Size-dependent modal interactions of a piezoelectrically laminated microarch resonator with 3:1 internal resonance

Abstract

The nonlinear interactions of a microarch resonator with 3:1 internal resonance are studied. The microarch is subjected to a combination of direct current (DC) and alternating current (AC) electric voltages. Thin piezoelectric layers are thoroughly bonded on the top and bottom surfaces of the microarch. The piezoelectric actuation is not only used to modulate the stiffness and resonance frequency of the resonator but also to provide the suitable linear frequency ratio for the activation of the internal resonance. The size effect is incorporated by using the so-called modified strain gradient theory. The system is highly nonlinear due to the co-existence of the initial curvature, the mid-plane stretching resulting from clamped anchors, and the electrostatic excitation. The eigenvalue problem is solved to conduct a frequency analysis and identify the possible regions for activating the internal resonance. The effects of the piezoelectric actuation, the electric excitation, and the small-scale effect are investigated on the internal resonance. Exclusive nonlinear phenomena such as Hopf bifurcation and hysteresis are identified in the microarch response. It is shown that by applying appropriate piezoelectric actuation, one is able to activate microarch internal resonance regardless of the initial rise level of the microarch. It is also disclosed that among all the parameters, AC electric voltage has the greatest effect on the energy exchange between the interacting modes. The results can be used to design resonators and internal resonance based micro-electro-mechanical system (MEMS) energy harvesters.