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对于复杂边界条件下的有抗弯刚度的拉索结构,其特征方程为超越方程,无法获得解析的频率表达式。文章针对此问题,提出了一种矩阵分析方法:首先建立动力学平衡方程,考虑边界条件,推导了特征方程的解析表达式;在此基础上,采用数值方法在给定的频率区间上求解特征方程的根,从而获得结构的固有频率解。该方法可将索的抗弯刚度、一般边界条件一并考虑,得到统一的求解方法。以实际索为例,对其动力特性进行了分析,并与有限元结果相比。结果表明,该方法的求解速度快、精度高,具有推广应用的价值。
For the cable structure with flexural rigidity under complex boundary conditions, the characteristic equation is transcendental equation, and the analytic frequency expression can not be obtained. In order to solve this problem, a matrix analysis method is proposed in this paper. Firstly, a dynamic equilibrium equation is established and the analytical expression of the characteristic equation is derived by considering the boundary conditions. On the basis of this, a numerical method is used to solve the characteristic in a given frequency range The root of the equation, so as to obtain the structure of the natural frequency solution. The method can take the bending stiffness of the cable and the general boundary conditions into consideration, and obtain a uniform solution method. Taking actual cable as an example, its dynamic characteristics are analyzed and compared with the finite element results. The results show that the method is fast, accurate and has the value of popularization and application.