Electro-Mechanical free vibrations analysis of composite rectangular piezoelectric nanoplate using modified shear deformation theories

The aim of this paper is to study the free vibration of composite rectangular piezoelectric nanoplate subjected to an electro-mechanical loading includes a biaxial force and an external voltage based on exponential shear deformation theory and trigonometric shear deformation theory in conjunction with the nonlocal elasticity theory under the simply supported boundary condition. The nonlocal theory states that stress at a point is a function of strains at all points in the continuum. The nonlocal elasticity theory becomes significant for small length scale in micro and nanostructures. In exponential shear deformation theory andtrigonometric shear deformation theory, exponential and trigonometric functions are used in terms of thickness coordinate to include the effect of transverse shear deformation and rotary inertia. Nonlocal elasticity theory is employed to investigate effect of small scale on natural frequency of composite rectangular piezoelectric nanoplate. It is assumed that the composite rectangular piezoelectric nanoplate made of PZT 4 composite piezoelectric material includes crystal compounds of Pb, Zr and Ti to achieve metal-ceramic and piezoelectric properties. The governingdifferential equations of the vibration of the composite rectangular piezoelectric nanoplate are derived by using the Hamilton’s principle, which are then solved by using the Navier method to obtain the natural frequencies of the composite rectangular piezoelectric nanoplate. The detailed parametric study is conducted to discuss the influences of the nonlocal parameter, biaxial force external electric voltage and geometrical ratios on the first six nondimensional frequencies of the composite rectangular piezoelectric nanoplate