薄板自由振动虚边界元解法

New Approach to Free Vibration Analysis of Plate Using Virtual Boundary Element

依据虚边界元法思想 ,提出了一种求解薄板自由振动问题的新算法 .通过采用薄板弯曲问题的静力基本解建立了薄板自由振动问题的虚边界积分方程 ,及满足边界条件和域内点动力位移方程 ,将薄板自由振动问题转变为代数特征值问题 ,可直接求解 .与边界元直接法相比 ,本方法无需处理奇异积分 ,避免了“边界层效应” ,而且思想简单 ,计算省时、方便 .

Based on the virtual boundary element method,a new approach to free vibration analysis of plate is presented.The integration equations on the virtual boundary about plate vibration problems are established by employing the fundamental solution on the question of thin plate bending.By way of satisfying boundary conditions and dynamical displacement equations at each point in domain,the question to free vibration of plate can be turned into one of algebraic characteristic value,which can be solved directly.In comparison with the direct formulation of boundary element method,it is shown that the treatment of singular integration is rendered unnecessarily in the presented method.And the idea of this method is simple and the amount of the work a little.The example proved the efficiency and calculating precision of the method.