Refined 6-DOF hyperbolic model for the free vibration analysis of multi-layered sandwich shallow shells

Sandwich shell panels are widely used in many engineering structures wherein those are subjected to dynamic forces, which leads to their failure. It is necessary to perform accurate dynamic analysis of multilayered sandwich shell panels to provide their safe design. To the best of the authors' knowledge, literature on the free vibration analysis of multi-layered sandwich shallow shells is limited and needs more attention. Therefore, the purpose of the present study is to find higher-order closed-form solutions for the free vibration problems of sandwich shallow shells with double curvature using refined computational model. In the present study, a new hyperbolic shape function is introduced in the refined shell theory to account for the effects of transverse shear and normal deformations. A theory involves six degrees of freedom and satisfies traction-free boundary conditions at the top and the bottom surfaces of the shell. The governing equations of motion and associated boundary conditions of the theory are produced by employing Hamilton's principle. Semi-analytical closed-form solutions for the free vibration problems are made by the Navier technique for simply supported boundary conditions of the shell. The nondimensional natural frequencies of five layered symmetric and anti-symmetric sandwich shells are obtained for various parameters such as a/h ratio, a/b ratio, tc/tf ratio, radii of curvature, and modes of vibration. The present results are compared with results that have already been published to confirm the accuracy and efficiency of the current higher-order hyperbolic shell theory. It is concluded from the comparison of results that the present theory is in excellent agreement while predicting the natural frequencies of sandwich plates and shells. Also, this study presented new benchmarks in vibration analysis of sandwich shells. This study demonstrates results for a typical fivelayer sandwich shell with composite faces and isotropic/foam cores. However, the proposed model can be readily extended to other material combinations and structural configurations.