Enhanced Super-Harmonic Resonance in Piezoelectrically Laminated Curved Microbeam Resonators Under Fringing-Field Electrostatic Actuation

Abstract

Achieving low-frequency MEMS resonators while maintaining the compact size of MEMS sensors has long been a challenge in MEMS design and fabrication. This study focuses on the super-harmonic resonance regions and associated bifurcation points of a curved microbeam sandwiched between two piezoelectric layers and subjected to fringing-field electrostatic actuation. The nonlinear equations of motion are derived, and the dependence of the electrostatic force on displacement is analysed using a finite element approach. The microbeam is excited by a combination of DC and AC electrostatic actuation, along with a tuning DC piezoelectric voltage. The influence of the piezoelectric voltage on the variation of the natural frequency under a given DC electrostatic excitation is examined. The frequency response curves are obtained over a broad excitation range, extending from below the primary resonance, through the super-harmonic regime, and beyond the primary resonance region. Bifurcation points are identified using Floquet multipliers. The results indicate that strong quadratic and cubic nonlinearities lead to the emergence of super-harmonic resonance zones of orders 1/2 and 1/3 in the frequency response, enabling the development of low-frequency resonators while retaining the advantages of MEMS-scale sensors. This effect is particularly significant in the design of MEMS energy harvesters, facilitating energy extraction from low-frequency mechanical noise. The simultaneous presence of nonlinearities of orders 1/2 and 1/3 and even higher orders generates multiple resonance zones within the super-harmonic regime, enabling the design of broadband low-frequency energy harvesters and MEMS wide-bandpass filters.

Keywords: Nonlinear Dynamics, Super-harmonic secondary resonance, Low-frequency MEMS resonators, Initially curved microbeam, Fringing-field electrostatic actuation, Piezoelectric actuation