矩形中厚板自由振动问题的辛本征展开定理

研究了矩形中厚板自由振动问题导出的一个Hamilton算子的本征值问题.在广义位移与内力构成的混合边界条件下,首先求解了相应算子的本征函数.接着,证明了本征函数系的完备性,这为使用分离变量法求解相应问题提供了可行性.最后,根据文中证明的展开定理获得了问题的一般解,并给出了具体的数值算例.

Symplectic eigenfunction expansion theorem for free vibration of moderately thick rectangular plates

The eigenvalue problem of the Hamiltonian operator associated with the free vibration of a moderately thick rectangular plate was investigated.First,the eigenfunctions of the operator with the mixed boundary conditions of the generalized displacements and generalized internal forces were solved directly.Then,the completeness of the eigenfunctinons was proved, demonstrating the feasibility of using separation of variables to solve the problems.Finally,the general solution was obtained by using the proved expansion theorem,and a concrete numerical example was given.