Multi-objective optimization research on nonlinear energy sink system of finite-length beam on elastic medium

Based on the nonlinear dynamic model of the elastic medium-beam coupling system under a semi-sinusoidal pulse, this paper analyzes the influence of variations in nonlinear stiffness, damping coefficient, and mass ratio on the energy dissipation capacity and vibration suppression effect of the beam system. Since the frequency domain response function of nonlinear system often lacks an exact analytical expression, a second-order polynomial expression between the objective function and the various system parameters is established using the response surface method. Furthermore, with the aim of improving the vibration suppression effect and energy dissipation capacity of the nonlinear energy sink, a multi-objective optimization design of the system parameters is conducted using the non-dominated sorting genetic algorithm. By combining the non-dominated sorting genetic algorithm with the response surface method, the Pareto front with the objectives of maximum amplitude reduction percentage and maximum energy dissipation ratio are determined, obtaining a more accurate set of parameter solutions, which enables the nonlinear energy sinks to have better vibration suppression effect and energy dissipation capacity.