Nonlinear oscillations of composite conical microshells with in-plane heterogeneity based upon a couple stress-based shell model

Abstract

Abstract The current investigation deals with the nonlinear oscillation response of conical microshells made of a composite material with functional graded (FG) in-plane heterogeneity is studied in the presence of the size dependency. To accomplish this purpose, various types of homogenization schemes including Voigt model, Reuss model, Mori-Tanaka model, and Hashin-Shtrikman bounds model are employed. The size-dependent characteristics are taken into consideration on the basis of the modified couple stress theory of elasticity within the framework of the higher-order shear deformation shell theory. The couple stress-based differential equations of motion are constructed via the Hamilton's principle. An efficient numerical solution methodology adopting generalized differential quadrature (GDQ) method together with the pseudo-arc technique is put to use to obtain the modified couple stress-based nonlinear frequency of homogenized FG composite conical microshells. It is demonstrated that by increasing the value of the maximum shell deflection, the couple stress type of size effect plays more important role in the nonlinear vibration response of FG composite conical microshells. Additionally, it is indicated by changing the boundary conditions from simply supported one to clamped one, the influence of couple stress size dependency decreases.