Dynamics of cantilever plates and its hybrid vibration control

作     者：Bo Ni Chao Hu 

作者机构：School of Aerospace Engineering and Applied MechanicsTongji University Shanghai Institute of Spaceflight Fundamental Technology College of Civil Science and EngineeringYangzhou University 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2013年第29卷第5期

页      面：738-748页

核心收录：

学科分类：08[工学] 080101[工学-一般力学与力学基础] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China(10572045) 

主　　题：Cantilever plate Hamiltonian formulism - Dis- persion equations Modal control Elastic wave control - Hybrid control 

摘      要：Applying Lagrange-Germain＇s theory of elas- tic thin plates and Hamiltonian formulation, the dynamics of cantilever plates and the problem of its vibration control are studied, and a general solution is finally given. Based on Hamiltonian and Lagrangian density function, we can obtain the flexural wave equation of the plate and the relationship between the transverse and the longitudinal eigenvalues. Based on eigenfunction expansion, dispersion equations of propagation mode of cantilever plates are deduced. By satisfying the boundary conditions of cantilever plates, the natural frequencies of the cantilever plate structure can be given. Then, analytic solution of the problem in plate structure is obtained. An hybrid wave/mode control approach, which is based on both independent modal space control and wave control methods, is described and adopted to analyze the active vibration control of cantilever plates. The low-order （controlled by modal control） and the high-order （controlled by wave control） frequency response of plates are both improved. The control spillover is avoided and the robustness of the system is also improved. Finally, simulation results are analyzed and discussed.