双索单梁组合结构非线性动力特性

Non-linear dynamics of cable-stayed beams

为了研究双索单梁组合体系的非线性动力响应,基于该组合体系的连续模型,建立索-梁组合结构的运动方程,在对方程进行约化处理后,结合回传射线矩阵法求解了结构平面内线性特征模态,研究组合体系中索和梁之间的相互作用,并以此为基础采用一阶模态截断的方式构造了单自由度非线性方程,用于研究结构非线性动力响应.通过变量转换,应用同伦分析法给出了结构受外部简谐荷载作用下稳态周期解的级数解形式,求解结构在一阶共振频率附近的非线性频率振幅曲线,并通过数值算例讨论了各种参数对非线性动力特性的影响.结果显示:同伦分析法与其他方法相比,在计算强非线性问题时具有较大的优势.

The governing equations for the in-plane motion of a cable-stayed beam were obtained based on a continuum model.The linear eigenmodes were obtained via the method of reverberation-ray matrix after a standard condensation procedure,and the interaction between cable and beam was investigated.On basis of solution for the linear eignproblem,a single-degree-of-freedom non-linear model was then derived by the single-mode discretization.Though the variable transformation the homotopy analysis method was successfully applied to find the steady-state solution of the structure subjected to harmonic force,then the frequency-amplitude relations near primary resonance frequency were obtained to characterize the influence of various parameters on the non-linear dynamic behaviour of the system.The result show that the homotopy analysis method is more powerful the traditional perturbation method in strong non-linear problems.