NONLINEAR FREE VIBRATIONS ANALYSIS AND BEHEVIOR OF THIN SHALLOW SPHERICAL ELASTIC SHELLS OF VARIABLE THICKNESS

Large amplitude (nonlinear) free vibration analysis of thin shallow spherical elastic shells of variable thickness with tangentially clamped immovable edges has been performed by using both (i) coupled governing differential equations derived in the Von Karman sense in terms of displacement components as well as (ii) decoupled nonlinear governing differential equations on the basis of Berger approximation (i.e. neglecting second strain invariant e(2)) derived from energy expression applying Hamilton's principle and Euler's variational equations. The governing differential equations are solved by Galerkin error minimizing technique incorporating clamped immovable edge conditions. A parametric study is presented to understand the effects of various parameters on nonlinear dynamic behavior of such structures and the same reveals some interesting features.