Computational technique to free vibration response in a multi-degree of freedom parametric system

Abstract

The free vibration response is helpful to understand the dynamic characteristics of parametric system, and further could be used as important information source for the failure diagnosis and health monitoring of structure. In this paper, the free vibration response of a multi-degree of freedom (MDOF) parametric system is approached as a closed-form solution, a special trigonometric series with a linear combination of the principal oscillation frequency and the parametric excitation frequency. By algebra operation of harmonic balance, the parametric equation can be transformed into a linear homogeneous algebraic equation, on which the characteristic equation is determined and some important solutions are given. Main contribution of the presented technique is that it not only solves the computational problem of principal oscillation frequencies and modes with high computational accuracy, but also gives the splitting mode, which is the amplitude ratio of the combined harmonic resonance in the parametric system. Besides, the mathematical approximation reflects the physic characteristics in the free vibration response of parametric system. An example of real life is used to illustrate the applicability of the presented computational technique. The more expansion terms in approximation series, the smaller the computational error. Therefore, the given approximation provides a powerful computational tool for the free vibration response in the MDOF parametric system.