Acoustic Design Sensitivity Analysis Research Articles

Design sensitivity analysis of three-dimensional acoustic problems using a fast multipole accelerated indirect BEM

In this paper, the design sensitivity formulations for three-dimensional acoustic problems are presented based on the indirect boundary element method (IBEM). The non-unique solution difficulty of the IBEM in solving exterior acoustic problems is avoided by applying a hybrid combination of single and double layer potentials. In order to accelerate the computational procedure easily, a set of non-singular indirect boundary integral equations (IBIEs) for the acoustic design sensitivity analysis are derived and then the fast multipole method (FMM) is employed to accelerate the matrix–vector products in the IBEM. The method is further extended to the design sensitivity analysis of thin-body acoustic problems above an infinite plane. Numerical examples are given to verify the effectiveness and accuracy of the method, and the simulations of thin-body acoustic problems show its potential in engineering applications.

A Fast Singular Boundary Method for the Acoustic Design Sensitivity Analysis of Arbitrary Two- and Three-Dimensional Structures

This paper proposes a fast meshless scheme for acoustic sensitivity analysis by using the Burton–Miller-type singular boundary method (BM-SBM) and recursive skeletonization factorization (RSF). The Burton–Miller formulation was adopted to circumvent the fictitious frequency that occurs in external acoustic analysis, and then the direct differentiation method was used to obtain the sensitivity of sound pressure to design variables. More importantly, RSF was employed to solve the resultant linear system obtained by the BM-SBM. RSF is a fast direct factorization technique based on multilevel matrix compression, which allows fast factorization and application of the inverse in solving dense matrices. Firstly, the BM-SBM is a boundary-type collocation method that is a straightforward and accurate scheme owing to the use of the fundamental solution. Secondly, the introduction of the fast solver can effectively reduce the requirement of computer memory and increase the calculation scale compared to the conventional BM-SBM. Three numerical examples including two- and three-dimensional geometries indicate the precision and efficiency of the proposed fast numerical technique for acoustic design sensitivity analysis associated with large-scale and complicated structures.

Singular boundary method for 2D and 3D acoustic design sensitivity analysis

In this paper, a novel Burton-Miller-type singular boundary method (BM-SBM) formulation is proposed for the acoustic design sensitivity analysis, with the help of the direct differentiation method. The Burton-Miller formulation is employed to overcome the fictitious frequency problem in the numerical solutions of exterior acoustic problems. The simple empirical formulas are used to estimate the origin intensity factors in the BM-SBM. Compared with the traditional methods, the present scheme is an accurate and semi-analytical approach with the merits of truly meshless, integration-free, mathematical simplicity, and easy-to-program. As a boundary-type method based on the fundamental solution, furthermore, the BM-SBM is straightforward for addressing the exterior Helmholtz problems encountered in the acoustic design sensitivity analysis. Numerical experiments, including 2D and 3D geometries with Neumann boundary conditions, indicate that the proposed methodology is an accurate, stable, and convergent numerical approach for the acoustic design sensitivity analysis.

A semi-analytical and boundary-type meshless method with adjoint variable formulation for acoustic design sensitivity analysis

This paper proposes a novel semi-analytical method for the two- and three-dimensional acoustic design sensitivity analysis by combining the Burton–Miller-type singular boundary method (BM-SBM) and the adjoint variable method. The BM-SBM is an accurate, stable and boundary-type meshless approach, and can effectively avoid the fictitious frequency issue in the numerical solutions of exterior acoustic problems due to the introduction of the Burton–Miller formula. The origin intensity factors in the BM-SBM are evaluated by employing the empirical formulas and the subtraction and adding-back technique, which is straightforward, accurate and efficient. Unlike the direct differentiation method, the adjoint variable method can save computation time and computer resources since it avoids computing the gradients of state variables by introducing adjoint state space equations. Compared with the existing methods, the present scheme can be regarded as a competitive alternative of acoustic design sensitivity analysis, due to the aforementioned merits. Three numerical examples are provided to illustrate the effectiveness and accuracy of the developed method.

An isogeometric approach of two dimensional acoustic design sensitivity analysis and topology optimization analysis for absorbing material distribution

A study of structural shape optimization and absorbing material distribution optimization of noise barrier structures based on the recently proposed isogeometric analysis method with exact geometric definitions is presented. The acoustic scattering is approximated using the basis functions that represent the geometry. A fast multipole method is applied to accelerate the solution of the boundary element method (BEM). The Burton–Miller formulation is used to overcome the fictitious frequency problem when a single Helmholtz boundary integral equation is used for the exterior boundary–value problem. The strongly singular integrals in the Burton–Miller formulation using the isogeometric BEM are evaluated explicitly and directly, particularly for the sensitivity formulation with a hyper-singular integral. The optimality criteria method is used for two types of optimization analyses, shape optimization and material distribution topology optimization. For the shape optimization, the design variables can be set to the locations of the control points because the control points determine the shape of structure. For the second optimization, a new material interpolation scheme for acoustic problems based on the solid isotropic material with penalization (SIMP) method is given, where the interpolation variable is not the real structural density used in a conventional SIMP, but a fictitious material density that determines the normalized surface admittance. Several examples are presented to demonstrate the validity and efficiency of the proposed algorithm.

