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

作　　者：卜中月 侯国林[1] BU Zhongyue;HOU Guolin(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China)

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021

出　　处：《内蒙古师范大学学报（自然科学版）》2024年第6期644-652,共9页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目“分块结构矩阵与Hamilton算子的拟谱理论研究”(12261064);“无界Hamilton算子谱的渐近性与广义本征函数系的块状基性质研究”(11861048);内蒙古自治区自然科学基金资助项目“弹性力学辛体系方法的理论与应用研究”(2021MS01004)。

摘　　要：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.

关 键 词：中厚板 部分弹性地基 Hamilton方法 自由振动 

分 类 号：O343.1[理学—固体力学]