaterial application in the multiphysical domain, for example, achieving systems that simultaneously allow noise insulation and fluid passage. Numerical methods such as FEM has been validated to test single metamaterial physics issue, and lately, mixed physics have been exploited for research and industrial purposes. However, there is still no precise method to follow when tuning acoustic metamaterials (AMMs) with different flow conditions in a multiphysical domain. For this reason, in this study, a Multiphysical FEM is evaluated to assess the implications of different flow characteristics on acoustic performance. First, two mono-physical models separately evaluate the fluid dynamic and acoustic problem. The two physical numerical models are then combined in the second stage, and a correlation between the two approaches (mono and multi-physical) is drawn. These preliminary results could be applied to many flow and frequency range case studies and implemented for Mechanical and Civil Engineering applications.

A high-order explicit time-domain FEM using 15-node tetrahedral elements for room acoustics modeling: Basic performance

Time-domain room acoustic modeling using mass-lumped higher-order tetrahedral finite elements with an explicit time-marching scheme is highly attractive because of its excellent geometrical flexibility with unstructured meshing and applicability into massively parallel computing. However, the standard mass-lumped tetrahedral elements yield an unstable scheme, and only implicit time-marching schemes are available. This study proposes a novel wave-based room acoustics solver based on a high-order explicit time-domain FEM. The present solver uses mass-lumped 15-node tetrahedral elements for spatial discretization and a dissipation-free two-stage partitioned Runge-Kutta time integration for time discretization. The 15-node tetrahedral elements had been developed to apply mass-lumping methods to 10-node tetrahedral elements, which are the most common finite element in engineering applications, but its applicability in room acoustics problems is unknown. Higher accuracy and efficiency of the proposed method over the standard method using 10-node tetrahedral elements is presented through an eigenvalue analysis of a long duct model and acoustic simulations in a small room. Additionally, frequency-dependent sound absorbing boundary is implemented by revising an auxiliary differential equation method.

Improved SPH method based on moving least square method for acoustic problems

Smoothed particle hydrodynamics is a widely used meshfree method. However, the order of the reproducing differential function is only the first order. To improve that, a corrective process termed as moving-least-square smoothed particle hydrodynamics, MLS-SPH, is introduced. Taylor expansion is used to modify the relation between arbitrarily distributed particles, and the concept of moving least square is used to approximate the value of the function and partial differential functions. This modified method can improve approximate accuracy effectively. Moreover, the order of approximate partial differential function becomes changeable, which expands the scope of its application. To investigate the advantages, a 2D complex surface approximation, a 2D model of Poisson problem with differential boundaries, and the acoustical modal of a rigid wall-bounded cavity are simulated.

A Boundary Element Method for Acoustic Problems in Relative Motion Between Source and Fluid

To calculate the acoustic problems of relative uniform motion between the acoustic source and the fluid, we propose a boundary element method (BEM) strategy that can calculate various forms of relative uniform motion in subsonic conditions in a unified framework and is simple to implement. The acceleration algorithm for the BEM, like the fast multipole method (FMM), in the relative motionless state between the source and the fluid can be directly used without major modifications to the program. We propose a two-step transformation method to unify the wave equations of different relative motion forms into the classical form. In the first step, we transform the wave equations for various forms of relative motion into the equation where the convective terms are present only in the source part. Then, in the second step, we propose an acoustic-analogy Lorentz (a-a Lorentz) transformation to apply Lorentz covariance further to eliminate the convection term and establish the wave equation with classical form in a-a Lorentz space. We implement the boundary integration in the transformed a-a Lorentz space and derive a transformation method to transform discretized geometry and boundary conditions in the original space to the a-a Lorentz space. The problem that the boundary conditions are difficult to apply when solving the boundary integral equation (BIE) after the time-space coordinate transformation is solved. Numerical validations for the proposed method are performed by comparing with analytical results over a wide range of relative velocities. The results show that the proposed method can efficiently compute such problems with high accuracy and concise formulation.

Bayesian Approach for the In Situ Estimation of the Acoustic Boundary Admittance

Interior acoustic problems require accurately representing the boundary conditions of all acoustically interacting surfaces to achieve precise acoustic predictions. The complex-valued boundary admittance fully characterizes these properties. Yet, conventional approaches to determine boundary admittances, such as the impedance tube, have limitations which do not accurately represent real-world conditions. This motivates in situ methods, where the acoustic boundary admittance is estimated in the actual mounting condition based on sound pressure measurements at certain observation points within the domain. In contrast to existing deterministic methods, a Bayesian approach is employed in this work, which provides probability distributions for the boundary admittances rather than point estimates. This offers valuable insights into the uncertainty associated with the estimation, proving beneficial for applications where a comprehensive understanding of uncertainty is desired. A finite element model is utilized to generate sound pressure data and serves as the forward model during the inference process. This makes it particularly suited for applications that involve pre-existing geometrical models, such as digital twin applications and model updating. The proposed method is applied to a two-dimensional car cabin model, demonstrating the framework’s efficacy in accurately inferring the acoustic boundary admittance using just ten observation points.