Structural–acoustic sensitivity analysis of radiated sound power using a finite element/ discontinuous fast multipole boundary element scheme

SummaryThe complete interaction between the structural domain and the acoustic domain needs to be considered in many engineering problems, especially for the acoustic analysis concerning thin structures immersed in water. This study employs the finite element method to model the structural parts and the fast multipole boundary element method to model the exterior acoustic domain. Discontinuous higher‐order boundary elements are developed for the acoustic domain to achieve higher accuracy in the coupling analysis. Structural–acoustic design sensitivity analysis can provide insights into the effects of design variables on radiated acoustic performance and thus is important to the structural–acoustic design and optimization processes. This study is the first to formulate equations for sound power sensitivity on structural surfaces based on an adjoint operator approach and equations for sound power sensitivity on arbitrary closed surfaces around the radiator based on the direct differentiation approach. The design variables include fluid density, structural density, Poisson's ratio, Young's modulus, and structural shape/size. A numerical example is presented to demonstrate the accuracy and validity of the proposed algorithm. Different types of coupled continuous and discontinuous boundary elements with finite elements are used for the numerical solution, and the performances of the different types of finite element/continuous and discontinuous boundary element coupling are presented and compared in detail. Copyright © 2016 John Wiley & Sons, Ltd.

FEM/wideband FMBEM coupling for structural–acoustic design sensitivity analysis

A coupling algorithm based on the finite element method (FEM) and the wideband fast multipole boundary element method (wideband FMBEM) is proposed for acoustic fluid–structure interaction simulation and structural–acoustic design sensitivity analysis by using the direct differentiation method. The wideband fast multipole method (FMM), which is developed by combining the original FMM and the diagonal form FMM, is used to accelerate the calculation of the matrix–vector products in boundary element analysis. The iterative solver generalized minimal residual method is applied to accelerate the calculation of the solution to the linear system of equations. The FEM/wideband FMBEM algorithm makes it possible to predict the effects of arbitrarily shaped vibrating structures on the sound field numerically. Numerical examples are presented to demonstrate the validity and efficiency of the proposed algorithm.

A wideband FMBEM for 2D acoustic design sensitivity analysis based on direct differentiation method

This paper presents a wideband fast multipole boundary element method (FMBEM) for two dimensional acoustic design sensitivity analysis based on the direct differentiation method. The wideband fast multipole method (FMM) formed by combining the original FMM and the diagonal form FMM is used to accelerate the matrix-vector products in the boundary element analysis. The Burton---Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The strongly singular and hypersingular integrals in the sensitivity equations can be evaluated explicitly and directly by using the piecewise constant discretization. The iterative solver GMRES is applied to accelerate the solution of the linear system of equations. A set of optimal parameters for the wideband FMBEM design sensitivity analysis are obtained by observing the performances of the wideband FMM algorithm in terms of computing time and memory usage. Numerical examples are presented to demonstrate the efficiency and validity of the proposed algorithm.

Topology optimization of composite material plate with respect to sound radiation

In this paper, topology optimization of composite material plate with respect to minimization of the sound power radiation has been studied. A new low noise design method based on topology optimization is proposed, which provides great guidance for acoustic designers. The structural vibrations are excited by external harmonic mechanical load with prescribed frequency and amplitude. The sound power is calculated using boundary element method. An extended solid isotropic material with penalization (SIMP) model is introduced for acoustic design sensitivity analysis in topology optimization, where the same penalization is applied for the stiffness and mass of the structural volume elements. Volumetric densities of stiffer material are chosen as design variables. Finally, taking a simple supported thin plate as a simulation example, the sound power radiation from structures subjected to forced vibration can be considerably reduced, leading to a reduction of 20 dB. It is shown that the optimal topology is easy to manufacture at low frequency, while as the loading frequency increases, the optimal topology shows a more and more complicated periodicity which makes it difficult to manufacture.

Acoustic design sensitivity analysis based on wave superposition approach

Research on the acoustic design sensitivity is significant for its ability to provide the optimized orientation for low noise design of radiating structures. In this paper, the wave superposition approach (WSA) is employed to calculate acoustic design sensitivity. The sensitivity formulations based on the wave superposition are presented in a direct differentiation way, by which the sensitivity of acoustic quantities with respect to the design variables such as structural parameters or physical properties can be obtained. This method is suitable for both shape and sizing sensitivity analysis of arbitrary shaped sources. Compared with the conventional direct differentiation boundary element method, the proposed method has improved accuracy and speed of computation, and has no inherent problem of singular integration which will make numerical processing more complicated. Numerical experiments are demonstrated to show the validity and feasibility of the proposed method.

