正交各向异性薄板振动响应的波函数法

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (24) : 244-249.

论文

正交各向异性薄板振动响应的波函数法

赖诗洋1，夏小均2，徐中明3

作者信息 +

Wave-based prediction technique for thin orthotropic plate vibration

LAI Shiyang1, XIA Xiaojun2, XU Zhongming3

Author information +

文章历史 +

摘要

提出了适用于正交各向异性薄板弯曲振动响应预测的波函数法，基于Kirchhoff正交各向异性薄板振动控制方程，推导了体现各主轴物理量且精确满足其控制方程的复合结构波函数。通过傅立叶变换，在波数域对响应函数进行角积分，得到处于外部激励下的无限正交各向异性板振动响应。结合正交各向异性薄板的物理边界，运用加权余量法求得各正交各向异性结构波函数的系数，得到薄板的弯曲振动响应。建立矩形正交各向异性板的波函数响应模型，通过双级数解法验证了方法的正确性，与有限元法的对比结果说明，波函数法对正交各向异性薄板在中频范围的振动响应预测有着更高的计算效率。

Abstract

The wave-based (WB) technique for predicting the vibration of thin orthotropic plate was proposed.The structure wave function that exactly satisfies the global governing vibration equation of orthotropic plate was deduced.The displacement response of infinite orthotropic plate under unit concentrated force was obtained utilizing the Fourier transformation.Further, the bending vibration of the thin orthotropic plate with WBM was achieved by a weighted residual method after computing the weight coefficient of each wave function combining the physical boundary of the plate.A rectangular thin orthotropic plate was introduced as a numerical example.The wave-based technique for predicting the vibration of the thin orthotropic plate was validated by comparing with series solution, and the computational efficiency of the proposed method is much higher than the finite element method for thin orthotropic plates in mid-frequency based on convergence analysis.

导出引用

赖诗洋1，夏小均2，徐中明3. 正交各向异性薄板振动响应的波函数法[J]. 振动与冲击, 2018, 37(24): 244-249

LAI Shiyang1, XIA Xiaojun2, XU Zhongming3. Wave-based prediction technique for thin orthotropic plate vibration[J]. Journal of Vibration and Shock, 2018, 37(24): 244-249

参考文献

[1] Deraemaeker A, Babuska I. Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions [J]. International Journal for Numerical Methods in Engineering, 1999, 46(4):471–499.
[2] Zienkiewicz O C, Taylor R L, Zhu J Z, et al. The finite element method – Vol. 1: Basic formulation and linear problems [M]. Butterworth-Heinemann, 2005.
[3] Lyon R, DeJong R. Theory and application of statistical energy analysis (2nd ed.) [M]. Butterworth Heinemann, 1995.
[4] Shorter P J. On the reciprocity relationship between direct field radiation and diffuse reverberant loading [J]. Journal of the Acoustical Society of America, 2005, 117(1):85-95.
[5] 陈书明, 王登峰, 昝建明. 基于FE-SEA混合模型的轿车车内噪声预测[J]. 汽车工程, 2011, 33(3): 236-240.
Chen Shuming, Wang Dengfeng, Zan Jianming. In-car noise prediction based on hybrid FE-SEA model[J]. Automotive Engineering, 2011, 33(3): 236-240.
[6] 胡莹,陈克安.基于FE-SEA混合法的梁弯曲振动响应分析[J].振动与冲击, 2008, 27(7): 91-96.
HU Ying, CHEN Ke-an. FE-SEA hybrid method for vibration analysis of complex structures [J]. Journal of Vibration and Shock, 2008, 27(7): 91-96.
[7] Kessentini A, Taktak M. Computation of the scattering matrix of guided acoustical propagation by the wave finite element approach [J]. Applied Acoustics, 2016, 108: 92-100.
[8] Giannini O, Carcaterra A. High frequency vibration analysis by the complex envelope vectorization [J]. Journal of the Acoustical Society of America, 2007, 121(6): 3472-3483.
[9] Kovalevsky, Louis, Ladevèze, et al. The Fourier version of the variational theory of complex rays for medium-frequency acoustics [J]. Computer Methods in Applied Mechanics and Engineering, 2012, 225-228: 142-153.
[10] Desmet W. A wave based prediction technique for coupled vibro-acoustic analysis [D]. Leuven, 1998.
[11] 杨念,陈炉云,张裕芳.基于波函数法的结构振动功率流研究[J].振动与冲击, 2014, 33(2): 173-177.
YANG Nian, CHEN Lu-yun, ZHANG Yu-fang. Wave based method for steady-state power flow analysis [J]. Journal of
Vibration and Shock, 2014, 33(2): 173-177.
[12] 夏小均,徐中明,张志飞等.基于波函数法的附加弹簧阻尼薄板的振动研究[J].振动与冲击, 2016,35(14):140-144.
XIA Xiao-jun, XU Zhong-ming, ZHANG Zhi-fei, et al. Vibration analysis of plates with spring -damper by using wave based method [J]. Journal of Vibration and Shock, 2016, 35(14): 140-144.
[13] Vanmaele C, Vandepitte D, Desmet W. An efficient wave based prediction technique for plate bending vibrations [J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196(33-34): 3178-3189.
[14] 何雪松,黄其柏,胡溧.WBM 法在薄板弯曲振动分析中的应用[J].华中科技大学学报(自然科学版),2008,36(7):97-99.
HE Xue-song, HUANG Qi-bai, HU Li. Application of wave based method to plate bending vibration analysis[J]. Journal of Huangzhong University of Science & Technology (Natural Science Edition), 2008, 36(7):97-99.
[15] Klanner M, Ellermann K. Wave based method for the steady-state vibrations of thick plates [J]. Journal of Sound and Vibration, 2015, 345: 146-161.
[16] Bergen B, Pluymers B, Genechten B V. A Trefftz based method for solving Helmholtz problems in semi-infinite domains. Engineering Analysis with Boundary Elements, 2012, 36(1): 30-38.
[17] Genechten B V, Atak O, Bergent 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.
[18] Deckers E, Horlin N E, Vandepitte D, et al. A wave based method for the efficient solution of the 2d poroelastic biot equations [J]. Computer Methods in Applied Mechanics and Engineering, 2012, 201-204(1): 245-262.
[19] 曾军才,王久法,姚望等.正交各向异性矩形板的自由振动特性分析[J].振动与冲击, 2015, 34(24): 123-127.
ZENG Jun-cai, WANG Jiu-fa, YAN Wang, et al. Free vibration characteristics of orthotropic rectangular plates [J]. Journal of
Vibration and Shock, 2015, 34(24): 123-127.
[20] Lekhnitskii S. Anisotropic plates [M]. Gordon and Breach, 1968.
[21] Papkov S О. Steady-state forced vibrations of a rectangular orthotropic plate [J]. Journal of Mathematical Sciences, 2013, 192(6): 691-702.
[22] Magliula E A, Mcdaniel J G, Pierce A D. Far-field approximation for a point-excited anisotropic plate [J]. Journal of the Acoustical Society of America, 2012, 1331(6): 4534-454 2.
[23] 蒋伟康，朱继梅.正交各向异性板动力响应的边界元方法[J].振动工程学报, 1988, 1(2): 55-62.
JIANG Wei-kang, ZHU Ji-mei. Boundary element method for dynamic response of orthotropic plate [J]. Journal of Vibration Engineering, 1988, 1(2): 55-62.