应用数学2018，Vol.31Issue(3)：674-682,9.
双参数弹性地基上正交各向异性矩形薄板自由振动问题的Hamilton方法
Free Vibration Problems of Orthotropic Rectangular Thin Plates on Two-Parameters Elastic Foundation by the Hamiltonian Method
摘要
Abstract
In this paper,the free vibration equations of orthotropic rectangular thin plates are trans-formed into Hamiltonian system by using pseudo-division algorithm for matrix multi-variable polynomial. And Hamiltonian operators are obtained by means of separation of variables method. By calculating, the eigenvalues and eigenvectors of the Hamiltonian operators for the problem with two opposites simply supported are derived. Then,the symplectic orthogonality and the completeness of the eigenvectors(in the sense of Cauchy's principal value)are proved. Based on the completeness of the eigenvectors,the general solutions of the Hamiltonian systems are obtained and the general solutions of orthotropic rectangular thin plates on two-parameters elastic foundation with two opposites simply supported can be obtained. Furthermore, two examples are given to illustrate that the frequency and deflection of the free vibration problems are directly solved by the present method.关键词
正交各向异性板/Hamilton系统/自由振动/双参数弹性地基/完备性Key words
Orthotropic rectangular thin plate/Hamiltonian system/Free vibration/Two-parameters elastic foundation/Completeness分类
数理科学引用本文复制引用
赵琴,额布日力吐..双参数弹性地基上正交各向异性矩形薄板自由振动问题的Hamilton方法[J].应用数学,2018,31(3):674-682,9.基金项目
国家自然科学基金项目(11362011,11761052) （11362011,11761052）
