Moderately large vibrations of doubly curved shallow open shells composed of thick layers

This paper addresses nonlinear flexural vibrations of shallow shells composed of three thick layers with different shear flexibility, which are symmetrically arranged with respect to the middle surface. The considered shell structures of polygonal planform are hard hinged simply supported (i.e. all in-plane rotations and the bending moment vanish) with the edges fully restraint against displacements in any direction. The kinematic field equations are formulated by layerwise application of a first-order shear deformation theory. A modification of Berger's theory is employed to model the nonlinear characteristics of the structural response. The continuity of the transverse shear stress across the interfaces is specified according to Hooke's law, and subsequently the equations of motion of this higher order problem can be derived in analogy to a homogeneous single-layer shear deformable shallow shell. Numerical results of rectangular shallow shells in nonlinear steady-state vibration are presented for various ratios of shell rise to thickness, and non-dimensional load amplitude.