Nonlinear modal coupling in a T-shaped piezoelectric resonator induced by stiffness hardening effect

doi:10.1007/s10483-022-2861-6

Abstract

Abstract: The nonlinear modal coupling in a T-shaped piezoelectric resonator, when the former two natural frequencies are away from 1:2, is studied. Experimentally sweeping up the exciting frequency shows that the horizontal beam exhibits a nonlinear hardening behavior. The first primary resonance of the vertical beam, owing to modal coupling, exhibits an abrupt amplitude increase, namely the Hopf bifurcation. The frequency comb phenomenon induced by modal coupling is measured experimentally. A Duffing-Mathieu coupled model is theoretically introduced to derive the conditions of the modal coupling and frequency comb phenomenon. The results demonstrate that the modal coupling results from nonlinear stiffness hardening and is strictly dependent on the loading range and sweeping form of the driving voltage and the frequency of the piezoelectric patches.

Key words: coupled vibration, resonator, nonlinear dynamics, bifurcation, hardening behavior, frequency comb

2010 MSC Number:

74J10

Lei LI, Hanbiao LIU, Jianxin HAN, Wenming ZHANG. Nonlinear modal coupling in a T-shaped piezoelectric resonator induced by stiffness hardening effect. Applied Mathematics and Mechanics (English Edition), 2022, 43(6): 777-792.

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References

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