Z型折叠板内共振下非线性振动特性研究

摘要

Z型折叠板是一类复杂多体结构,在工程实际中应用广泛.以大型的空间可展开结构为实际工程背景,考虑了Z型折叠板折叠过程中各部件的运动耦合关系,基于Reddy经典板理论和von-Karman几何非线性应变位移关系,利用Hamilton原理建立了Z型折叠板的非线性动力学控制方程.利用有限元分析得到了Z型折叠板结构的模态函数,运用二阶Galerkin截断,得到了Z型折叠板二自由度的非线性常微分方程.考虑系统主参数共振-1∶2内共振的情况,通过摄动分析得到系统四维直角坐标形式的平均方程,最后利用数值模拟方法研究了横向激励对Z型折叠板非线性动力学特性的影响.%The Z type folding plate is a kind of complex multi-body structure,which is widely applied to many engineering fields.Based on the classical laminated plate theory and the yon Karman type equation,the nonlinear dynamic equations of the Z-type folding plates are obtained by using the Hamilton's principle.The mode functions of the Z-type folding plates are analyzed with the ANSYS.Then,the Galerk in procedure is used to obtain the normal differential governing equations of the nonlinear system.The case of primary parametric resonance 1 ∶ 2 inner resonance is considered.Based on the averaged equation obtained with the method of multiple scales,the numerical simulation is performed to indicate the nonlinear dynamical chara-teristics of the system.