论文部分内容阅读
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。
Aiming at the problems of unfolded nonlinear dynamics caused by hinges in a developable structure, a dynamic model of a hinged structure is established. Based on the geometrical constraint relationship between the lateral and radial directions of the hinge, the nonlinear characteristics of the hinge under different constraints are analyzed. Based on the Harmonic Balance Method (HBM), the harmonic variables of the hinge-containing nonlinear variables are first harmonic expanded to obtain the harmonic expansion expressions of the nonlinear force of the hinge, and the nonlinear dynamic equations of the hinged expandable structure are transformed into the algebraic equation. The influence of various parameters of the hinge on the dynamic characteristics of the structure under different nonlinearities is analyzed. The variation of the natural frequency of the structure with the clearance, stiffness and exciting force of the hinge is obtained. Considering the nonlinear characteristic of the hinge, the natural frequency ridge is solved by the natural frequency ridge to obtain the changing surface of the structure natural frequency extremum with the number, position and stiffness of the hinge, and nonlinearly fitting it to obtain the influence function of the hinge parameter on the natural frequency of the structure , The calculation methods and results have some extensibility in the multi-dimensional complex structure, which provides a reference for the design and research of the expandable structure. The non-linear structure is numerically simulated by Runge-Kutta method, and the natural frequency curve of the structure is obtained. The simulation results show the correctness of the dynamic analysis of the hinge-hinged structure by using HBM.