Dynamics of the Mindlin plate and its modal vibration control

Abstract

Based on Mindlin’s theory of elastic thick plates and Hamiltonian formulism to structural vibration of cantilever plates, the solution of the problem is given. Using Lagrangian density function and Hamiltonian function, the flexural wave equation of plates is derived, and the relation of the transverse eigenvalue and longitudinal eigenvalue is given. Different from traditional engineering analysis, dispersion equations of the propagation mode of the Mindlin plate are deduced from the eigenfunction expansion method. By satisfying the boundary conditions of plates, the wavenumber of vibration modes in the plate structure can be obtained. The independent modal space control is applied to study the active vibration control of cantilever plates. Feedback gain is adjusted to change the eigenstructure of the original vibration system in order to improve the modal damping and stiffness of the system. The applicability of plates based on two theories (Mindlin’s theory and classical thin plate theory) is studied. Finally, the results are analyzed and discussed by numerical simulations.