Acoustic Sensitivity Analysis Research Articles

Acoustic sensitivity analysis for 3D structure with constant cross-section using 2.5D singular boundary method

In this paper, a 2.5D singular boundary method (SBM) in conjunction with the direct differentiation method (DDM) and adjoint variable method (AVM) are formulated for the sensitivity analysis of 3D longitudinally invariant structures. The assumption of a constant cross-section in the longitude direction enables it possible to decouple the 3D system into 2D problems at every wavenumber, and thus makes it a 2.5D-problem. The 2D sensitivity problem is solved by a boundary-type method, SBM. The SBM solves a problem with a linear combination of the fundamental solutions with respect to boundary collocation points. The fundamental solution makes the SBM available for exterior problems without the artificial truncated boundary. The source singularity issue of fundamental solution is overcome by a simple analytical formula and its derivatives. Numerical experiments present the accuracy, efficiency and feasibility of the proposed methods, and indicate that the proposed methods can be considered as an effective alternative in 3D problems with a longitudinally invariant cross-section.

Impedance Sensitivity Analysis Based on Discontinuous Isogeometric Boundary Element Method in Automotive Acoustics

Abstract Acoustic sensitivity analysis is an essential technique to determine the direction of structural-acoustic optimization by evaluating the gradient of the objective functions with respect to the design variables. However, acoustic sensitivity analysis with respect to acoustic impedance, which is an important parameter representing the interior absorbent material in automotive acoustics, is lacking in the study. Moreover, acoustic sensitivity analysis implemented with conventional numerical methods is time and effort-consuming in automotive acoustics, due to the large-scale mesh generation. In this work, the impedance sensitivity analysis for automotive acoustics based on the discontinuous isogeometric boundary element method is presented. The regularized boundary integral equation with impedance boundary conditions is established, then the sensitivity is derived by differentiating the boundary integral equation. The efficiency of the proposed method is improved by employing the parallel technique and generalized minimal residual solver. A long duct example with an analytical solution validates the accuracy of the proposed method, and an automotive passenger compartment subjecting to impedance boundary conditions illustrates that the computing time of the proposed method is one order of magnitude less than the conventional method. This work presents an easily implementable and efficient tool to investigate acoustic sensitivity with respect to impedance, showing great potential in the application of automotive acoustics.

An ACA-BM-SBM for 2D acoustic sensitivity analysis

<abstract> <p>In this paper, we present a novel computational approach (named ACA-BM-SBM) for the calculation of 2D acoustic sensitivity by combining the Burton-Miller-type singular boundary method (BM-SBM) with the adaptive cross-approximation (ACA) algorithm. The BM-SBM circumvents the source singularities of the fundamental solutions by introducing the origin intensity factors, and it eliminates the fictitious frequency problem in external acoustic fields by introducing the Burton-Miller formula. As a semi-analysis meshless method, the BM-SBM can accurately solve the external acoustic problem governed by the Helmholtz equation. Nevertheless, the computational inefficiency introduced by the dense coefficient matrix renders this method suboptimal, particularly for large-scale simulations. As the number of nodes increases, the computation time and store memory increase dramatically. ACA is a purely algebraic method based on hierarchical matrices which can be used to partition the coefficient matrix step by step. By employing ACA, the BM-SBM can be effectively accelerated, and this results in less computation time, as well as fewer memory requirements. Numerical experiments, including Dirichlet and Neumann boundary conditions, illustrate that the proposed approach is an accurate, efficient and fast numerical method for acoustic sensitivity analysis.</p> </abstract>

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.

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.

Structural acoustics analysis and optimization of an enclosed box-damped structure based on response surface methodology

In this paper, the structural acoustics analysis and optimization of an enclosed box-damped structure are investigated by using the response surface methodology (RSM). Acoustic frequency response function analysis, i.e. a unit harmonic force imposing on structure and calculating the sound pressure in cavity, is applied to achieve the critical frequency. The acoustic sensitivity analysis of sound pressure level with respect to the thicknesses of damping layer panels are employed to identify the significant variables. With the help of faced central composite design, an efficient set of sample points are generated, and then the second order polynomial function of the sound pressure response at critical frequency is computed and verified by the adjusted coefficient of multiple determination. After the response surface function is verified, the effect of the thicknesses of damping layer panels on sound pressure is analyzed quantitatively, and the thicknesses of damping layer panels are further optimized to minimize the sound pressure response of the target node. The results indicate that, by using the RSM, the computational time for structural acoustic is saved and the optimization process is simple. The sound pressure of the target node is controlled effectively with less damping material used.

