Optimal Design of Parameters in Nonlinear Energy Vibration Impact attached to a beam

In this paper, to reduce the energy of an underwater beam, a vibro-impact nonlinear energy sink is used and the force due to water is considered as a sinusoidal harmonic force and a constant load. A nonlinear energy sink consists of a cavity and a ball in the cavity. First, the governing equations for the beams and the nonlinear energy sink are obtained. With optimization, the minimum time to transfer 95% of the energy of the beam to the absorber is obtained. To optimize the four parameters of cavity length, the mass ratio of the nonlinear energy sink and the beam, restitute coefficient, and adsorbent position on the beam, which is the first time that all parameters of vibro-impact nonlinear energy sink are considered for optimal design. In the following, each of these parameters is considered, and the optimal value for each of these parameters is calculated. Finally, it is shown that the dynamic response of the system with two impacts per cycle (symmetric) is the most optimal response of the system.