梁的动力稳定性分析的有限元方法

Finite Element Method for Dynamic StabilityAnalysis of Beams

提出了对梁进行动力学稳定性分析的有限元方法──给出了单元质量矩阵，抗弯刚度矩阵，几何刚度矩阵及相应的Ｍａｔｈｉｅｕ方程，通过坐标变换消除了方程的动力与静力耦合，然后说明了由这种具有参数激励耦合的多自由度系统的Ｍａｔｈｉｅｕ方程求得系统一般参数共振及组合参数共振的过渡曲线的约束参数方法与多尺度方法。最后作为算例求出了均匀简支梁受简谐轴向力作用时的过渡曲线。

Finite element method for dynamic stability of beams is presented in this paper.The mass,stiff-ness as well as geometrical stiffness matrixes and corresponding Hill equation of parametrically excitedvibration of beams are given. By ccordinate transformation methed,the normal Mathieu equation ofmultidegrees of freedom systems is obtained.The method of strained parameters and the method ofmultiple scales for analysis of parametric resonance and combinational parametric resonance are given.Finally, parametrically excited vibration of a simple supporting beam is pressented as an example.