Vibration of a Two-Layer Metal plus PZT Plate Contacting with Viscous Fluid

Abstract

The present work investigates the mechanically forced vibration of the hydro-elasto-piezoelectric system consisting of a two-layer plate elastic+PZT, a compressible viscous fluid, and a rigid wall. It is assumed that the PZT (piezoelectric) layer of the plate is in contact with the fluid and time-harmonic linear forces act on the free surface of the elastic-metallic layer. This study is valuable because it considers for the first time the mechanical vibration of the metal+piezoelectric bilayer plate in contact with a fluid. It is also the first time that the influence of the volumetric concentration of the constituents on the vibration of the hydro-elasto-piezoelectric system is studied. Another value of the present work is the use of the exact equations and relations of elasto-electrodynamics for elastic and piezoelectric materials to describe the motion of the plate layers within the framework of the piecewise homogeneous body model and the use of the linearized Navier-Stokes equations to describe the flow of the compressible viscous fluid. The plane-strain state in the plate and the plane flow in the fluid take place. For the solution of the corresponding boundary-value problem, the Fourier transform is used with respect to the spatial coordinate on the axis along the laying direction of the plate. The analytical expressions of the Fourier transform of all the sought values of each component of the system are determined. The origins of the searched values are determined numerically, after which numerical results on the stress on the fluid and plate interface planes are presented and discussed. These results are obtained for the case where PZT-2 is chosen as the piezoelectric material, steel and aluminum as the elastic metal materials, and Glycerin as the fluid. Analysis of these results allows conclusions to be drawn about the character of the problem parameters on the frequency response of the interfacial stress. In particular, it was found that after a certain value of the vibration frequency, the presence of the metal layer in the two-layer plate led to an increase in the absolute values of the above interfacial stress.