基于增量谐波平衡法的含索铰可折展桁架非线性动力学特性

为了揭示含索铰可折展桁架的非线性动力学行为,建立了考虑铰链间隙、刚度和阻尼及索非线性特性的可折展桁架纯弯曲动力学模型。对非线性动力学方程进行一次泰勒展开和参量的多次谐波描述,实现了非线性动力学方程到代数方程的转化,通过迭代进行非线性动力学系统的响应计算。并利用龙格库塔方法对非线性系统进行数值分析,与增量谐波平衡(IHB)法进行对比,验证了IHB法计算的正确性。以激振频率为变化参数,对悬臂支撑的含索铰桁架结构进行解的稳定性分析,得到铰链间隙、铰链刚度、激振力和索对结构响应稳定性的影响。基于IHB法可快速准确的进行多自由度可折展结构动力学求解,为研究大型折展桁架的动力学行为奠定了基础。

Nonlinear Dynamic Characteristics of Deployable Structures with Joints and Cables Based on the Incremental Harmonic Balance Method

A purely bending model considering the clearance, stiffness, damping of joints and nonlinear cables, is derived to show the nonlinear dynamic characteristics of jointed deployable structures. The Taylor series expansion of nonlinear differential equation and harmonic expansion of variables are used to convert the nonlinear dynamic equation to nonlinear algebraic one. The response of the deployable structures can be analyzed by iteration method. The numerical analysis by Runge-Kutta method for deployable structures is employed to validate the incremental harmonic balance (IHB) method. IHB method is used to analyze the stability of response for deployable structures when the exciting frequency changes, which is based on the nonlinear dynamic model. The stability of deployable structure response are presented in a frequency range when the clearance and stiffness of joint, exciting force and cable change. The IHB method can be used for multi-degree deployable structures to obtain the steady response and nonlinear dynamic characteristics, which provides a method for further research of the dynamics of jointed deployable structures.