求解结构自振频率的精细传递矩阵法

Precise transfer matrix method for resolving natural frequencies of structures

将高精度的精细积分法和力学概念清晰的传递矩阵法结合起来,以微分方程和矩阵分析理论为基础,提出了一种新的精细传递矩阵形式,并用于求解结构自振频率。推导了该方法的计算公式。与传统的传递矩阵法相比,无需对微分方程进行求解,只需按照迭代公式进行计算,就可以得到所需要的传递矩阵。提出的方法虽然是条件稳定的,但是稳定性条件极易满足。算例表明本方法具有较高的精度和效率。可以对任意结构进行自振频率求解。

This paper combines the high-precision integration with the clear concept of transfer matrix method, based on the theory of differential equations and matrix analysis, provides a new precise transfer matrix form, then it is applied to solve the natural frequencies of a structure. The calculation formula of the method is derived. Comparing with the traditional transfer matrix method, this method needs not to solve the differential equations, but just follows the iterative formula to get the necessary transfer matrix, and based on the search method it can to get the natural frequencies of structures. Although the method is conditional stable, the stable condition is easy to meet. Examples show that this method is effective and high-precision. It can solve the natural frequency of any structure.