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

摘要

A purely bending dynamic model considering clearance,stiffness and damping of joints and nonlinear cables was established to show the nonlinear dynamic characteristics of jointed deployable structures.Taylor series expansion of variables for the nonlinear differential equation and harmonic description of parameters were used to convert the nonlinear dynamic equation to a nonlinear algebraic one.The dynamic response of a deployable structure was computed with the iteration method.The numerical analysis with Runge-Kutta method for a deployable structure was performed,its results were compared with those using the incremental harmonic balance (IHB)method.The comparison showed the correctness of the IHB method.The IHB method was used to analyze the response stability for a deployable structure when exciting frequency changed using the nonlinear dynamic model.The stability of the deployable structure response was presented in a frequency range when clearance and stiffness of joints,exciting force and cable changed.It was shown that the IHB method is very effective for dynamic analysis of deployable structures with multi-DOF,and it provided a basis for further study of large-scale deployable structures with joints and cables.%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。