The Effect of porosity distribution on the free vibration of tapered nanocomposite sandwich beam

Abstract

In this research, free vibration of tapered sandwich beam with variable thickness is investigated. The core is made of porous aluminum foam, which is included by two composite skins reinforced with carbon nanotubes. In order to derive the equations of motion, first the constitutive equations of the core and skins are expressed. Then the kinetic and strain energies of the beam are calculated. Formerly, with the aid of applying Hamilton's principle, the equations of motion of the beam, which are of the type of partial differential equations, and also the equations of the boundary conditions are derived. Next, using the differential quadrature method, the equations of motion and boundary conditions are discretized in the form of algebraic equations and rewritten in the form of the standard eigenvalue equation. By solving the eigenvalue problem, the natural frequency is evaluated. In order to validation of modeling and solution method, the present results are compared with those available in the literature. Finally, the effect of porosity distribution, porosity coefficient, core thickness and beam length on the natural frequency is investigated.