广义边界梁的动力学建模与动态特征  

Dynamic Modeling and Modal Analysis of a Beam with Generalized Boundary Conditions

作　　者：肖世富[1] 陈学前[1] 刘信恩[1] 

机构地区：[1]中国工程物理研究院,绵阳621900

出　　处：《应用力学学报》2009年第4期628-632,共5页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金-中国工程物理研究院联合基金(10876100);中国工程物理研究院双百人才基金(ZX04002)

摘　　要：对于广义边界条件Euler-Bernoulli梁,采用相对描述方式建立了可描述梁整体运动和相对变形的几何非线性及其线性化动力学模型,应用线性变换得到了该类梁的线性经典动力学方程,得到了广义边界条件下梁的横向振动代数特征方程、特征函数及特征值的退化表达式。算例分析了边界小扰动对固支-固支梁横向振动特征的影响规律。For Euler-Bernoulli beam with generalized boundary conditions, a nonlinear dynamic model with large deformation and the corresponding linearized equation are established in relative description by Hamilton form of the principle of least action. Both the nonlinear and linear models can describe the overall motions and relative vibrations of Euler-Bernoulli beam. And the flexural vibration equation in the linear coupling model is linearly transformed to the classical flexural vibration equations of Euler-Bernoulli beam with generalized boundary conditions. Algebra eigenvalue equation, eigenfunctions and simplified eigenvalue expressions of the beam flexural vibration are analytically obtained. Based on the simplified eigenvalue expressions, the flexural vibration eigenvalues with estimations of error bounds are provided for the beam with classical boundary conditions in appendix. As examples, the flexural vibration characteristics affected by little change of the fixed-fixed boundary condition are analyzed by perturbed method.

关 键 词：EULER-BERNOULLI梁 广义边界条件 相对描述 特征方程 特征值 

分 类 号：O324[理学—一般力学与力学基础]