Development of Algorithm for Vibration Analysis with High Speed and with High Accuracy

本文采用传递影响系数法，将直线结构、多层结构、二维和三维树形结构以及力学特性连续变化的变参数系统的弯曲横向线性自由振动视为集中质量系统和分布质量系统。传递影响系数法的算法基于动态影响系数逐次传递的概念。该方法具有以下优点：(1)利用线性弹簧常数和旋转弹簧常数统一了边界条件；(2)简化了编程，不需要对具有中间刚性支撑的结构进行特殊处理；(3)相对于使用等分法，基于频率方程中产生的极点的发生机制，可以简单地消除假根。并将该方法应用于直线结构的线性受弯振动和直线结构的非线性振动分析。为了分析非线性振动系统，采用增量法将谐波平衡法的概念与传递影响系数法的概念相结合，提出了一种新的分析方法——增量传递影响系数法。在个人计算机上比较简单的算例结果表明，与常用的传递矩阵法相比，该方法具有较高的数值精度和较高的计算速度。

In this investigation, the flexural lateral linear free vibrations of straight line structure, multiple layered structure, two and three dimensional tree structure and systems with variable parameters mechanical characteristics of which change continuously were treated regarded as the lumped mass system and the distributed mass system, using the transfer influence coefficient method. The algorithm of the transfer influence coefficient method is based on the concept of the successive transmission of the dynamic influence coefficients.The present method has the following advantages : (1) The unification of the boundary conditions by virtue of the linear and rotational spring constants, (2) simplification of the programming and absence of the need for special treatment for a structure with intermediate stiff supports, and (3) a simple approach to eliminate the false roots based on the occurrence mechanism of the poles generated in the frequency equation relative to the use of the bisection method.Furthermore, the present method was applied to the analysis of the linear flexural forced vibration for a straight line structure and the nonlinear vibration for a in-line structure. To analyze the nonlinear vibration systems, incremental transfer influence coefficient method was anew presented as a analytical method which combined the concept of the method of harmonic balance with the one of the transfer influence coefficient method by using the incremental method.The results of the comparatively simple computational examples on a personal computer demonstrate the validity of the present algorithm, that is, the high numerical accuracy and the high speed of the present method, as compared with the transfer matrix method by which the vibration analysis is often carried out.