Vibration analysis of elastically supported sandwich beam with damaged core and functionally graded face sheets

This paper presents the influence of carbon nanotubes (CNTs) waviness, aspect ratio and damaged core 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-totube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. A damage model is introduced to provide an analytical description of an irreversible rheological process that causes the decay of the mechanical properties, in terms of engineering constants. An isotropic damage is considered for the core of the sandwich beams. 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 the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution and boundary conditions. Also, the effects of carbon nanotubes (CNTs) waviness, CNT aspect ratio, Winkler foundation modulus, shear elastic foundation modulus and geometrical conditions on the vibrational behavior of the sandwich structure are studied.