On the vibrational behavior of three-layered higher-order smart porous microplates with nanocomposite piezoelectric patches

A porous microplate embedded with two nanocomposite piezoelectric layers is investigated in the current work. All three layers are functionally graded and completely attached to each other, and the microstructure lies on a bi-parameter elastic foundation that withstands shear and normal forces simultaneously. Also, an external voltage is subjected to the piezoelectric patches. The mentioned patches are reinforced with carbon nanotubes to enhance their electro-mechanical performance. A higher-order shear deformation theory and von Karman's assumptions are hired to demonstrate the kinematic relations. Next, applying Hamilton's principle and variational technique, the governing motion equations are derived with the help of the modified couple stress theory to capture the scale influence. To solve the system of differential equations, a closed-form Navier method is employed, and by ensuring the correctness of the results, then it turns to investigate the impact of different factors including porosity percentage and also pores' distribution patterns, nanotubes dispersion patterns, and other important factors on the natural frequencies of the model. Obtained results show that symmetric and uniform porosity distributions have the maximum and minimum amounts of natural frequencies. Moreover, the maximum difference between natural frequencies of three different porosity distribution occurs in e(0) = 0.95 and is approximately 32%. The current study results may consider to design and produce smart structures and devices with improved performance.