摘要
The eigenvalue problem for the Hamiltonian operator associated with the mathematical model for the deflection of a thin elastic plate is investigated.First,the problem for a rectangular plate with simply supported edges is solved directly.Then,the completeness of the eigenfunctions is proved,thereby demonstrating the feasibility of using separation of variables to solve the problem. Finally,the general solution is obtained by using the proved expansion theorem.
The eigenvalue problem for the Hamiltonian operator associated with the mathematical model for the deflection of a thin elastic plate is investigated.First,the problem for a rectangular plate with simply supported edges is solved directly.Then,the completeness of the eigenfunctions is proved,thereby demonstrating the feasibility of using separation of variables to solve the problem. Finally,the general solution is obtained by using the proved expansion theorem.
基金
supported by the National Natural Science Foundation of China(Grant No.10962004)
the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20070126002)
the Natural Science Foundation of Inner Mongolia(Grant No. 20080404MS0104)
the Research Foundation for Talented Scholars of Inner Mongolia University(Grant No. 207066)
