Dynamic modeling of a multi-scale sandwich composite panel containing flexible core and MR smart layer

Abstract

This is the first research on the nonlinear vibration of a composite sandwich doubly curved shell with a flexible core and MR layers, which we do by employing the Homotopy Perturbation Method (HPM). By using a new higher-order shear deformable theory (TSDT) the face sheets and third-order polynomial theory of the flexible core the strains and stresses are obtained. It is assumed a smart model including a multiscale composite layers shell with a flexible core and magnetorheological layer (MR) that is led up by the nonlinearity of the in-plane and the vertical displacements of the core. Three-phase composites shells with polymer/Carbon nanotube/fiber (PCF) and polymer/Graphene platelet/fiber (PGF) according to the Halpin-Tsai model have been considered. For investigating the effect of pattern distribution versus fundamental frequencies various distributions patterns such as U (uniform), X, A and O are considered. The governing equations of the multiscale shell have been derived by implementing Hamilton's principle and the shell considered to be simply supported. For investigating correctness and accuracy, this paper is validated by other previous researches. Finally, different parameters such as temperature rise, various distributions patterns, magnetic fields and curvature ratio are considered in this article. The results presented that the sandwich multiscale doubly curved shell with flexible core show a complex behavior and the homogeneous composite shells are simpler than the vibration patterns of the multiscale composite panels.