Nonlocal Free Vibration Analysis of FG-Porous Shear and Normal Deformable Sandwich Nanoplate with Piezoelectric Face Sheets Resting on Silica Aerogel Foundation

The present work is devoted to the free vibration analysis of sandwich nanoplate with functionally graded porous core and piezoelectric face sheets. The rectangular elastic sandwich nanoplate is resting on silica aerogel foundation based on Vlasov's model foundation. Material properties of the core layer such as Young's modulus, shear modulus and density are supposed to vary along the thickness direction by means of uniform and nonuniform function. The governing equations of motion are derived from Hamilton's principle using sinusoidal shear and normal deformation theory. An iterative technique is presented to solve seven governing equations of motion. After all, the natural frequency verification with corresponding studies is surveyed. Eventually, the numerical results are scrutinized for plate aspect ratio, thickness ratio, nonlocal parameter, porosity index, Young's modulus and height of silica aerogel foundation. The numerical results indicate that the Young's moduli and height of silica aerogel foundation, porosity index of core layer, thickness ratio and nonlocal parameter have significant effects on free vibration response of the sandwich nanoplate.