Acoustic Boundary Element Method Research Articles

Design sensitivity analysis of modal frequencies of elastic structures submerged in an infinite fluid domain

SummaryThis paper presents a numerical approach for the design sensitivity analysis of modal frequencies of elastic structures submerged in an unbounded heavy fluid domain. Because the feedback of sound pressure onto the fluid‐loaded structures has to be taken into account in this case, a fully coupled scheme which combines the structural finite element method (FEM) and the acoustic boundary element method (BEM) is employed in the numerical simulation. The resulting nonlinear eigenvalue problem created by the coupled finite element and boundary element (FE‐BE) method is converted into a generalized eigenvalue problem (GEP) of reduced dimension by using a contour integral method. The design sensitivity formulation for non‐repeated eigenvalues is derived based on an adjoint method which uses both the left and right eigenvectors, and a small GEP is formed to calculate the gradients of repeated eigenvalues. The Burton‐Miller formulation is employed to shift the fictitious eigenfrequencies and their derivatives, and the parameter setting which is beneficial to the filtering of fictitious eigenfrequencies is investigated. Numerical examples are given to verify the accuracy and effectiveness of the developed method.

Sensitivity of compressor aerodynamic noise prediction to time setup of CFD simulations using hybrid CAA method

This paper numerically studies the aerodynamic noise of a centrifugal compressor in a vehicle engine turbocharger. The hybrid CAA approach based on computational fluid dynamics (CFD) and acoustic boundary element method (BEM) in the prediction of aerodynamic noise is validated. The impacts of the time setup of unsteady CFD simulations on the prediction of compressor flow and aerodynamic noise are discussed. The results show that a large time step would result in unreliable numerical results, in which severe reverse flow and flow separation can be observed. The middle time step 2 deg. can get accurately predicted results while reducing the computational efforts. It is also found that a large total simulation time with a reasonable time step is helpful to improve predicted noise spectra. Moreover, the overall sound pressure level discrepancy of aerodynamic noise between numerical prediction and experimental measurement is less than 0.5 dB.

Geometrical influence of structures in close proximity to a railway wheel on its sound radiation

The most important noise source from railways is rolling noise. It is produced by vibration of the track and wheel, which is induced by their combined surface roughness at the wheel/rail contact. The component of noise radiated by the wheel is generally often the greatest above 2 kHz. The current models used to predict the sound radiation from the wheel consider this to be in free space; in practice, however, the rail beneath the wheel, the ground in close proximity and the bogie frame around it have geometrical effects on the wheel radiation. This paper investigates their influence in terms of the sound power and the directivity at 7.5 m from the track center. The sound radiation of a single wheel in free space is analysed first by using the combination of vibration finite element method and acoustic boundary element method in 3D. The geometry of the rail and ground beneath the wheel are then introduced and their effects on the wheel radiation are predicted. The bogie frame is also introduced to find its influence on the sound radiation from the wheel.

A Fast Multi-Frequency Iterative Acoustic Boundary Element Method Solver Based on a Preconditioned Accelerated Recycling Strategy

Common multi-frequency solution strategies for acoustic systems are either associated with high computational costs or resort to model reduction strategies, which potentially induce considerable approximation errors. In that context, this work proposes a fast multi-frequency solver for acoustic Boundary Element Method (BEM) analyses that combines conventional preconditioners with an accelerated recycling strategy, achieving in that way a fast and accurate iterative solution. Specifically, by approximating both the system and the related preconditioner by individual affine expressions, an upfront Galerkin projection on a global deflation basis is facilitated, therefore enabling the deployment of the accelerated recycling scheme. The latter acts by accelerating the construction of the related deflation projectors, therefore leading to a significantly faster recycling procedure. Finally, the efficiency of the global deflation basis is guaranteed through an Automatic Krylov subspaces Recycling for Deflation (AKR-D) [D. Panagiotopoulos, W. Desmet and E. Deckers, An accelerated subspaces recycling strategy for the deflation of parametric linear systems based on model order reduction, Comput. Methods Appl. Mech. Eng. 403 (2023) 115765] algorithm and thus, the cumulative number of iterations required by an iterative solver within a frequency sweep is drastically decreased. The proposed multi-frequency solver is tested on two industrially relevant examples of an interior and an exterior scattering problem, benchmarked against the traditional solution strategies.

