Essentially nonlinear piezoelectric shunt circuits applied to mistuned bladed disks

Abstract

An essentially nonlinear piezoelectric shunt circuit is proposed for the practical realization of nonlinear energy sink, and then applied to a mistuned bladed disk for blade vibration reduction. First, the global dynamics of a single degree-of-freedom linear mechanical oscillator, coupled to an essentially nonlinear shunted piezoelectric attachment, is studied. Under certain conditions, the nonlinear targeted energy transfer, i.e. a fast, passive energy transfer from the mechanical oscillator to the nonlinear attachment is observed. A numerical method, referred to as the variable-coefficient harmonic balance method, is developed to calculate quasi-periodic responses arising in the electromechanical system under harmonic forcing. Characterized by the nonexistence of a resonance frequency, the essentially nonlinear shunt circuit is able to work robustly over a broad frequency band with a smaller inductance requirement compared with the linear resonant shunt circuit. The application of piezoelectric shunt damping to simplified blade–disk structures is then taken into consideration. Shunted piezoelectrics are attached onto the disk surface in our damping strategy in order to reduce blade vibrations. Essential nonlinearity is also introduced into the piezoelectric shunted bladed disk system. Since the piezoelectric-based nonlinear energy sink is not a priori tuned to any specific frequency, a sound damping performance is achieved when blades become inevitably mistuned.