中文摘要：

针对可展结构中铰链带来的展开后非线性动力学问题,建立了含铰结构的动力学模型.基于铰链侧向和径向的几何约束关系,分析了不同约束条件下的铰链非线性特性.基于谐波平衡法（HBM）,对含铰结构的非线性变量进行一次谐波展开,得到铰链非线性力的谐波展开表达式,将含铰可展结构的非线性动力学方程转化为代数方程.分析了铰链在不同非线性特性下各参数对结构动态特性的影响,得到结构固有频率随铰链间隙、刚度和激振力的变化规律.考虑铰链的非线性特性,通过固有频率脊线求解,得到结构固有频率极值随铰链数量、位置和刚度的变化曲面,并对其进行非线性拟合,得到铰链参数对结构固有频率的影响函数,其计算方法和结果在多维复杂结构中具有一定的扩展性,为可展结构的设计和研究提供参考.利用龙格库塔法对非线性结构进行数值仿真,得到结构的固有频率变化曲线,仿真结果表明了利用HBM进行含铰结构动力学分析的正确性.

英文摘要：

A dynamic model of articulated structures is proposed in view of the nonlinear dynamic characteristics of deployable structures caused by joints.Based on the lateral and radial geometric constraints of joints,the nonlinear characteristics of different size joints can be analyzed.The harmonic expressions of articulated structure parameters with nonlinear characteristics are obtained by using harmonic balance method （HBM）.The expression can be introduced into the dynamic analysis of deployable structures for the purpose of converting the nonlinear dynamic equation of deployable structure into nonlinear algebraic equation.The effects of joints parameters on the dynamics of deployable structures are analyzed when the joints characteristics are changed.The natural frequency variation of structure with joints clearance,joints stiffness and excitation force is got.Considering the nonlinear characteristics of joints,the change law of natural frequency of structures with joints location and number is analyzed by solving the natural frequency ridge of structures.The influence function of the joints location and number upon the natural frequency of articulated structures is built,which can be extended to multi-dimensional and complex structures and can provide a method for the design and research of deployable structure.Runge-Kutta method is adopted to analyze the nonlinear structure to get the amplitude-frequency curve.The numerical results can validate the HBM for dynamic simulation of articulated structures.