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

Abstract 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.