On the free vibration of moderately thick spherical shell panel—A new exact closed-form procedure

A new exact closed-form procedure for free vibration analysis of moderately thick spherical shell panel is presented based on the first-order shear deformation theory. The strain–displacement relations of Donnell and Sanders theories are used to illustrate the procedure. The shell has two opposite edges simply supported (i.e., Lévy-type). Based on the present solution, the governing equations of the vibrated spherical shell panel were exactly solved by introducing the new auxiliary and potential functions as well as using the separation method of variables. The accuracy and superiority of the formulations are validated by comparing the results with those available in the literature and the 3D finite element analysis. The effects of various stretching–bending couplings on the frequency parameters are discussed. Finally, the validity and the range of applicability of the Sanders and Donnell shell theories are investigated.