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

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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.

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Authors and Affiliations

  1. School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo, Shandong Province, 255049, China

    Lei Li & Hanbiao Liu

  2. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Lei Li & Wenming Zhang

  3. Tianjin Key Laboratory of High Speed Cutting and Precision Machining, Tianjin University of Technology and Education, Tianjin, 300222, China

    Jianxin Han

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  1. Lei Li
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  2. Hanbiao Liu
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Correspondence to Wenming Zhang.

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Citation: LI, L., LIU, H. B., HAN, J. X., and ZHANG, W. M. Nonlinear modal coupling in a T-shaped piezoelectric resonator induced by stiffness hardening effect. Applied Mathematics and Mechanics (English Edition), 43(6), 777–792 (2022) https://doi.org/10.1007/s10483-022-2861-6

Project supported by the National Natural Science Foundation of China (No. 11902182), the Program of Shanghai Academic/Technology Research Leader of China (No. 19XD1421600), the China Postdoctoral Science Foundation (No. 2019M651485), the Natural Science Foundation of Shandong Province of China (No. ZR2019BA001), and the Natural Science Foundation of Tianjin of China (No. 20JCQNJC01070)

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Li, L., Liu, H., Han, J. et al. Nonlinear modal coupling in a T-shaped piezoelectric resonator induced by stiffness hardening effect. Appl. Math. Mech.-Engl. Ed. 43, 777–792 (2022). https://doi.org/10.1007/s10483-022-2861-6

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  • DOI: https://doi.org/10.1007/s10483-022-2861-6

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