Targeted Energy Transfer Evaluation for Nonlinear Vibrations of Elastic Medium-Finite Length Beam System Using Nonlinear Energy Sink Theory

Abstract

The elastic medium can usually reduce the vibration of supporting structure, and the impact of the interaction on the vibration characteristics of the structure is similar to the characteristic of nonlinear energy sink. At present, the dynamic research of beam on elastic foundation considering soil motion has been paid more and more attention. According to the modified Winkler model, the finite-depth elastic medium can be considered to the nonlinear energy sink mass, and the vibration energy dissipation capacity and parameter optimization of the elastic medium supporting finite-length beam under half sine pulse are studied. The Galerkin truncation is applied to the discretization of the governing equations. The numerical solution of the beam coupling system with simple support on the elastic medium is obtained by applying the fourth-order Runge–Kutta method. Based on this, the input energy ratio of the elastic medium dissipation is investigated. Furthermore, through the analysis and optimization of targeted energy transfer and dissipation, the dissipation effect of the finite range elastic medium on the vibration energy of its supporting beam is revealed, and the optimal parameter range of the elastic medium is proved. The results show that after adjusting the elastic medium parameters by technical means, the nonlinear energy sink can absorb most of the vibration energy of the beam quickly and effectively, and the optimal energy dissipation ratio can reach 95.16[Formula: see text]. The quantitative evaluation of the energy dissipation in elastic medium within soil–structure interaction effect is realized.