Vibration behavior of functionally graded sandwich beam with porous core and nanocomposite layers

Abstract

This paper presents the influence of carbon nanotubes (CNTs) waviness, aspect ratio, internal pores and graphene platelets (GPLs) on the vibrational behavior of functionally graded nanocomposite sandwich beams resting on two-parameter elastic foundations. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness of upper and bottom layers of the sandwich beam and their mechanical properties are estimated by an extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes\' effective aspect ratio as the filler content increases. The core of structure is porous and the internal pores and graphene platelets (GPLs) are distributed in the matrix of core either uniformly or non-uniformly according to three different patterns. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. The equations of motion are derived based on Timoshenko beam theory and employing Hamilton\'s principle. The problem is modeled using a semi-analytical approach composed of generalized differential quadrature method (GDQM) and series solution adopted to solve the equations of motion. Detailed parametric studies are carried out to investigate carbon nanotubes (CNTs) waviness, CNT aspect ratio, porosity coefficient, porosity distribution, graphene platelets (GPLs) distribution, Winkler foundation modulus, shear elastic foundation modulus and geometrical conditions on the vibrational behavior of the sandwich structure.