Nonlinear vibration and modal analysis of FG nanocomposite sandwich beams reinforced by aggregated CNTs

Abstract

In the present work, by considering the aggregation effect of single‐walled carbon nanotubes (SWCNT), the nonlinear vibration of functionally graded (FG) nanocomposite sandwich Timoshenko beams resting on Pasternak foundation are presented. The material properties of the FG nanocomposite sandwich beam are estimated using the Eshelby–Mori–Tanaka approach and differential quadrature method (DQM) is used to obtain natural frequency. The nonlinear governing equations and boundary conditions are derived using the Hamilton principle and von Kármán geometric nonlinearity. The higher order nonlinear governing equations and boundary conditions are calculated using the Hamilton principle. A direct iterative method is employed to determine the nonlinear frequencies and mode shapes of the beams. It is shown that the mechanical properties and therefore vibration of functionally graded carbon nanotube reinforced (FG‐CNTR) sandwich beams are severely affected by CNTs aggregation. A detailed parametric study is carried out to investigate the influences of Winkler foundation modulus, shear elastic foundation modulus, length to span ratio, thicknesses of face sheets on the nonlinear vibration of the structure. POLYM. ENG. SCI., 59:1362–1370 2019. © 2019 Society of Plastics Engineers