简支多边形薄板振动问题的准格林函数方法  

Green quasifunction method for vibration of simple-supported thin polygonic plates

作　　者：李善倾[1] 袁鸿[1] 

机构地区：[1]暨南大学应用力学研究所,广东广州510632

出　　处：《暨南大学学报（自然科学与医学版）》2007年第1期36-39,共4页Journal of Jinan University(Natural Science & Medicine Edition)

基　　金：暨南大学广东省高校<工程结构故障诊断>重点实验室开放基金项目(2005)

摘　　要：提出一种新的数值方法——准格林函数方法.以简支多边形薄板的振动问题为例,详细阐明了准格林函数方法的思想.即利用问题的基本解和边界方程构造一个准格林函数,这个函数满足了问题的齐次边界条件,采用格林公式将薄板振动问题的振形控制微分方程化为两个耦合的第二类Fredholm积分方程.边界方程有多种选择,在选定一种边界方程的基础上,可以通过建立一个新的边界方程来表示问题的边界,以克服积分核的奇异性;最后由积分方程的离散化方程组有非平凡解的条件,求得固有频率.数值算例表明,该方法具有较高的精度.A Green quasifunction method is proposed. The idea of this method is clarified by taking a vibration problem of simply-supported thin polygonic plate. The Green quasifunction is established by using the fundamental solution and boundary equation with a homogeneous boundary condition. The mode shape differential equation of vibration problem of the plate is reduced to two simultaneous Fredholm second kind integral equations 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 overcame, Finally, natural frequency is obtained by the existence condition of nontrivial solution of the discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the method proposed.

关 键 词：格林函数 积分方程 薄板 自由振动 

分 类 号：O326[理学—一般力学与力学基础]