Effects of blade tip thicknesses on hydrodynamic and noise performance of ducted propellers

Propeller noise plays an important role in underwater radiated noise. The radiated noise of a ducted propeller is closely related to the vorticity intensity in the gap between the blade tip and the inner wall surface of the duct. To investigate the influence of blade tip thickening on the hydrodynamic and noise performance of ducted propellers, six different models of ducted propellers with varying blade tip thicknesses are presented. The Reynolds-averaged Navier–Stokes (RANS) method is used to simulate the flow around the ducted propellers, and a combination of Detached Eddy Simulation (DES) and acoustic boundary element method (BEM) is employed to predict the noise. The results show that thickening the blade tips leads to a 4.15% efficiency loss at J = 0.6, but improves efficiency by 17.61% at J = 0.8. As the blade tip thickness increases, the length of the blade tip vortex gradually decreases, and the turbulent kinetic energy (TKE) in the chordwise middle region of the blade tip decreases. Additionally, the peak values of thrust and torque fluctuations of the blades primarily occur at the blade passing frequency (BPF) and its harmonics, with the minimum amplitudes of the BPF at the maximum blade tip thickness. Thickening the blade tips results in a maximum overall sound pressure level reduction of 0.50 dB for the ducted propeller, with a maximum sound pressure level (SPL) reduction of 4.24 dB at certain dominant frequencies.

Vibro-acoustic characteristics of a rail transit viaduct paved with trapezoidal sleeper track

To investigate the effects of a trapezoidal sleeper track (TST) on the vibration and noise of rail transit viaducts, the wheel–rail interaction model was first built according to the vehicle–track coupling dynamics theory. Subsequently, the vibration responses of the viaduct were analyzed using the beam–slab finite element method, and its radiated noise was calculated using the acoustic boundary element method. The modeling method was verified based on the test data of a 3 × 40 m continuous rigid frame bridge. Taking the Jialing River Bridge of Chongqing Rail Transit Line 9 as the background, the control effects of the TST on the vibration and noise of the viaduct and the effective laws of different track parameters on the bridge noise were analyzed. Results show that the simulated and measured values are in good agreement; for example, the modeling methods are reliable; the radiated noise of the viaduct is influenced by the vibration responses under the action of train load, which are jointly determined by dynamic wheel–rail force (external excitation) and displacement admittance (self-vibration characteristics); compared with embedded sleeper track (EST), the TST can reduce the overall vibration acceleration level and sound pressure level of the box girder web plate by 13.9 dB and 7.8 dB, respectively; the stiffness of the damping path is the primary factor influencing the noise of the elevated box girder, followed by the sleeper thickness and the fastener stiffness; taking the bottom plate as an example, the stiffness of the damping pad is reduced by 1 and the overall sound pressure level can be reduced by approximately 3 dB; the sleeper thickness is increased by 1, and the overall sound pressure level can be reduced by 1–2 dB; and the fastener stiffness is reduced by 1, and the noise reduction is within 1 dB.

A fast multipole boundary element method for acoustics in viscothermal fluids

Standard numerical models in acoustics rely on the isentropic Helmholtz equation. Its derivation assumes adiabatic and reversible, i.e., dissipation-free, wave propagation. Sound waves in fluids are, however, subject to viscous and thermal losses. These losses originate from viscous friction and heat conduction, leading to the formation of acoustic boundary layers. Considering these effects becomes significant in setups with acoustic cavities of similar dimension as the boundary layers. Recently, boundary element methods (BEM) accounting for the viscothermal dissipation have been proposed. These methods limit the discretization to the surface of the fluid domain and require significantly fewer degrees of freedom than comparable finite element models. However, the BEM coefficient matrices are fully populated, resulting in high computational costs and storage requirements. This study develops a new BEM formulation for acoustics in viscothermal fluids that uses the fast multipole method - a low-rank approximation technique based on a hierarchical subdivision of the computational domain - to alleviate this shortcoming. It is shown that the fast viscothermal BEM improves the algorithmic complexity over the conventional formulation, reducing both the memory requirements and solution time. The results indicate good scalability of the method making it feasible for larger applications such as acoustic metamaterials.

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.

