Dynamic stability of nonlocal strain gradient FGM truncated conical microshells integrated with magnetostrictive facesheets resting on a nonlinear viscoelastic foundation

Abstract

The objective of this investigation is to predict the size-dependent dynamic stability of truncated conical microshells made of a functionally graded material (FGM) integrated with magnetostrictive facesheets. The microshells are subjected to a combination of axial compressive load and magnetic field in the presence of the nonlocality and strain gradient size dependencies. The conical microshells are assumed to be surrounded by a two-parameter Winkler-Pasternak medium augmented via a Kelvin-Voigt viscoelastic approach taking a nonlinear cubic stiffness into account. The nonlocal strain gradient-based differential equations of motion are constructed based upon the third-order shear deformation conical shell theory including the magnetic permeability tensor together with the magnetic fluxes. The discretization process within the framework of the generalized differential quadrature technique is employed to achieve the nonlocal strain gradient-based load-frequency responses. It is found that increasing the material gradient index results in to decrease the nonlocal strain gradient frequency obtained for a specific value of the axial compression within the prebuckling regime. However, within the postbuckling domain, an increment in the value of the material gradient index plays an opposite role. Also, the gap between the load-frequency curves associated with various material gradient indexes are more prominent for the nonlocal strain gradient cases in comparison with the classical one.