Discrete Acoustics: ARMA-modeling of Time Processes, Theory

In physics, in particular, acoustics, time is traditionally considered as a continuous coordinate. Some exception is signal processing, where sampling is necessary for calculations on computers. But all acoustic problems are formulated and solved using time-continuous models described by differential equations and their solutions in the form of continuous time functions. Meanwhile, these problems can be formulated and solved in an equivalent way using discrete-time models described by finite-difference equations and their solutions in the form of time series. As the experience of some other fields of science, for example, control theory, shows, the discrete approach has a number of advantages over the continuous approach, the useof which greatly facilitates the solution of many problems. This paper aims to partially fill the gap in acoustics that exists here and is aimed at creating the theoretical foundations of a discrete-time approach to solving acoustic problems. The paper is limited to the consideration of one oscillatory system widely used in acoustics— a linear structure with N degrees of freedom consisting of lumped inertial, elastic and dissipative elements, to which, in particular, the finite element method leads. For several continuous models of this system, equivalentdiscrete-time models are constructed in the paper, finite-difference equations are derived and their solutions are obtained. The criterion of equivalence of continuous and discrete models in the paper is the mathematically exact equality of the corresponding solutions at all discrete points in time. Based on this criterion, analytical relations have been established between the parameters of continuous and discrete models and their equations, which make it possible to build its discrete-time model based on a continuous model of the systemand, conversely, to build its continuous model based on a known discrete model. Special attention is paid in the paper to the forced vibrations of the system under the action of kinematic excitation, which is important in many acoustic problems, whereas in the literature only force excitation is considered. The paper also discussesone of the most useful properties of discrete modeling—the simplicity of constructing discrete models based on experimentally measured signals. A corresponding example is given. Note that the term “ARMAmodel” is an abbreviation for “autoregressive and moving average model”, generally accepted in control theory, systems theory and other fields of science.

An improved localized boundary knot method for 3D acoustic problems

In this paper, an improved localized boundary knot method (LBKM) is proposed for 3D acoustic problems. The domain is divided into many small subdomains, and the solutions at the nodes of each subdomain are approximated by using the linear combination of the non-singular general solutions in the LBKM. However, the interpolant matrix generation for each subdomain in the original LBKM is associated with the variables at both domain and boundary nodes. In the present method, only the variables at domain nodes are considered for the matrix generation, and the boundary conditions are directly imposed during the matrix generation. As a consequence, the computational efficiency of the LBKM should be raised. Two examples are provided to illustrate the performance of the present method.

Acoustic Radiation Prediction Model Rationality and Mechanism of Steel-Spring Floating-Slab Tracks on Bridges

In the actual operation of urban rail transit (URT), the vibrations of steel-spring floating-slab tracks (SSFSTs) are amplified, and the track structure has strong low-frequency acoustic radiation; therefore, it is necessary to study the acoustic radiation of SSFSTs. In addition, multi-block short track structures are often laid within the URT lines; however, many researchers studying the reduction of vibration track service performance problems only select one or several block tracks to study. In reality, many short track structures will become sound sources when a train passes, and different sound sources will have various acoustic effects during the propagation process; therefore, it is necessary to study the rationality of any track acoustic model that analyzes the acoustic radiation problem. In order to more accurately predict the acoustic characteristics of steel-spring short floating-slab tracks (SSSFSTs) on a one-span bridge, train-track-bridge interaction theory and the acoustic boundary element method (BEM) were adopted to study the acoustical differences and mechanism of the float-slab number in the acoustic model. The results showed that with the increase in the floating-slab number in the acoustic model, the acoustic radiation ability of SSSFSTs and the sound pressure in the sound field increased; however, it was not a simple linear increase. Thus, the floating-slab number in the acoustic model not only affected the acoustic radiation ability but also caused acoustic effects during the propagation process, which affected the predicted results. The vibration characteristics of each floating-slab were different, and the acoustic input conditions of different numbers of floating-slabs in the acoustic model led to significant differences in the acoustic analysis. There was also obviously a different acoustic contribution of each floating-slab to the same sound field point, which led to the significant influence of the sound pressure at the sound field points when using different acoustic models. Therefore, using acoustic models with different floating-slab numbers had a significant effect on the acoustic analysis of SSSFSTs. In order to study the acoustic characteristics of SSSFSTs on a one-span bridge, it was necessary to establish a complete acoustic model.