Adaptive time stepping for generalized convolution quadrature

AbstractThrough the current work, we aim to improve the boundary element method (BEM) in acoustics. The proposed adaptivity is based on a time‐domain boundary element formulation. In this setting, an elegant method for solving the acoustic problem is through the transformation of the underlying partial differential equation on to the boundary of the domain as a space–time boundary integral equation. However, accurate modeling of temporal behavior is crucial, requiring careful consideration of the time step size to ensure numerical stability and capture the dynamics of the system accurately. The boundary integral equation in the time domain has a convolution in time and the generalized convolution quadrature method (gCQ) is introduced, providing a framework for numerically evaluating the convolution integral within the boundary integral equation. The gCQ method under consideration uses a higher order time stepping method from the Runge–Kutta family. The gCQ method allows for adaptive time stepping, enabling the refinement of the time step size to focus computational resources where they are most needed. The current work shows that an approach similar to that of the ordinary differential equations can be included in the gCQ to introduce an adaptive control of the time step size in the 3D boundary element formulation. Numerical experiments are conducted to validate the effectiveness of the proposed approach. The results demonstrate improved solution resolution, particularly in capturing steep changes and localized variations through the adaptive time stepping scheme. The proposed method shows promising performance, dynamically adjusting the time step size based on the evolving solution, thereby enabling efficient and accurate computations in BEM simulations of radiation phenomena.

Realizations of the generalized adaptive cross approximation in an acoustic time domain boundary element method

AbstractIn acoustics, the boundary element method (BEM) is much more common compared to elasticity. This is driven by the applications, which are in acoustics very often radiation problems causing trouble in finite element or finite volume methods. Nevertheless, for a time domain calculation, still an efficient BE formulations is lacking. We consider the time domain BEM for the homogeneous wave equation with vanishing initial conditions and given Dirichlet boundary conditions. The generalized convolution quadrature method (gCQ) developed by Lopez‐Fernandez and Sauter is used for the temporal discretisation. The spatial discretisation is done classically. Essentially, the gCQ requires to establish boundary element matrices of the corresponding elliptic problem in Laplace domain at several complex frequencies. Consequently, an array of system matrices is obtained. This array of system matrices can be interpreted as a three‐dimensional array of data, which should be approximated by a data‐sparse representation. The adaptive cross approximation (ACA) can be generalized to handle these three‐dimensional data arrays. Adaptively, the rank of the three‐dimensional data array is increased until a prescribed accuracy is obtained. On a pure algebraic level, it is decided whether a low‐rank approximation of the three‐dimensional data array is close enough to the original matrix. Hierarchical matrices are used in the two spatial dimensions and the third dimension are the complex frequencies. Hence, the algorithm makes not only a data sparse approximation in the two spatial dimensions but detects adaptively how much frequencies are necessary for which matrix block.

Numerical analysis and experimental measurement on segmented ring transducer acoustic fields

In order to overcome the shortcomings of the two traditional methods of finite element method (FEM) and direct coupling of mechanical FEM and acoustic boundary element method (BEM) in the comprehensive simulation of acoustic characteristics of non-two-dimensional axisymmetrical transducers, the acoustic FEM and acoustic BEM coupling method is adopted in this study to model, calculate and analyze the three-dimensional (3D) model of the segmented ring transducer. Firstly, the basic theory of FEM, BEM and FEM-BEM coupling calculation of the transducer is introduced. Secondly, a 1/8 3D model of the segmented ring transducer is built to simulate the underwater electro-acoustic characteristics of the transducer. Finally, a transducer prototype is manufactured according to the numerical model, and the electro-acoustic performance of the transducer is measured in the anechoic tank. The numerical results of transmission voltage response (TVR), admittance and radiation directivity curves are in good agreement with the experimentally measured results, which indicate that the proposed method is correct and effective. Therefore, the method could be used to comprehensively calculate the acoustic characteristics of the segmented ring transducer. In addition, the method could be used not only to study the acoustic problems of other transducers or transducers arrays with complex structures that are non-two-dimensional axisymmetrical, but also to comprehensively analyze and predict the near-field and far-field acoustic characteristics of any transducers including two-dimensional (2D) axisymmetrical transducers.

Non-Singular Burton–Miller Boundary Element Method for Acoustics

The problem of non-unique solutions at fictitious frequencies that can appear in the boundary element method for external acoustic phenomena described by the Helmholtz equation is studied. We propose a method to fully desingularise in an analytical way the otherwise hyper-singular Burton–Miller framework, where the original boundary element method and its normal derivative are combined. The method considerably simplifies the use of higher-order elements, for example, quadratic curved surface elements. The concept is validated using the example of scattering on a rigid sphere and a rigid cube, and its robustness and effectiveness for external sound-wave problems are confirmed.

