Green Quasifunction Method for Free Vibration of Clamped Thin Plates

被引：0
作者：
Shanqing Li
Hong Yuan
机构：
[1] Jinan University,MOE Key Laboratory of Disaster Forecast and Control in Engineering, Institute of Applied Mechanics
来源：
Acta Mechanica Solida Sinica | 2012年 / 25卷
关键词：
Green function; integral equation; R-function; clamped thin plates; free vibration;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The Green quasifunction method is employed to solve the free vibration problem of clamped thin plates. A Green quasifunction is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem. The mode shape differential equation of the free vibration problem of clamped thin plates is reduced to Fredholm integral equation of the second kind by Green formula. Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation. Two examples demonstrate the validity of the present method. Comparison with both the series solution and ANSYS finite-element solution shows fine agreement. The present method is a novel and effective mathematical one.
引用
收藏
页码：37 / 45
页数：8
相关论文
共 100 条
[1]  
Xu Q(2001)New approach to free vibration analysis of plate using virtual boundary element Journal of Tong Ji University 29 888-892
[2]  
Zhu JL(2009)Study on free vibration of circular plate with concentrated mass at arbitrary positions by integral equation method Journal of Mechanical Strength 31 832-836
[3]  
Zhao Z(2004)Analytical and experimental investingation on transverse vibrations of solid, circular and annular plates carrying a concentrated mass at an arbitrary position with marine applications Ocean Engineering 31 127-138
[4]  
Wang WD(2006)Transverse vibration of thin solid and annular circular plate with attached discrete masses Journal of Sound and Vibration 292 999-1003
[5]  
Cheng G(2004)An analysis of free vibration problem for a thin plate by local Petrov-Galerkin method Chinese Quarterly of Mechanics 25 577-582
[6]  
Cheng Q(2003)Analysis of free vibration of thin plates by the element-free method Mechanics in Engineering 25 37-40
[7]  
Bambill DV(1993)Application of the Green’s function method to calculate the natural frequency of plates with arbitrary shape and arbitrarily distributed point supports along edges Acta Mechanica Solida Sinica 14 54-58
[8]  
La MS(2000)Free vibration analysis of completely free rectangular plates by the superposition-Galerkin method Journal of Sound and Vibration 237 901-914
[9]  
Rossit CA(2001)Free vibration analysis of arbitrarily shaped plates with clamped edges using wave-type functions Journal of Sound and Vibration 242 9-26
[10]  
Laura PAA(2002)Free vibration analysis of arbitrarily shaped plates with a mixed boundary condition using non-dimensional dynamic influence functions Journal of Sound and Vibration 256 533-549
12345678910