Free vibration analysis of nonlinear resilient impact dampers

In the present study, free vibration of a vibratory system equipped with an impact damper, which incorporates the Hertzian contact theory, is investigated. A nonlinear model of an impact damper is constructed using spring, mass, and viscous damper. To increase accuracy of the solution, deformation of the impact damper during the collision with and the main mass is considered. The governing coupled nonlinear differential equations of a cantilever beam equipped with the impact damper are solved using the parameter expanding perturbation method. Contact durations, which are obtained using the presented method, are compared with previous results. Gap sizes of the impact dampers are classified to two main parts. The effects of selecting the gap sizes regarding to the discussed classification are investigated on the application of the impact dampers. Based on types of collision between colliding masses, the so-called “effectiveness” is defined. Finally, it is shown variation of the damping inclination with the gap size is similar to variation of the effectiveness.