Investigation of the effect of parameters of a nonlinear dynamic absorber on reducing the vibration amplitude of a nonlinear system

Purpose of paper is to use a nonlinear dynamic absorber as beam with concentrated mass at its end to reduce the amplitude of resonant nonlinear oscillator vibration. Primary vibration system consists of mass, nonlinear spring, and viscous damping, and harmonic force is applied to it and causes the system to intensify. Nonlinear dynamic absorber has been used to reduce vibration amplitude. First, the kinetic energy and potential energy of system are calculated, and then governing equations of the system are extracted using Lagrange's equations. To solve the governing equations, the method of multiple scales is used. Numerical solution, in the negligible case of considering the mass of the absorber and the stiffness of the nonlinear Duffing spring, the validation of results is done. The effect of nonlinear dynamic vibration absorber on reducing the amplitude of resonant oscillator vibration can be seen well. Influence of the main parameters of the nonlinear dynamic absorber on vibration amplitude of primary system is investigated.