A New Higher-Order Shear and Normal Deformation Theory for the Free Vibration Analysis of Laminated Shells

In this paper, the free vibration analysis of laminated composite and sandwich, cylindrical and spherical shells is presented using a new higher-order shear and normal deformation theory. The novelty of the present theory is that it includes the effects of both transverse shear and normal deformations along with higher order expansions of displacement field. A fifth-order polynomial type shape function is used in the in-plane displacements to represent the effect of transverse shear deformation for the first time whereas transverse displacement is a function of x, y, and z coordinates to account for the effect of transverse normal deformation. The equations of motion are derived using Hamilton’s principle. Navier’s solution technique is employed to obtain the non-dimensional fundamental frequencies. To validate the accuracy of the present theory, the present results are compared with other higher-order theories available in the literature. It is observed that the values of fundamental frequencies obtained using the present theory are in close agreement with those available in the literature.