Nonlinear dynamics of a functionally graded piezoelectric micro-resonator in the vicinity of the primary resonance

TL;DR

This paper investigates the nonlinear behavior of a functionally graded piezoelectric micro-resonator near its primary resonance, highlighting how piezoelectric tuning and electrostatic actuation influence its dynamics and stability.

Contribution

It introduces a mathematical model for a piezoelectric micro-resonator with functional grading and analyzes its nonlinear dynamics near primary resonance using numerical methods.

Findings

Higher amplitude periodic orbits have smaller basins of attraction.

Piezoelectric actuation effectively shifts the resonance frequency.

The stability of periodic solutions depends on the amplitude and actuation parameters.

Abstract

This research is on the nonlinear dynamics of a two-sided electrostatically actuated capacitive micro-beam. The microresonator is composed of silicon and PZT as a piezoelectric material. PZT is functionally distributed along the height of the micro-beam according to the power law distribution. The micro-resonator is simultaneously subjected to DC piezoelectric and two-sided electrostatic actuations. The DC piezoelectric actuation leads to the generation of an axial force along the length of the micro-beam and this is used as a tuning tool to shift the primary resonance of the micro-resonator. The governing equation of the motion is derived by the minimization of the Hamiltonian and generalized to the viscously damped systems. The periodic solutions in the vicinity of the primary resonance are detected by means of the shooting method and their stability is investigated by determining the so-called Floquet exponents of the perturbed motions. The basins of attraction corresponding to three individual periodic orbits are determined. The results depict that the higher the amplitude of the periodic orbit, the smaller is the area of the attractor