Active Vibration Absorber for a Nonlinear System with Time-Delay Acceleration Feedback for Superharmonic and Subharmonic Resonance Conditions

Abstract

In the present work, dynamic analysis of a spring, mass, and damper-based nonlinear active vibration absorber, and a nonlinear primary system are carried out by time-delay acceleration feedback. The primary system is subjected to multi-harmonic hard excitation and parametric excitation. It is proposed to reduce vibration of both the primary system and the absorber by attaching a lead zirconate titanate (PZT) stack actuator connected in series with which it acts as an active vibration absorber. Due to the external excitation, strain is developed in the PZT sensor, which produces voltage and this voltage is converted into a counteracting force by the PZT actuator to suppress the vibration of the primary system. Second-order method of multiple scales (MMS) is used to obtain the approximate solution of the system. Frequency responses and time responses for the different parameter of the system are studied for simultaneous superharmonic and subharmonic resonance conditions.