A parametric study on the structural noise radiation characteristics of a steel spring floating slab track

It is a common experience that the interior noise of an underground train vehicle increases suddenly when it just runs into a track section with steel spring floating slabs, significantly reducing passengers’ comfort. This paper investigates the reasons, and control, of such noise through field tests and model simulations. The effect of rail surface irregularity on interior noise was investigated first by analysing data collected from interior noise tests, rail surface irregularity measurement and by analysing the modal behaviour of the slab. Noise radiation of the track slab was then analysed using the acoustic boundary element method while the vibration of the steel spring floating slab track is predicted based on an infinitely long periodic structure model; And finally with the prediction models, a parameter study was performed for the steel spring floating slab, on the purpose of improving the parameters to make the track less noisy. The research presented in this paper may provide a reference for the design of steel spring floating slabs in terms of noise control.

Parametric model order reduction for acoustic boundary element method systems through a multiparameter Krylov subspaces recycling strategy

AbstractThe recently introduced framework enabling model order reduction (MOR) for systems arising within the acoustic boundary element method (BEM), allows for fast frequency sweeps to obtain the detailed response of an acoustic system. Nevertheless, in many cases it is desirable to include additional parameters in the MOR scheme to facilitate iterations among different configurations of a specific design. In that context, this work proposes a multiparameter Krylov subspaces recycling scheme, based on the algorithms proposed in Reference 23 for a single parameter, aiming at the parametric MOR of acoustic BEM systems. The proposed scheme allows to include multiple parameters along with the non‐affine wavenumber kernel dependency and thus facilitates the fast solution of parametric acoustic systems. The article distinguishes among three different parametrizations of BEM systems: (i) a right‐hand side parametrization, (ii) an affine, and (iii) a non‐affine parametrization of the system matrix. The two former cases allow for the construction of a cheap residual error estimator and thus facilitate the deployment of a greedy sampling strategy. This work proposes the employment of such a greedy strategy in the context of Krylov subspaces recycling, which combined with the automatic Krylov subspaces recycling (AKR) algorithm, enables the construction of a global reduction basis incorporating such parametric variations. On the contrary, since in case of non‐affine parametrizations a cheap residual error estimator is not directly available, a multiparameter AKR algorithm is deployed to ensure the predefined residual level. The performance of the proposed methods is benchmarked against a reduced basis method‐type approach, which follows the same assumptions as the AKR for the case of non‐affine systems. The potential of the algorithms is demonstrated on academic BEM examples including source position, material, and shape parametrizations and significant reductions in the sampling required for the construction of the respective reduction bases are reported.

Modification and Noise Reduction Design of Gear Transmission System of EMU Based on Generalized Regression Neural Network

In view of traction gear vibration and noise affecting the performance of the transmission system and the comfort of passengers when the electric multiple units (EMU) is running at high speed, taking the traction gear transmission system of an EMU as the research object by using Romax software to construct the parametric modification model of the gear transmission system based on gear modification theory. Combined with multibody dynamics, the vibration response characteristics of the transmission system are simulated and analyzed. A radiated noise prediction model is established using the acoustic boundary element method, based on the generalized regression neural network (GRNN). To further explore the influence of gear modification methods and parameters on vibration and noise characteristics and minimize gear transmission’s radiation noise. A particle swarm optimization (PSO) algorithm is designed to solve the optimal modification parameters. The simulation results reveal that after the optimization and modification, the gear transmission error is significantly reduced, the contact status is considerably improved, and the root mean square value of the acoustic power level is reduced by 13.10 dB, which is a reduction of 14%. It shows that the design can effectively reduce the radiation noise of EMU gear trans-mission system.

Benchmarking of finite-difference time-domain method and fast multipole boundary element method for room acoustics

Compared to geometrical acoustics, wave-based methods which solve the wave equation either in the time domain or in the frequency domain are known for their high accuracy. However, their systematic use as professional room acoustic simulation tools is less popular due to the modelling effort and computational time requirements, especially in the case of complex scenarios. This paper aims at providing guidelines for the use of two wave-based methods in complex room acoustics simulations, namely the finite-difference time-domain (FDTD) method and the fast multipole boundary element method (FMBEM). Numerical experiments are conducted to address the convergence issues of the two solvers, more specifically, the selection of the convergence tolerance of the iterative solver in FMBEM and the temporal sampling frequency in FDTD. To evaluate the capability of the solvers in simulating complex scenarios, five cases with increasing complexity of material input data are presented. The results show that both solvers give close predictions for various room acoustics parameters. In addition, an uncertainty sensitivity study is performed in a case where experimental data is available. Large deviations between measured and simulated reverberation time reveal that typical material data-sets poorly represent the behaviour of real materials in a room acoustics context. Lastly, the efficiency of the two solvers is discussed. With parallelization implemented, both solvers can simulate sizeable room acoustic problems with good accuracy within a reasonable time.

