Application of galerkin method in deflection stability and vibration of rectangular clamped plates of variable thickness

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The variational method is an effective tool for solving complicated differential equations for which exact solutions are not available. The Galerkin method is known to be one of the most rapidly converging methods and has been applied successfully in the past for the solution of many types of linear differential equations in applied mechanics. In the present study, the suitability of the method for solution of deflection, stability and free vibration analysis of plates of variable thickness is investigated The effects of the taper parameter and the plate aspect ratio on behaviour of plates of variable thickness are presented. It is shown that the stiffness of the plate of variable thickness tends to increase with increase in taper parameter and aspect ratio. The parameters taken into consideration for the analysis of the problem under investigation are the plate aspect ratio, taper parameter and load ratios. To determine the center deflection of plates of variable thickness on elastic foundation, various foundation moduli were also taken into consideration. The deflection of plates of variable thickness is expressed in term of polynomials satisfying the boundary conditions. The definite integrals involved in the formulation of the Galerkin algebraic equations from the governing differential equations are evaluated by using trapezoidal rule. This results in a set of simultaneous linear homogeneous algebraic equations in terms of the coefficients C;. The algebraic eigen-value problem is then solved for