3 / 2019-06-06 15:17:09

A Computational Technique for Free Vibration Response of a 2-DOF Parametric System

2DOF paranetric system, Free vibration response, Mode, Trigonometric series , Splitting mode

In this paper, the free vibration response of a two-degree-of-freedom (2-DOF) parametric system is investigated using a computational technique with special trigonometric series, and it can be approached with a closed-form solution. The proposed technique extends the concept of modulation feedback to the problem of 2-DOF parametric system, and a model approach for the free vibration response comes from an equivalent dynamic system. The characteristic equation is obtained by applying harmonic balance to a parametric equation, and the principal oscillation frequencies are computed. Computations of the modes and splitting modes are performed by operating on a mixed matrix. The arbitrary constants in the general solution are determined for given initial conditions. In this study, a real-world example of a coupled inverted-pendulum system is used to illustrate the applicability of the proposed approach. An interesting feature of this study is that the time-periodic coefficient creates a changeability of the mode of the 2-DOF parametric system and excites the splitting mode in the harmonic combination resonance. Numerical experiments show that the proposed computational technique not only has a high approaching accuracy but also reveals some new nonlinear phenomena in the parametric system, such as characteristics of the mode and splitting mode. Therefore, the presented technique is valuable for theoretical research and engineering applications of parametric systems.