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

作　　者：Lei LI Hanbiao LIU Jianxin HAN Wenming ZHANG 

机构地区：[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

出　　处：《Applied Mathematics and Mechanics(English Edition)》2022年第6期777-792,共16页应用数学和力学（英文版）

基　　金：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);the Natural Science Foundation of Tianjin of China(No.20JCQNJC01070)。

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 

分 类 号：TN751.2[电子电信—电路与系统]