摘要
在Hamilton辛对偶力学体系下,给出了求解一对边简支平面自由振动问题精确解的一般方法,并用该方法求得了一对边简支另一对边固支的矩形平面自由振动问题的精确解.首先用空间变量分离方法,求解矩形域平面自由振动问题的Hamilton正则方程,得到两个坐标方向的本征值关系;再利用Hamilton算子矩阵本征向量之间的共轭辛正交关系,得到广义振型函数向量的一般表达式;最后引入边界条件确定了两个空间本征值、频率方程和广义振型函数向量;讨论了固有振动频率与空间本征值的对应关系.把辛对偶方法和经典方法进行了比较,结果说明了本文方法的正确性和普适性.
In Hamiltonian symplectic dual system, the general method for solving exact solutions of free vibrations of rectangular plane problem with two opposite edges simply-supported are given directly by solving the Hamiltonian canonical equations using separation-of-variables method, and the analytical expressions of mode function and frequency equation of rectangular plane problem with two opposite edges simply-supported and the other two opposite edges clamped are obtained. The corresponding relationships of the two spatial eigenvalues with natural frequency are derived and discussed, and the generalized mode function vectors are obtained by using the conjugate symplectic ortho-normalization relationship of eigenvector. Based on boundary conditions, the exact frequency equations, two spatial eigenvalues and coefficients of generalized mode function are determined. Finally, present method is compared with the method based on Lagrange system, the correctness and universality of present method are validated.
作者
邢誉峰
张慧敏
钱志英
XING YuFeng ZHANG HuiMin QIAN ZhiYing(Institute of Solid Mechanics, Beihang University, Beijing 100183, China China Academy of Space Technology, Beijing 100094, China)
出处
《中国科学：技术科学》
EI
CSCD
北大核心
2016年第12期1219-1224,共6页
Scientia Sinica(Technologica)
基金
国家自然科学基金(批准号:11172028
1372021)
高等学校博士学科点专项科研基金(编号:20131102110039)资助项目
