On the nonlocal nonlinear vibration of electro-magneto piezoelectric porous visco-microbeam reinforced with agglomerated CNTs considering surface effects

The purpose of this paper is nonlinear vibration analysis of porous piezoelectric nanocomposite microbeams resting on elastic medium exposed to electro-magneto fields. The microbeam is armed by carbon nanotubes (CNTs) in which the Mori–Tanaka theory is applied in order to obtain the structure equivalent material characteristics assuming CNTs agglomeration. The elastic foundation is modeled by two shear, spring and damper elements. The smart nanocomposite structure is subjected to electric fields. The effects of size are supposed by Eringen's nonlocal theory and the surface effects are assumed by Gurtin–Murdoch theory. The structural damping is considered utilizing Kelvin-Voigt theory. In the analytical formulation, normal and shear stresses are considered by Timoshenko–Ehrenfest beam model. The final equations are obtained by Hamilton's principle and energy method considering nonlinear Von-Karman strains. The differential quadrature (DQ) method is utilized in order to calculate the nonlinear frequency in the porous smart nanocomposite microbeam. The influences of various parameters such as nonlocal parameter, viscoelastic medium, microbeam thickness, external voltage, structural damping, magnetic field, different types of porosity parameter, boundary conditions, surface effects and agglomeration of CNTs on the nonlinear frequency of nanocomposite structure are presented. The accuracy of this work is compared by other articles in the literature. Numerical results show that considering agglomeration of CNTs, the nonlinear frequency will be decreased. In addition, the surface effects can enhance the nonlinear frequency significantly.