Automotive Interior Noise Prediction Based on Single Sound Cavity Using Statistical Energy Analysis Method

In order to predict car interior noises at the car design and development stage, the statistical energy analysis (SEA) method was used. All the input parameters – modal density (MD), damping loss factor (DLF) and coupling loss factor (CLF) were calculated with SEA principle. Meanwhile, the sound excitation was calculated with sound power experiment data of internal combustion engine given by the engine manufacturer and sound source radiation formula. Engine mount excitation was also computed through the acceleration at initiative side of the engine mount and the transmissibility. A car virtual prototype was built to calculate a car body suspension receiving excitation from road roughness. A computational fluid dynamics (CFD) model was also built up to analyze the wind excitation on the outside surfaces. The car interior noises were predicted by the SEA model with all of the parameters and excitations. A good agreement was indicated by comparing predicted results with measured ones. The maximum relative error between prediction and measurement results is less than 3%, and the maximum absolute error is less than 2.5 dB (A). The above predicted results satisfy engineering precision requirements and as well as showing that using SEA method to predict car internal noises is feasible. The acoustic sensitivity analysis was made at the end. The car internal noise prediction method presented in the paper can be used at car design and development stage.

Acoustic Sensitivity Analysis Using the Distributed Source Energy Boundary Point Method

The determination of the sensitivity of the acoustical characteristics of vibrating systems with respect to the variation of the design parameters can provide a method to low-noise design of mechanical structure objectively and quantitatively. Using the Distributed source energy boundary point method, the expressions of the change of the acoustical energy density with respect to design variable is presented in this paper. The Distributed source energy boundary point method is a speedy and precise method which can avoid the complex computing of the singularity integral in EBEM. The correctness and availability is validated by the numerical simulation.

Explicit evaluation of hypersingular boundary integral equations for acoustic sensitivity analysis based on direct differentiation method

This paper presents a new set of boundary integral equations for three dimensional acoustic shape sensitivity analysis based on the direct differentiation method. A linear combination of the derived equations is used to avoid the fictitious eigenfrequency problem associated with the conventional boundary integral equation method when solving exterior acoustic problems. The strongly singular and hypersingular boundary integrals contained in the equations are evaluated as the Cauchy principal values and Hadamard finite parts for constant element discretization without using any regularization technique in this study. The present boundary integral equations are more efficient to use than the usual ones based on any other singularity subtraction technique and can be applied to the fast multipole boundary element method more readily and efficiently. The effectiveness and accuracy of the present equations are demonstrated through some numerical examples.

PEM Based Sensitivity Analysis for Acoustic Radiation Problems of Random Responses

A new effective method for computing the acoustic radiation and its sensitivity analysis of a structure subjected to stochastic excitation is presented. Previous work in the area of structural and acoustic sensitivity analysis systems was mostly focused on the deterministic excitation. New methods are developed to account for stochastic excitation. The structural-acoustic response is calculated using finite element method and boundary element method combined with stochastic analysis techniques. An accurate and highly efficient algorithm series for structural stationary random response analysis, pseudo-excitation method (PEM), is extended to acoustic random analysis in this paper, which was used to calculate structural random analysis in the past. So the acoustic radiation problems of random responses are transformed to the structural-acoustic harmonic analyses. This is a time-saving progress in comparison with traditional method. Based on the PEM, the acoustic radiation sensitivities of the structure are developed in emphasis that are transformed to harmonic sensitivity analyses. They are validated by comparing with the results of finite difference sensitivity method. Numerical examples are given to demonstrate the effectiveness of the methods and the program.

