Green quasifunction method for vibration of simply-supported thin polygonic plates on Pasternak foundation  

作　　者：袁鸿 李善倾 刘人怀 

机构地区：[1]Institute of Applied Mechanics,Jinan University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2007年第7期847-853,共7页应用数学和力学（英文版）

基　　金：Project supported by the Key Laboratory of Disaster Forecast and Control in Engineering,Ministry of Education of China the Key Laboratory of Diagnosis of Fault in Engineering Structures of Guangdong Province of China

摘　　要：A new numerical method-Green quasifunction is proposed. The idea of Green quasifunction method is clarified in detail by considering a vibration problem of simply-supported thin polygonic plates on Pasternak foundation. 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 vibration problem of simply-supported thin plates on Pasternak foundation is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the Green quasifunction method.A new numerical method-Green quasifunction is proposed. The idea of Green quasifunction method is clarified in detail by considering a vibration problem of simply-supported thin polygonic plates on Pasternak foundation. 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 vibration problem of simply-supported thin plates on Pasternak foundation is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equation, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the Green quasifunction method.

关 键 词：Green function integral equation vibration of thin plates Pasternak foundation 

分 类 号：TU470[建筑科学—结构工程]