Bi-material topology optimization for fully coupled structural-acoustic systems with isogeometric FEM–BEM

This paper presents a novel method for topology optimization of vibrating structures interacted with acoustic wave for the purpose of minimizing radiated sound power level. We consider exterior acoustic fields and bi-material shell models without damping in this work. Within the isogeometric analysis framework, we employ Catmull–Clark subdivision surfaces to construct geometries and discretize physical fields. The isogeometric finite element method with Kirchhoff–Love shell elements is coupled with the isogeometric boundary element method in acoustics. The topology optimization is performed through density-based approaches, in which the sensitivities are evaluated with adjoint variable methods. Numerical experiments demonstrate the validity and effectiveness of the algorithm for topology optimization of structural-acoustic interaction systems.

Validation of the Time-Domain Boundary Element Method in Acoustics regarding Flexible Multibody Simulations and Acoustic Measurements

With flexible multibody simulation, the dynamical behaviour of vehicle components as well as entire systems can be simulated in an efficient way. In addition to structural vibrations, noise emissions play an important role in terms of comfort in the vehicle industry. While the dynamics of the structures can be simulated directly in the time-domain, the sound radiation is usually calculated in the frequency-domain. This process enables an efficient investigation of steady-state operating conditions but not of transient operating conditions. The time-domain Boundary Element Method (TD-BEM) in acoustics allows to determine the sound pressure directly in the time-domain, without complicated transformation from the frequency-domain. Existing work concentrates on stability criteria and general theoretical applicability. The validation on real test cases with measurement results, however, has rarely been focused. On this work, we aim to close this gap between theory and practical applications with the help of real housing structures and test cases. In order to set up an acoustic validation, meaningful measurements need to be combined with validated structural simulations that match the physical world with regard to the sound radiation as closely as possible. Therefore, several test set-ups are used to measure the real dynamic and acoustic behaviour in an anechoic chamber with multiple accelerometers, a laser vibrometer, various microphones and a sound intensity PU probe. Based on these measurements, multibody and BE-models are created, representing the same scenarios with numerical methods. Derived from the simulated surface accelerations, the acoustic radiation is calculated in the time-domain. Comparisons at a simple oval-shaped housing show that the method generates very promising results. The mean deviation between the measured and simulated sound pressure levels (time-domain) is less than 1 dB and the frequency spectra show a high quantitative correlation as well.

Numerical simulation of radiated noise during combustion of energetic materials in a closed bomb

In this study, based on a closed bomb test combined with computational fluid dynamics, a structural finite element method, and an acoustic boundary element method, a fluid-solid acoustic one-way coupling calculation model is established for the combustion process of energetic materials in a closed bomb, and the effectiveness of the model is verified by experiments. It is found that the maximum peak sound pressure increases exponentially with an increase in loading doses or gas pressure. However, a change in the combustion coefficient of the energetic materials has little effect on the noise generated during the combustion process in the closed bomb. When the combustion coefficient is reduced by a multiple of 16, the maximum transient sound pressure is reduced by 1.79 dB, and the sound pressure level in the frequency band is reduced by 1.75 dB. With an increase in shell thickness, the combustion noise of the energetic materials in the closed bomb decreases, and the reduction range of the combustion noise increases with the increase in shell thickness.

Low-Rank Iteration Schemes for the Multi-Frequency Solution of Acoustic Boundary Element Equations

The implicit frequency dependence of linear systems arising from the acoustic boundary element method necessitates an efficient treatment for problems in a frequency range. Instead of solving the linear systems independently at each frequency point, this paper is concerned with solving them simultaneously at multiple frequency points within a single iteration scheme. The proposed concept is based on truncation of the frequency range solution and is incorporated into two well-known iterative solvers - BiCGstab and GMRes. The proposed method is applied to two acoustic interior problems as well as to an exterior problem in order to assess the underlying approximations and to study the convergence behavior. While this paper provides the proof of concept, its application to large-scale acoustic problems necessitates efficient preconditioning for multi-frequency systems, which are yet to be developed.