Parameters optimization of a nonlinear dynamic absorber for a nonlinear system

Abstract

One of the important methods to prevent the intensification of the main vibration system is using a dynamic vibration absorber (DVA). A DVA is a mechanical subsystem used to reduce Vibration amplitude and prevent the main vibration system from resonance. This paper aims to use a nonlinear dynamic absorber as a cantilever beam with a concentrated mass at its end to reduce the amplitude of the intensified oscillator vibration. The primary vibration system consists of mass, nonlinear spring, and viscous damping, and a harmonic excitation force is applied to it, resonance the system. In this case, using a nonlinear dynamic absorber reduces the vibration amplitude. For this purpose, first, the kinetic energy and the potential energy of the vibration system are calculated, and then, using Lagrange equations, the governing equations are extracted. Due to the nonlinearity of the equations of motion, the multiple scales method is used to solve the governing equations. In the results, the effect of nonlinear DVA on reducing the amplitude of intensified oscillator vibration is well visible. The effect of the main parameters of nonlinear dynamic absorbers on the vibration amplitude of the initial system is also investigated. Finally, the vibration amplitude of the system is optimized as a target function by the genetic algorithm method, and the optimal parameters of the nonlinear dynamic absorber and the optimal vibration amplitude are studied. Considering the main resonant vibration system as a structure under earthquake, the results of this research in reducing the vibration amplitude can be widely used in earthquake engineering.