Free Vibration Analysis of Thick Laminated Composite Shells Using Analytical and Finite Element Method

Purpose The aim of this work is to investigate the free vibration study of sandwich cylindrical and spherical shells made of laminated composite by applying the finite element method utilizing the computer code ANSYS 19 and the revised shear deformation theory with four-variable. Methods The study uses two approaches that combine analytical and finite element methods to fully understand the vibration response in these complex structures. The suggested theoretical model’s kinematics is determined by an undetermined integral component, and it incorporates the effects of transverse shear stresses through the thickness of the plate/shell using the hyperbolic form function. The present model guarantees the fulfillment of zero shear stress conditions at the upper and lower surfaces of the plate/shell without the need for a shear correction factor, in contrast to typical first order shear deformation theories (FSDTs). The equations of motion are identified and solved using the Navier method and the Hamilton’s principle. Results The current results are compared with other higher-order theories found in the literature to verify the veracity of the current hypothesis. It has been noted that the fundamental frequency values derived using the current theory are very similar to those found in the literature. In addition, the effects of the radius of curvature aspect ratio and mode vibration are considered. Conclusions Based on the analysis, it can be said that the kinematics based on the indeterminate integral component are very efficient and, when used in the study of laminated plates and shells, lead to higher accuracy than conventional approaches.