On the size-dependent vibrations of doubly curved porous shear deformable FGM microshells

This paper aims to analyse the free vibrations of doubly curved imperfect shear deformable functionally graded material microshells using a five-parameter shear deformable model. Porosity is modeled via the modified power-law rule by a logarithmic-uneven variation along the thickness. Coupled axial, transverse, and rotational motion equations for general doubly curved microsystems are obtained by a virtual work/energy of Hamilton's principle using a modified first-order shear deformable theory including small size dependence. The modal decomposition method is then used to obtain a solution for different geometries of microshells: spherical, elliptical, hyperbolic, and cylindrical. A detailed study on the influence of material gradation and porosity, small-length scale coefficient, and geometrical parameters on the frequency characteristics of the microsystem is conducted for different shell geometries.