Ventilation Performance of Air Duct in Double Loaded Corridor Building: A Case Study

Buildings with double-loaded corridor types are often found in Indonesia and generally function as offices or lecture rooms. This type of building is popular because of its efficient circulation path to accommodate the movement of occupants. However, a wall separating the room from the corridor makes it impossible to put windows to implement a cross-ventilation system due to acoustic problems. Hence, to achieve indoor thermal comfort, this type of building relies on using an air conditioning (AC) system. However, with the WHO's call to reduce the use of AC during the COVID-19 pandemic, it is necessary to evaluate cross-ventilation in double-loaded corridor buildings to meet comfort standards while still preventing acoustic problems due to noise from corridors and other spaces. The study proposes a new natural ventilation system using air ducts placed above the corridor ceiling to create cross-ventilation in lecture buildings. The E-ITERA building was chosen as a case study in this research. The building has a glass facade with several small windows that can be opened outside. The corridor of this building is designed with openings at both ends, allowing for direct connection to the outside air. The walls facing the passage have a single door and four small ventilations on the aisle's upper side. Simulations were carried out in two classrooms on the 3rd floor using CFD (Computational Fluid Dynamics) software. Experiments were carried out to change the size of the air duct and the size of the ventilation on the wall that leads to the corridor. The results showed that the air duct was able to create cross-ventilation. Ventilation performance is improved when the WWR air duct is the same as the WWR window. The highest air velocity in the centre of the room is 0.6 m/s. Doi: 10.28991/CEJ-2023-09-10-06 Full Text: PDF

Analysis of the sound field in circular spaces using small scale models and parallel phase-shift interferometry

In acoustic design, the use of circular spaces is generally avoided. This is because these spaces present several acoustic problems, for example, “whispering gallery,” and low diffusivity of sound. These room acoustic problems have generally been dealt with by installing diffusers on walls. In this study, we designed the acoustics of the circular space by applying diffusers based on primitive roots and analyze the sound field. These diffusers were proposed by Schroeder and take advantage of the randomness of the numerical sequence generated from primitive roots. We designed several small circular models attached the diffusers and printed them with a 3D printer. The sound field in the models were measured and visualized using parallel phase-shifting interferometry, one of the optical sound measurement methods. As a result, “whispering gallery” phenomenon was improved, and focal points were less likely to occur by the application of diffusers based on primitive roots.

Boundary and Contact Conditions of Higher Order of Accuracy for Grid-Characteristic Schemes in Acoustic Problems

Boundary and Contact Conditions of Higher Order of Accuracy for Grid-Characteristic Schemes in Acoustic Problems

Boundary and Contact Conditions of Higher Order of Accuracy for Grid-Characteristic Schemes in Acoustic Problems

Seismic wave propagation through geological media is described by linear hyperbolic systems of equations. They correspond to acoustic, isotropic, and anisotropic linear elastic porous fluid-saturated models. They can be solved numerically by applying grid-characteristic schemes, which take into account propagation of solution discontinuities along characteristics. An important property of schemes used in practice is their high order of accuracy, due to which signal wavefronts can be clearly resolved. Previously, much attention was given to this property at interior points of the computational domain. In this paper, we study the order of a scheme up to the boundary of the domain inclusive. An approach is proposed whereby arbitrary linear boundary and contact conditions can be set up to high accuracy. The presentation is given for the system of one-dimensional acoustic equations with constant coefficients.

Sound pressure and particle motion calculations considering pile skin friction

Modelling sound propagation over seabeds where the seabed cannot be approximated as an equivalent fluid due to limestone layers with high shear wave speeds is a common underwater acoustic propagation modelling problem for Australian shallow marine environments. With the increase in prospective areas for offshore windfarm development across Australia, construction operations across large regions of the continental shelf area are set to increase. Windfarm construction will require the installation of a large number of foundation piles near potentially sensitive marine habitat areas. Predicting the underwater noise from these activities requires suitable models. This paper investigates the modelling approaches for including a full elastic parameterisation of the seabed when conducting numerical predictions of pile driving sound emissions. The approach considers buried sources and the excitation of shear waves via a skin friction model for the stress–strain relation at the pile-seabed boundary. Shear waves are considered in the source model and in the propagation model. Sound pressure level metrics and particle motion metrics are considered as part of the numerical predictions.

