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

doi:10.1007/s10483-022-2861-6

Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (6): 777-792.doi: https://doi.org/10.1007/s10483-022-2861-6

• 论文 • 下一篇

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

Lei LI^1,2, Hanbiao LIU¹, Jianxin HAN³, Wenming ZHANG²

1. School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255049, Shandong Province, China;
2. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;
3. Tianjin Key Laboratory of High Speed Cutting and Precision Machining, Tianjin University of Technology and Education, Tianjin 300222, China

收稿日期:2022-01-21 修回日期:2022-04-12 出版日期:2022-06-01 发布日期:2022-06-11
通讯作者: Wenming ZHANG, E-mail:wenmingz@sjtu.edu.cn
基金资助:
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)

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

Lei LI^1,2, Hanbiao LIU¹, Jianxin HAN³, Wenming ZHANG²

1. School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255049, Shandong Province, China;
2. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;
3. Tianjin Key Laboratory of High Speed Cutting and Precision Machining, Tianjin University of Technology and Education, Tianjin 300222, China

Received:2022-01-21 Revised:2022-04-12 Online:2022-06-01 Published:2022-06-11
Contact: Wenming ZHANG, E-mail:wenmingz@sjtu.edu.cn
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)

摘要/Abstract

摘要： 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.

关键词: coupled vibration, resonator, nonlinear dynamics, bifurcation, hardening behavior, frequency comb

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

中图分类号:

74J10

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

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

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

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