An efficient higher order shear deformation theory for free vibration analysis of functionally graded shells

In this study, a simple and efficient higher order shear deformation theory is formulated for free vibration analysis of functionally graded (FG) shells. By introducing the undetermined integral terms in displacement field, the number of generated unknowns and their related governing equations is reduced in contrast to previously published theories, and therefore the differentiability of governing motion equations is decreased , this motivation turns the present theory simpler and easily exploited for functionally graded shell mechanical simulation. Both strains and stress rise through the thickness coordinate as function of hyperbolical distribution. The Hamilton's principle is deployed to derive the governing and motion equations. Closed form solutions are obtained for free vibration problems using Navier's method. Furthermore, detailed comparisons with other shear deformation theories are presented to illustrate the efficiency and accuracy of the developed theory. From this perspective, various perceptions on the impact of some important parameters such as material distribution, geometrical configuration, thickness and curvature ratios are studied and discussed. The non-trivial aspects in predicting the free vibration responses of FG shells are also pointed out.

Automated summary

This study presents a simple and efficient higher order shear deformation theory for free vibration analysis of functionally graded shells, which reduces the number of unknowns and governing equations by introducing undetermined integral terms in the displacement field. The theory, derived using Hamilton's principle and Navier's method, provides closed form solutions and is compared with other theories to demonstrate its efficiency and accuracy. Various parameters including material distribution, geometrical configuration, thickness, and curvature ratios are studied to understand their impact on the free vibration responses of FG shells.