Effect of General Thermal Boundary Conditions on the Dynamic and Buckling of Polymeric Hybrid Nanocomposite Beam with Variable Thickness

Abstract

This paper deals with the effect of general thermal boundary conditions on the dynamic and buckling of polymeric hybrid nanocomposite beam. The Timoshenko beam with variable thickness is made of a polymer matrix reinforced with a combination of carbon nanotubes (CNT) and nanoclay (NC) particles. The thermal and mechanical properties of the hybrid nanocomposite beam are obtained by Halpin–Tsai micromechanical method. The governing equations are derived through using Hamilton's principle and then solved by using the differential quadrature method (DQM). In this work, for the first time, the general thermal boundary conditions are applied to hybrid nanocomposite beam with variable thickness. The numerical results of dynamic response are obtained for different thermal and mechanical boundary conditions. Besides the effects of the amount as well as shape factor of the nanofiller, and different types of thermal boundary conditions on the natural frequencies and critical buckling load are investigated. The results show that the dynamic response of the beam with uniform thickness is more affected by changes in the amount of nanoclay, while beam with non-uniform thickness is more sensitive to changes in the amount of CNT. In addition, thermal boundary conditions involving a constant heat flux on one side have different responses with the increase of CNT value.