悬索非线性动力学中的直接法与离散法

以悬索为例对结构非线性动力学中直接法与离散法的应用进行了研究. 针对悬索面内运动的第$n$阶模态的主共振，分别利用这两种方法对悬索的非线性响应进行求解，得到悬索非线性响应的二次近似解以及相应的幅频响应曲线，并比较和讨论了这两种方法得到的结果及其差异. 通过分析得知：离散法在用于非对称结构非线性动力学的求解时可能导致错误的结果.

Direct treatment and discretizations of non-linear dynamics of suspended cable

The applications of direct treatment and discretizations of non-linear dynamics are investigated in this paper. These two approaches are applied to attack the primary resonance of the nth mode of suspended cables. These lead to obtain the second order approximate solutions and the associated frequency-response curves. The results obtained with these two approaches are compared. And the differences of these results are discussed. Finally, the results are obtained that the discretization of nonlinear dynamic of non-symmetric structure may lead to erroneous results.