Semi analytical solution of coupled nonlinear differential equations of free vibration of 1-DOF system equipped with resilient impact damper using variational iteration method (VIM)
Restricted accessResearch articleFirst published online April, 2025
Semi analytical solution of coupled nonlinear differential equations of free vibration of 1-DOF system equipped with resilient impact damper using variational iteration method (VIM)
There are many sources of vibration in either industrial or homemade environments which must be controlled or reduced. Impact dampers (ID) are one of the passive techniques of the control techniques for reducing undesirable vibrations. The impact dampers are divided into two types, rigid and resilient. In the resilient impact damper, the equations of motion are a set of equations containing two coupled nonlinear ordinary differential equations that have no analytical solution. In this paper, semi analytical solutions of these coupled nonlinear equations are provided using variational iteration method (VIM). Three zones of impact damper effect on vibration reduction are introduced and discussed, impact zone, friction zone, and no-impact zone. The most effective of the impact damper in free vibration of the 1-DOF system is the damping inclination. The damping inclination is the decreasing rate of the amplitude of motion of 1-DOF system. The damping inclination of various resilient impact dampers is proposed. The results show the validation between the present study and previous studies.
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