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JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE)  2017, Vol. 51 Issue (10): 2039-2045    DOI: 10.3785/j.issn.1008-973X.2017.10.019
Civil Engineering, Transportation Engineering     
Mid-frequency acoustic response analysis of cavity with spline boundary based on wave-based method
XIA Xiao-jun1,2, XU Zhong-ming1,2, ZHANG Zhi-fei1,2, HE Yan-song1,2
1. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400030, China;
2. College of Automotive Engineering, Chongqing University, Chongqing 400030, China
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Abstract  

An acoustic predictive method for sound field including B-spline curve boundary with wave-based method (WBM) adopted was proposed based on the theory study of WBM and B-spline. The method was complemented through two different integrate methods. Two different analysis acoustic domains were obtained by changing the control parameters of spline curve, and the acoustic responses were calculated through the use of WBM and finite element method (FEM) with different sizes. The comparisons of the pressure distribution, the frequency response of reference point and the convergence of the two methods indicate that the proposed method can effectively extend the application of WBM in acoustic prediction with spline curve boundary, realize the variable parameter modeling more conveniently, and show the high precision and efficiency for mid-frequency acoustic calculation and analysis. The Gauss integral method is more rapid and steady in calculation of such boundary compared with Newton integral method.



Received: 29 August 2016      Published: 27 September 2017
CLC:  U461  
Cite this article:

XIA Xiao-jun, XU Zhong-ming, ZHANG Zhi-fei, HE Yan-song. Mid-frequency acoustic response analysis of cavity with spline boundary based on wave-based method. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2017, 51(10): 2039-2045.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2017.10.019     OR     http://www.zjujournals.com/eng/Y2017/V51/I10/2039


基于波函数法的样条边界声学域中频响应

基于波函数法(WBM)和B样条理论,提出将波函数法引入到含有B样条曲线边界的声腔中进行声学预测的方法,以2种数值积分方法实现.通过改变样条曲线的控制参数,得到2个不同的分析声学域,分别运用波函数法和不同单元尺度的有限元法对该声学域进行计算.对比2种方法下声学域的声压分布、参考点的频率响应以及2种方法的收敛情况.结果表明:采用该方法能够有效地将波函数法应用于含样条边界的声学域中,更加便捷地实现变参数建模.运用波函数法对中频声学响应进行计算分析,具有更高的精度和效率.Gauss积分与Newton积分法的对比,表明了Gauss积分法在该类边界计算中的快收敛与稳健性.

[1] WANG D, MONK N A. A least-squares method for the Helmholtz equation[J]. Computer Methods in Applied Mechanics and Engineering, 1999,175(1/2):121-136.
[2] BABUŠKA I, IHLENBURG F. A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution[J]. Computer Methods in Applied Mechanics and Engineering, 1995, 128(3/4):325-359.
[3] LOULA A,FERNANDES D T. A quasi optimal Petrov-Galerkin method for Helmholtz problem[J]. International Journal of Numerical Methods Engineering, 2009, 80(12):1595-1622.
[4] MELEN K,BABUSKA I. Approximation with harmonic and generalized harmonic polynomials in the partition of unity method[J]. Computer Assisted Mechanics and Engineering Sciences, 1997, 4(3):607-632.
[5] E PERREY D,TREVELYAN J,BETTESS P. Wave boundary elements:a theoretical overview presenting applications in scattering of short waves[J]. Engineering Analysis with Boundary Elements, 2004, 28(2):131-141.
[6] HARARI I,HUGHES T. Galerkin/least-squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains[J]. Computer Methods in Applied Mechanics and Engineering, 1992, 98(3):411-454.
[7] MACE B,SHORTER P. Energy flow models from finite element analysis[J]. Journal of Sound and Vibration, 2000, 233(3):369-389.
[8] MAXIT L,GUYADER J. Estimation of SEA coupling loss factors using a dual formulation and FEM modal information, part I:theory[J]. Journal of Sound and Vibration, 2001, 239(5):907-930.
[9] LANGLEY R S,BREMNER P. A hybrid method for the vibration analysis of complex structural acoustic systems[J]. Journal of the Acoustical Society of America, 1999, 105(3):1657-1671.
[10] SAPENA J. Interior noise prediction in high-speed rolling stock driver's cab:focus on structure-borne paths (mechanical and aero sources)[J]. Mathematical Problems in Engineering, 2011, 118:445-452.
[11] SHORTER P, LANGLEY R. Modeling structure-borne noise with the hybrid FE-SEA method[C]//6th International Conference on Structural Dynamics. Paris:Cambridge University Press, 2005:1205-1210.
[12] SULEAU P. Element-free Galerkin solutions for Helmholtz problems:formulation and numerical assessment of the pollution effect[J]. Computer Methods in Applied Mechanics and Engineering, 1998, 162(1-4):317-335.
[13] FARHAT C, HARARI I, FRANCA C. The discontinuous enrichment method[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 190(48):6455-6479.
[14] EZE R. The variational theory of complex rays:a predictive tool for medium frequency vibrations[J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(28):3301-3315.
[15] DESMET W. A wave based prediction technique for coupled vibro-acoustic analysis[D]. Leuven, Belgium:University of Leuven, 1998:2053-2063.
[16] VERGOTE K,VANMAELE C,VANDEPITTE D. An efficient wave based approach for the time-harmonic vibration analysis of 3D plate assemblies[J]. Journal of Sound and Vibration, 2013, 332(8):1930-1946.
[17] DECKERS E,BERGEN B,GENECHTEN B V. An efficient Wave Based Method for 2D acoustic problems containing corner singularities[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 241-244(9):286-301.
[18] GENECHTEN B V,ATAK O,BERGEN B. An efficient Wave Based Method for solving Helmholtz problems in three-dimensional bounded domains[J]. Engineering Analysis with Boundary Elements, 2012,36(1):63-75.
[19] 马大猷.现代声学理论基础[M]. 北京:科学出版社, 2004:10-15.
[20] PIEGL L, TILLER W. The NURBS book[M]. 2nd ed. Berlin:Springer, 1997:50-99.
[21] KIUSALAAS J. Numerical methods engineering with MATLAB[M]. 2nd ed. Cambridge:Cambridge University Press, 2009:182-249.

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