20505 自動車のドア閉まり音の快音化設計(一般講演 振動(2))

The vibration and noise of automobiles by lightening might cause decreasing the product value. In this study, an improvement of the door closing sound of lightened door and a structural modification of the door outer panel were investigated in consideration of human sensibility. To forecast by CAE easily, a series of verifications was done with a simplified door experiment model. Acoustic sensitivity analysis was used to detect an effective position for structural changing. Finally, an actual door closing sound was designed to a pleasant sound.

605 境界要素法の音響感度解析への応用(OS6. 境界要素法の高度化と最新応用(2),オーガナイズドセッション講演)

605 境界要素法の音響感度解析への応用(OS6. 境界要素法の高度化と最新応用(2),オーガナイズドセッション講演)

Proposal of a Methodology for Multidisciplinary Design of Multifunctional Vehicle Structures including an Acoustic Sensitivity Study

In this paper, a design methodology is proposed, wherein tools and knowledge from the areas of structural design, numerical optimization, and noise, vibration and harshness (NVH) engineering are combined into a single toolbox for vehicle design. The methodology attempts to address the topic of sustainable development from both economic and environmental perspectives within the vehicle industry. A brief review of the topics of NVH and numerical optimization is given for the purposes of disseminating knowledge. Finite element codes for predicting structural and acoustic response are implemented within the iterative design methodology, which is explained for generic problems. Specific focus is placed on the need for understanding functional requirements of the entire system rather than its components. The methodology is implemented in an automotive case study. The results in terms of design solution and development framework are evaluated and discussed. As part of this evaluation, and integral to the design process, an acoustic sensitivity analysis of the final solution is performed and the results are presented.

A multi-domain boundary element formulation for acoustic frequency sensitivity analysis

The determination of acoustic sensitivity characteristics for vibrating structures with respect to the design parameters is a necessary and an important step of the acoustic design and optimization process. Acoustic frequency sensitivity analysis, as one kind of the sensitivity analysis, is extremely useful for large models in which only a few discrete frequencies can be analyzed due to high computational cost. Through frequency sensitivity analysis, the acoustic performance can be obtained near the initial frequency for less cost than a second full analysis. However, based on single-domain boundary element method (BEM), acoustic sensitivity analysis also has low computation efficiency. When many forces, with the same frequency, act on one vibrating structure, it is hard to decide which one should be improved. On the contrary, by using multi-domain BEM, the sensitivity figure can clearly show which exciting frequency has the greatest influence on acoustic characteristics with lower computational cost. Adopting multi-domain BEM, the expressions of the change of acoustical characteristic with respect to the change of the frequency are presented for exterior problems. The sensitivities of coefficient matrix are computed by analytical differentiation of the discrete Helmholtz integral equation. Finally, several examples are given to demonstrate the validation and availability of the presented method.

Coupled Acoustic-structural Finite Element Analysis of Vehicle Interior Noise Based on Acoustic Sensitivity

It is very important to predict the acoustic radiation of vehicle body for the control of interior noise. Firstly, the control equation of acoustic-structural coupled finite element method (FEM) is derived. The computational methods of modal participation factors and panel acoustic contributions are obtained. Then the acoustic-structural coupled finite element model of a commercial vehicle, including body and interior cavity, is created on the basis of virtual proving ground technique which is employed for the prediction of vehicle interior noise. The connection points between the body and the chassis are chosen as the excitation points of acoustic sensitivity analysis. The acoustic sensitivity from each suspension point to the ears of driver is obtained by using the acoustic-structural coupled FEM. The result of acoustic sensitivity analysis shows that there exist biggish peaks of body modal at its formants which are 70 Hz, 138 Hz and 200 Hz. The frequency points of the three peaks and their structures are studied. The structural and acoustic modal participation factors and panel acoustic contributions are computed. Finally, those panels and structural modals that have most influence on the acoustic response of vehicle are obtained.

