LARGE-AMPLITUDE FREE-VIBRATION OF THICK SHALLOW SHELLS SUPPORTED BY SHEAR DIAPHRAGMS

The effect of thickness and curvature upon the large amplitude vibration of shallow shells is studied in this paper. For this purpose, the non-linear governing equations for thick shallow shells which have principle curvatures and rectangular planform are derived by Hamilton's principle using first order shear deformation theory. Applying Galerkin's procedure and eliminating variables except for transverse displacement, the governing equations are reduced to an elliptic ordinary differential equation in time. The period of vibration for the shell is calculated by integrating the equation using a Gauss-Legendre integration method. The present method is applied to a shallow shell which has a rectangular boundary supported by shear diaphragms.