Nonlocal wave propagation in double bonded Visco-elastically micro plate embedded in Visco-Pasternak foundation and electric field

The three-dimensional wave propagation of double bonded viscoelastically micro Polyvinylidene fluoride (PVDF) plate is presented. In order to obtaining frequency of wave propagation, an analytical approach is applied. The coupled plates is surrounded by Visco-Pasternak foundation. Quasi-3D sinusoidal shear deformation plate theory (Quasi-3D SSDPT) of thick plates is employed to account for the effect of transverse shear and bending deformation of the plates. To simulate the real behavior of viscoelasticity property, Kelvin-Voigt model is used. Material properties of micro plates are assumed have piezoelectric property, therefore electro field can be utilized as a controlling parameter. Strain energy, kinetic energy and work of external forces are calculated. Then, based on the nonlocal piezoelasticity theory and Hamilton s principle the equations of motion are obtained. Finally, the effects of external voltage and damping coefficient of micro plate on frequency of system will be studied. After that, dimensionless frequency, cut-off frequency and escape frequency of system is plotted for different types of wave propagation in system, such as inphase, out-of-phase and one of plate fixed. Results show out-of-phase type has more remarkable effect on frequency of system in comparison with inphase and one of plate fixed. Results of this study can be applied for optimum design of smart micro plates as micro-electro-mechanical sensors and actuators.