Linear and Nonlinear Analysis of Piezoelectric Based Vibration Absorber with Acceleration Feedback

In the present paper, analysis of a single degree of freedom spring-mass-damper primary system with a piezoelectric based dynamic vibration absorber (DVA) is carried out. The proposed DVA model consisting of a lead zirconate titanate (PZT) actuator which is connected in series with a spring. The analysis is done in two section by considering a static force and a harmonic force acting on the primary system respectively. In the first section linear stiffness is considered in the primary mass and in the second section cubic nonlinear stiffness along with the linear stiffness is considered. The voltage applied to the stack PZT actuator is considered to be proportional to the acceleration of the primary mass. Method of multiple scales (MMS) is used to obtain the system response in the nonlinear analysis and compared with linear analysis. For linear system optimum system parameters of the absorber are obtained using fixed point theory of optimization and Routh's stability criterion is used for stability analysis. Primary resonance condition is studied in the nonlinear analysis. In the proposed model as a spring is connected in series with PZT actuator for which force developed by the absorber to suppress the vibration of the primary system is not solely depend upon the voltage, so one can use small voltage to reduce the vibration of primary system.