Boundary Element Method for Acoustic Sensitivity Analysis of Vibrating Structures

The determination of the acoustic sensitivity characteristics with respect to the variation of the design parameters can provide a method for low-noise design of mechanical structure objectively and quantitatively.Based on the boundary element method, the expressions of sensitivities of the acoustic pressure with respect to changes in frequency and surface vibration velocity are presented.The sensitivities of coefficient matrix are computed by differentiation directly,instead of finite difference approximation. Using displaced points method,the singular integral can be obtained fast and correctly.Numerical sensitivity results obtained by the boundary element method are compared to analytical solutions,and the validation and availability of the present method are proved. These acoustic sensitivity analysis methods can lay a solid foundation for the low-noise design of mechanical structure.

FEM–BEM-coupling and structural–acoustic sensitivity analysis for shell geometries

Passive noise control by modification of structural geometry moves more and more into the field of vision for designers. This structural–acoustic optimization shows high potential in minimization of radiated noise especially for thin shell geometries. Since computer systems have been enhanced dramatically in recent years numerical simulation of structural vibration and acoustic field was accelerated significantly. But still the sensitivity analysis represents the bottle neck in computational efforts of gradient-based optimization. Furthermore, the coupling between FE and BE analysis in structural–acoustic simulation of large scale models will occur as an additional challenge because of non-matching meshes. In this paper, a fast method for computation of sensitivities of acoustic properties with respect to shell geometry is presented. Therefore, a concept to parameterize the structural geometry is explained. Additionally, the coupling procedure is simplified to reduce computational effort. Finally, this method is applied to an academic example. The sensitivity of the sound pressure at an internal point of an oblique box is investigated, when one side of this six-sided box is geometrically modified.

Acoustic sensitivity analysis of optimal asset allocation for ASW

In 1946, Koopman [Operations Evaluation Group Report 56, Navy Department] characterized optimal search for a stationary target in terms of arbitrary space-time effort density, with the searcher’s effectiveness defined by cumulative detection probability (given by the exponential search formula). Koopman’s solution maximizes target exposure at time t, given failure to detect at all previous times. This plan is myopic because it does not look into the future. In 1980, Brown [Operations Research 28, 1275–1289] generalized this result for a moving target. Brown’s algorithm allocates effort to maximize target exposure, given failure to detect by all prior and future search efforts. It converges to an optimal allocation, and typically converges rapidly because it simplifies sensor performance to a single factor (sweep rate in each cell), which eliminates the need for detailed sensor performance predictions. Experience has shown that sweep rate is an excellent predictor of search effectiveness, for high-level analyses. This work describes an approach to optimize several searchers simultaneously and investigates optimal asset allocation for coordinated, multiship missions under detailed conditions. The results show that attention to acoustic details can significantly increase overall search effectiveness, especially when using sensors with different capabilities. [Work sponsored by ONR.]

Efficient optimization of a noise transfer function by modification of a shell structure geometry - Part I: Theory

In the early stages of vehicle body development trends for the acoustic behaviour of the whole vehicle are, on the one hand, of great importance, but difficult to achieve. Geometry based, parametric model descriptions and optimization techniques enable the engineer to find out these trends. This paper starts with a review of structural acoustic sensitivity analysis and optimization. Then, the noise transfer function including structural harmonic analysis, acoustic influence coefficients and their coupling is described. This is followed by some remarks on the optimization process, discussing objective functions, useful design parameters and optimization techniques. Finally, a section on sensitivity analysis presents a numerical and a semianalytic method. In the case of small design modifications the sensitivity calculation mainly reduces to the well-known semianalytic calculation of harmonic displacement sensitivities. Part II presents the design optimization of a sedan dashboard.

Engine radiation noise reduction with bem acoustic sensitivity analysis Kyoichi Umemura, Sasaki Katsuo, Kenji Nishikawa, Kiyoshi Miyazaki (Honda R & D Co., Ltd., Tochigi R&D Center), Tetsuo Horie (Honda R&D North-America Inc.)

Engine radiation noise reduction with bem acoustic sensitivity analysis Kyoichi Umemura, Sasaki Katsuo, Kenji Nishikawa, Kiyoshi Miyazaki (Honda R & D Co., Ltd., Tochigi R&D Center), Tetsuo Horie (Honda R&D North-America Inc.)