Active Nonlinear Vibration Absorber for a Harmonically Excited Beam System

Abstract

An active nonlinear vibration absorber (ANVA) using displacement, velocity, and acceleration feedback from the absorber mass is proposed to reduce the vibration of an Euler–Bernoulli beam subjected to a harmonical point force. The ANVA comprises mass, linear spring, cubic nonlinear spring and actuator. The steady-state equation of the system is obtained by solving the governing differential equation by harmonic balance method. From the steady state equations, the stability and vibration reduction of the beam are investigated by frequency responses, time responses and phase portraits using Newton’s method and fourth-order Runge–Kutta method. The analysis is carried out by studying the effects of different feedback control gains and cubic nonlinear stiffness of the absorber to suppress the vibration of the beam for the first three modal frequencies under different boundary conditions, namely fixed-fixed, simply supported and cantilevered type. The performance of the absorber is found to be better with cubic nonlinear stiffness in the absorber which reduces the vibration of the beam more effectively than the linear passive or active vibration absorber.