Numerical analysis of the dynamic characteristics of rotating deformed structures

Abstract

This study presents an algorithm based on the finite element method for the numerical solution of the problem on free and forced vibrations of rotating dynamically symmetric bodies. To obtain all the information on «the dynamic passport of a system», in addition to the problem on free and forced vibrations of rotating elastic bodies it is necessary to consider the non-conservative elastic stability problem. Judging from the character of the found eigen values, the conclusion can be drawn regarding the stability of the system, for instance in the framework of Lyapunov's theorems on stability in a first approximation/ It is proposed to seek the eigen modes of the non-conservative problem in the form of an expansion in eigen modes of the conservative problem, which reduces the dimensionality of matrices and allows us to solve the complex eigen value problem using the developed and verified schemes. The amplitude-frequency characteristics of the non-conservative system are constructed for different values of the angular velocity parameter referred to stable and unstable modes.