全局弱式无网格方法求解消声器横向模态
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摘要
应用全局弱式无网格方法求解消声器的横向模态,使用径向基函数点插值法离散本征方程,使用伽辽金加权残数法进行数值积分。分别应用全局弱式无网格方法计算了圆形截面,不规则截面以及含有穿孔截面的本征值和本征向量,计算结果与解析方法和二维有限元方法计算结果吻合较好,并且与二维有限元方法相比,全局弱式无网格方法比较节省计算时间。进而分析了支持域的尺寸以及径向基函数中形状参数对计算精度的影响。
The transverse modes of silencers are extracted by using the global weak-form mesh-free method(MFM).The radial base-function point interpolation method is used for dispersing the eigenvalue equations and the Galerkin method is used for numerical integration. Utilizing the global weak-form mesh-free method, the eigenvalues and eigenvectors of the model with circular section, irregular section and perforated section are calculated respectively. Results of computation are in good agreement with those of analytical solution and 2 D finite element solution. Compared with 2 D finite element method,the global weak-form mesh-free method has less computer-time consuming. Additionally, the effects of size of support domain and shape parameters of the radial basis functions on the calculation accuracy are evaluated.
The transverse modes of silencers are extracted by using the global weak-form mesh-free method(MFM).The radial base-function point interpolation method is used for dispersing the eigenvalue equations and the Galerkin method is used for numerical integration. Utilizing the global weak-form mesh-free method, the eigenvalues and eigenvectors of the model with circular section, irregular section and perforated section are calculated respectively. Results of computation are in good agreement with those of analytical solution and 2 D finite element solution. Compared with 2 D finite element method,the global weak-form mesh-free method has less computer-time consuming. Additionally, the effects of size of support domain and shape parameters of the radial basis functions on the calculation accuracy are evaluated.
引文
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[8]胡海,郭文勇,马龙.结构声辐射计算的边界无网格法[J].噪声与振动控声与振动控制,2012,32(5):37-41.
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[10]曾向阳,王海涛,杜博凯.基于声粒子分布积分的无网格声场计算方法[J].应用声学,2016,5(1):84-89.
[11]FANG Z,LIU C Y.Combined mesh free method and mode matching approach for transmission loss predictions of expansion chamber silencers[J].Eng.Anal.Bound Elem.,2017(84):168-177.
[12]I Z L,FANG Z.On the acoustic impedance of perforates and its application to acoustic attenuation predictions for perforated tube silencers[C].Inter-noise 2011,Osaka,Japan,September,2011.
[13]方智,季振林.穿孔管阻性消声器横截面模态及消声特性计算与分析[J].振动与冲击,2014,33(7):138-146.
[2]ZHAO S.On the spurious solutions in the high-order finite element methods for eigenvalue problems[J].Comput Mthod Appl.M.,2007,196(49-52):5031-5036.
[3]LIU G R,GU Y T.An introduction to meshfree methods and their programming[M].New York:Springer,2005.
[4]BOUILLARD P,SULEAUB S.Element-free Galerkin solutions for helmholtz problems:formulation and numerical assessment of the pollution effect[J].Comput Mthod Appl.M.,1998,162:317-335.
[5]CHEN J T,CHANG M H,CHEN K H,at al.Boundary collocation method for acoustic eigen analysis of threedimensional cavities using radial basis function[J].Comput Mech.,2002,29(4):392-408.
[6]李美香,张宏伟,李卫国.基于点插值的配点型无网格方法解Helmholtz问题[J].计算力学学报,2010,27(3):533-536.
[7]姚凌云,于德介,臧献国.声学数值计算的分区光滑径向点插值无网格法[J].振动与冲击振动与冲击,2011,30(10):188-192.
[8]胡海,郭文勇,马龙.结构声辐射计算的边界无网格法[J].噪声与振动控声与振动控制,2012,32(5):37-41.
[9]LI K,HUANG Q B,WANG J L,LIN L G.An improved localized radial basis function meshless method for computational aeroacoustics[J].Eng.Anal.Bound Elem.,2011(35):47-55.
[10]曾向阳,王海涛,杜博凯.基于声粒子分布积分的无网格声场计算方法[J].应用声学,2016,5(1):84-89.
[11]FANG Z,LIU C Y.Combined mesh free method and mode matching approach for transmission loss predictions of expansion chamber silencers[J].Eng.Anal.Bound Elem.,2017(84):168-177.
[12]I Z L,FANG Z.On the acoustic impedance of perforates and its application to acoustic attenuation predictions for perforated tube silencers[C].Inter-noise 2011,Osaka,Japan,September,2011.
[13]方智,季振林.穿孔管阻性消声器横截面模态及消声特性计算与分析[J].振动与冲击,2014,33(7):138-146.