Forced vibration analysis for two-degree-of-freedom spring-mass system with gap

Abstract

Collision vibration systems are usually modeled as a nonlinear spring whose characteristics are described by the broken line model. These systems are called piecewise-linear systems. A piecewise-linear system is highly nonlinear, and it is usually difficult to predict the system response using any general analytical solution. If the effects of design parameters such as clearance size and dynamic nonlinearity of the systems are known, the structures can be designed to be safer and more comfortable. This paper deals with forced collision vibration in a mass-spring system for two-degree-of-freedom. The analytical model is mass-damper-spring system having two masses in which one mass is subjected to an exciting vibration with arbitrary functions. Then the restoring force, which has characteristics of an asymmetric piecewise-linear system, collides elastically to another mass when amplitude of the mass increases farther than clearance. In order to analyze resulting vibration and colliding force, the Fourier series method is applied and analytical solutions for this system are derived. Next, following the analytical solutions, numerical calculations are performed. Effects of amplitude ratio of excitation, nonlinearity of the system and mass ratio on the resonance curve and colliding force are shown numerically. For verification of the analytical solutions, numerical simulations are performed by the Runge-Kutta method, and numerical results based on analytical solutions are compared with numerical simulation results. As a result, the analytical solutions are in a fairy good agreement with the numerical simulation results.