Nonlinear dynamics of a cantilevered piezoelectric rectangular plate with voltage excitation

2nd International Conference on Advances in Energy Resources and Environment Engineering

能源学;生态环境科学

Yang, J.H.^1,2 ; Zhang, W.^1 ; Yao, M.H.^1 ; Zhu, G.^2

College of Mechanical Engineering, Beijing University of Technology, Beijing, China^1

Beijing Vocational College of Agriculture, Beijing, China^2

关键词: Bifurcation diagram;    Four degree of freedom;    Hamilton's principle;    Partial differential;    Piezoelectric layers;    Piezoelectric plate;    Steady-state response;    Voltage excitations;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/59/1/012010/pdf
DOI  :  10.1088/1755-1315/59/1/012010

学科分类：环境科学（综合）

来源: IOP

【 摘 要 】

The nonlinear dynamics of a cantilevered piezoelectric rectangular plate are studied, which are simultaneously forced by the base excitation and the excitation loaded by piezoelectric layers. The nonlinear partial differential governing equations of motion for the system are established by using the Hamilton's principle. The Galerkin approach is used to discretize the partial differential equations to the ordinary differential equations with four-degree-of-freedom. Numerical simulations are presented to investigate the effects of the voltage excitation on the steady-state responses of the cantilevered piezoelectric plate. The bifurcation diagram of the system for w1, w2, w3, w4, via the voltage excitation amplitude is obtained. The motions of the system can be shown as follows: the chaotic motion → the multiple periodic motion → the periodic motion → the chaotic motion. Based on the above bifurcation diagrams, the voltage excitation amplitude are changed to obtain the waveforms, two-dimensional phase portraits, three-dimensional phase portraits and Poincare maps. The results show that the amplitude of the system can reduce effectively and keep the stability by adjusting the voltage excitation.