Modeling Epidemics: Neural Network Based on Data and SIR-Model

Earlier, a method for constructing an initial approximation for solving the inverse problem of acoustics by a gradient method based on a convolutional neural network trained to predict the distribution of velocities in a medium from wave response was proposed [9]. It was shown that the neural network trained on responses from simple layered media can be successfully used for solving the inverse problem for a significantly more complex model. In this paper, we present algorithms for processing data about epidemics and an example of applying a neural network for modeling the propagation of COVID-19 in Novosibirsk region (Russia) based only on data. A neural network NN-COVID-19 that uses data about the epidemics is constructed. It is shown that this neural network predicts the propagation of COVID-19 for five days by an order of magnitude better than SEIR-HCD. When a new variant (Omicron) appeared, this neural network was able to predict (after retraining) the propagation of the epidemics more accurately. Note that the proposed neural network uses not only epidemiological data but also social ones (such as holidays, restrictive measures, etc.). The proposed approach makes it possible to refine mathematical models. A comparison of the curves constructed by SEIR-HCD model and by the neural network shows that the plots of solutions of the direct problem almost coincide with the plots constructed by the neural network. This helps refine coefficients of the differential model.

Multi-fidelity models based on Gaussian processes in acoustic applications

Accurate predictions are generally accompanied with high costs and expenses. As a conesquence, system observations can only be generated for a few samples. The idea of multi-fidelity modeling aims to merge observations from different models of varying complexities and costs. This contribution introduces multi-fidelity models applied to acoustic problems. Therefore, we deploy models with different fidelity levels to treat the frequency-dependent Helmholtz equation. While the spatial solution is acquired with the boundary element method, Gaussian processes are used as surrogates to approximate the system’s response in the frequency dimension. This way, multi-fidelity models are adopted to efficiently approximate the solution of the Helmholtz equation for a certain frequency range. For validation purposes, the low frequency booming noise problem occurring in vehicle cabins is treated. Our findings demonstrate that multi-fidelity models yield an accurate approximation. In addition, the computational costs are reduced when compared with the high-fidelity solution at each frequency. In the sense of a Bayesian technique, multi-fidelity models based on Gaussian processes allow to consider uncertainties. Beyond fast and accurate predictions, the proposed method paves the way for accelerated decision-making processes in early design stages, where uncertainties due to limited information on the model or simplifying assumptions are omnipresent.

Understanding and applications of striation-based beamforming in underwater acoustics

Utilizing the shallow water acoustic interference phenomenon in the range-frequency domain, striation-based beamforming (SBF) was proposed to estimate waveguide invariant and enhance active sonar output. In the past decade, SBF has also been applied to enhance LOFARgrams to improve tracking performance. In this paper, the correlation theory is used to understand SBF, and some further applications of SBF in underwater acoustic problems are also discussed. It shows that SBF essentially selects the optimal signal components with the best correlation. During the process, the correlation of array signals is improved and the ability to converge signals arriving via different paths is achieved to ensure array gain. The level of gain improvement is related to the direction of striation-based processing. Hence, a cost function can be constructed to facilitate the implementations of SBF in tasks such as striation slope estimation and source range estimation. Additionally, the SBF technique can be further applied to estimate the Green's function by introducing the cross-correlation preprocessing. Utilizing the mathematical connection between SBF and CBF, SBF can also be naturally extended to other beamforming algorithms and improve their performance, such as the subspace algorithms. The above is explained using simulation and experimental results.

Predicting the acoustic response of a cylindrical shell immersed in an underwater waveguide using a substructuring technique

Sound radiation from structures in an underwater waveguide presents a challenging underwater acoustics problem typically resolved with numerical methods. This can be computationally inefficient and limited to low-frequency analysis. Hybrid approaches improve on these limitations by combining numerical methods with analytical solutions. This study utilises a substructuring technique called the condensed transfer function approach (CTF) and a decoupling technique called the reverse condensed transfer function approach (rCTF). The hybrid CTF-rCTF approach builds systems by coupling and decoupling simpler subsystems. Each subsystem is represented at the junction interfaces, described by condensed transfer functions (CTFs) that can be analytically or numerically determined. These CTFs are decomposed into orthonormal condensation functions (CFs), for example, gate or exponential functions. To demonstrate the potential of CTF-rCTF, the acoustic response of an infinitely long cylindrical shell under line-distributed load and immersed in an underwater waveguide composed of an upper free surface and lower rigid floor is predicted. This system is built from an underwater waveguide decoupled with a fluid volume and coupled with an excited shell that takes place of the decoupled fluid. Acoustic pressures received in the fluid domain are predicted and verified against an analytical solution. It is particularly shown that using exponential functions as the CFs improves the prediction quality compared to gate functions.