A study on the applications of the acoustic design sensitivity analysis of vibrating bodies

The determination of the sensitivity of the acoustical characteristics of vibrating systems with respect to the variation of the design parameters predicting these characteristics is a necessary and important step of the acoustic design and optimization process. Acoustic design sensitivity analysis includes the computation and evaluation of the sensitivity information required for this procedure. In this study, a boundary element code performing the sensitivity analysis of the acoustic pressure by using the matrix sensitivities with respect to different design variables has been developed. The effect of the precision of boundary element discretization on the acoustic pressure sensitivity is examined via this code. The formulation is applied to a multi-source system and the dimension sensitivity analysis of near field pressures of two-dilating-spherical source is performed. The last application is devoted to a real sound source: a washing machine sitting on the floor. Sensitivity of the field pressures to the machine’s dimensions (size), surface velocity and frequency is examined on the bases of the boundary element model of the machine and half-space condition. The impacts of these variables are compared; and a limiting speed for the machine responding both the acoustical and operational requirements is determined.

Acoustic Design Sensitivity Analysis and Optimization for Reduced Exterior Noise

A program, global acoustic design sensitivity analyzer, is developed that can perform a global acoustic design sensitivity analysis of exterior noise with respect to structural sizing design variables. A system for global acoustic design sensitivity is introduced and implemented numerically by employing the continuum sensitivity analysis. A half-scale automobile cavity model is considered as a numerical example. By using a continuum method, we obtained accurate and efe cient sensitivities when the number of design variables was large. Also, the tendency plotsof element sensitivities and energy contribution for global acousticsensitivities areavailable. Finally, a design optimization was performed to simultaneously reduce the weight and sound pressure level at interesting points and frequencies. I. Introduction T HE range of engineering problems that can be solved through numericalanalyses hasbeen greatlybroadened with the advent of high-speed digital computers. In addition, the development of the e nite element method (FEM)and the boundary element method (BEM) has also been important to engineering analysis. These two typesofanalysesareassociatedwithanalyticalstructure-bornenoise prediction. FEM is commonly used to compute the vibration of the structure emitting noise, and BEM can be used to predict the generated noise. Other methods for acoustic prediction, such as statistical energy analysis, are also available. In this paper, the focus is on FEM and BEM. In a gradient-based optimization scheme, it is important to have accurate gradients (sensitivities ) of the objective function and constraints with respect to the design variables. Formulation of global acoustic sensitivity through chain-ruled derivatives using FEM and BEM has been studied and implemented by many researchers. Coyette et al. 1 have previously investigated the computation and utilizationofacousticsensitivitieswith respecttosizingdesignvariables. Two types of sensitivities were considered. One was acoustic sensitivity with respect to the normal velocity ofvibratingstructure, and the other was structural sensitivity of structural velocities with respect to physical sizing design variables such as thickness. The acoustic sensitivities and structural sensitivities were calculated using BEM and FEM, respectively, and then these sensitivities were combined to obtain a globalacousticsensitivity.In addition,this approach was implemented to the commercial code, SYSNOISE. The same approach was presented in the articles by Cunefare et al., 2;3 who focused on e nding the best optimization formulation by comparing the relative performance and results obtained through the use of several different objective functions and constraints. They obtained acoustic sensitivities and structural sensitivities from the commercial codes NASTRAN and COMET. They also developed COMIN to combine the acoustic and structural sensitivities. Most researchers who studied global acoustic design sensitivity analysis (DSA) and acoustic optimization have used the structural sensitivity analysis module supported by commercial codes and have thus faced limitations in the accuracy and number of design variables. There are several reasons for the limitations of the semianalytical method. First, when the semianalytical method is used forstructural sensitivity analysis, a slight error could occur due to the amount of perturbation. For this paper, we used a continuum approach 4i6 to calculate the structural sensitivity combined with acoustic sensitiv

Acoustic design sensitivity analysis and optimization for reduced exterior noise

Acoustic design sensitivity analysis and optimization for reduced exterior noise

Acoustic Design Sensitivity for Structural Radiators

An analysis technique designated as acoustic design sensitivity (ADS) analysis is developed via the numerical treatment of a discrete quadratic expression for the total acoustic power radiated by a three-dimensional extended structure. A boundary element formulation of the Helmholtz Integral Equation is the basis of the analysis leading to the quadratic power expression. Partial differentiation of the quadratic power expression with respect to a known surface velocity distribution leads to a sensitivity distribution, represented by a distribution of values on the surface of a structure. The sensitivity values represent a linear approximation to the change in the total radiated power caused by changes in the surface velocity distribution. For a structure vibrating with some portions of its surface rigid and such that the acoustic wavelength is long compared to a characteristic dimension of the structure, ADS analysis reveals that the rigid surfaces strongly influence the sensitivity distribution, as expected. Under such conditions, the rigid surfaces can exhibit the maximum value of the entire sensitivity distribution, even though the acoustic intensity is identically zero on a rigid surface. As the frequency increases, and the acoustic wavelength becomes comparable to a characteristic dimension of the structure, the position of the maximum value of the sensitivity distribution will coincide with the region of the maximum surface acoustic intensity.