部分弹性地基Mindlin板自由振动的Hamilton方法

Hamiltonian Method of Free Vibration for Mindlin Plates Partially Resting on the Elastic Foundation

采用Hamilton方法研究Pasternak型部分弹性地基上Mindlin板自由振动问题。引入合适的状态向量,将Mindlin板的控制微分方程转化为相应的Hamilton形式,进一步求解Hamilton算子的本征值和本征函数系,并给出具体的数值算例,数值模拟了部分弹性地基上板的固有频率。

Rectangular moderately thick plates are widely used in practice,and the vibration problem of elastic foundation is also the focus of many scholars.The Hamiltonian method was used in the paper for research of the free vibration of Mindlin plates partially resting on the Pasternak elastic foundation.Firstly,by introducing a suitable state vector,the governing differential equations of the Mindlin plates are transformed into the corresponding Hamiltonian form.And then,the eigenvalues and eigenfunction systems of the Hamiltonian operator are solved.Finally,some numerical examples are given to simulate the natural frequency of the plates on a partially elastic foundation.