可伸缩复合材料悬臂梁的非线性动力学建模及分析

NONLINEAR DYNAMICS MODELING AND NUMERICAL ANALYSIS OF TELESCOPING-AND-TRANSLATING COMPOSITE LAMINATED CANTILEVER BEAM

首先,根据Reddy给出的考虑高阶剪切效应的层合理论,气动弹性活塞理论,利用Hamilton原理,对考虑采用基于活塞理论的一阶非线性气动力和面内参数激励的联合作用下的轴向可伸缩复合材料悬臂梁进行非线性动力学进行建模,得到其偏微分动力学控制方程.然后对控制方程无量纲化,利用Galerkin方法对控制方程进行了截断,得到三个可反映可伸缩悬臂梁横向振动的无量纲形式的常微分非线性动力学方程,只要选取适合的复合材料及其相关参数,使用数值方法就对模型在外伸和回收过程中的相关振动特性进行了分析.

Firstly, based on the Reddy higher-order shear deformation theory and the pneumatic elastic piston theory, the nonlinear governing equations of motion for an axially moving cantilever beam were established by using the generalized Hamilton＇s principle, and the first order nonlinear aerodynamic force and parametric excitation in-plane were obtained. After introducing dimensionless variables and parameters, the nonlinear governing equations became dimensionless equations. At last, according to Galerkin＇ s approach, the governing equations of motion were simplified to three ordinary differential nonlinear dynamic equations. As long as the suitable composite material and relevant parameters are given, the relevant vibration characters of the modeling during deployment and retrieval can be analyzed by using numerical method.