Dynamic Analysis of Active Vibration Absorber by Time Delay Acceleration Feedback Using Higher Order Method of Multiple Scales

Abstract

In the present work, analysis of a nonlinear active vibration absorber is carried out by time delay acceleration feedback. The primary system consisting of spring, mass and damper is subjected to multi harmonic and parametric excitation. It is proposed to reduce the vibration of both the primary system and the absorber by attaching a lead zirconate titanate (PZT) stack actuator connected in series with a spring in absorber configuration which act as an active vibration absorber. Due to the external excitation on the primary mass strain is developed in the PZT sensor, which produces voltage and this voltage converted to a counter acting force by the PZT actuator to suppress the vibration of the primary system. Second order method of multiple scales (MMS) is used to obtain approximate solution of the system to study frequency responses for simultaneous primary resonance, principal parametric and 1:1 internal resonance conditions. The analysis is performed for the mass ratio of 0.01 between the absorber and the primary mass.