Resonant analysis of systems equipped with nonlinear displacement-dependent (NDD) dampers

Abstract

Resonant analysis of a vibration system equipped with a nonlinear displacement-dependent (NDD) damper is investigated. The frequency of the external forcing is chosen to be close to the natural frequency of the system. The system is modeled and the approximate analytical solution of the governing equation is developed using the multiple scales method (MSM). Several case studies with various amounts of external force’s frequencies are performed to investigate the resonant excitation analysis. The proposed analytical solution is also verified by the fourth order Runge-Kutta method. Moreover, the performance of the used NDD damper is analyzed and compared with the ordinary linear damper through the same periodic resonant excitation. It is found that the NDD damper has a superior performance in reducing the vibration amplitude, compared to the traditional linear damper when resonance occurs. In addition, utilizing the NDD damper in the resonantexcited system provides a smaller force transmitted to the base than the system with the ordinary linear damper.