No abstract

The paper presents a theoretical formulation based on Ibearugbulem's shape function and application of Ritz method. In this study, the free vibration of simply supported plate with one free edge was analyzed. The Ibearugbulem's shape function derived was substituted into the potential energy functional, which was minimized to obtain the fundamental natural frequency. Aspect ratios from 0.1 to 2.0 with 0.1 increments were considered. The values of fundamental natural frequencies of the first mode were determined for different aspect ratio. For aspect ratio of 1.0, the value of nondimensional parameter of fundamental natural frequency obtained was 23.86. Comparison was made for values of nondimensional parameter of fundamental natural frequencies obtained in this study with those of previous research works. It was seen that there is no significant difference between values obtained in this study with those of previous studies.

Abstract

The work is to use the energy approach in the form of indirect variational principle (Galerkin's method) for buckling analysis elastic of thin rectangular plates with all edges clamped. The Galerkin method has been used to solve problems in structural engineering such as structural mechanics, dynamics, fluid flow, heat and mass transfer, acoustics, neutron transport and others. The Galerkin method can be used to approximate the solution to ordinary differential equations, partial differential equations and integral equations with a polynomial involving a set of parameters called characteristic orthogonal polynomials. The buckling loads from this study were compared with those of previous researches. The results showed that the average percentage differences recorded for CCCC plates are 0.735 to 4.702. These differences showed that the shape functions formulated by COP has rapid convergence and is very good approximation of the exact displacement functions of the deformed thin rectangular plate under in-plane loading when applied to Galerkin's buckling load for isotropic plates. An indirect variation principle (based on Galerkin's method) could be used in confidence to satisfactorily analyze real time rectangular thin plates of various boundary conditions under in-plane loadings. The results obtained herein are very close to the results obtained by previous research works that used different methods of analysis.

The use of polynomial series function in the buckling analysis of a CCFC is presented. The polynomial series shape function was truncated at the fifth orthogonal terms, which satisfied all the boundary conditions of the plate to obtain a peculiar shape function, which was applied in Ritz method. The peculiar shape function is substituted into the total potential energy functional, which was minimized, and the critical buckling load of the plate was obtained. The critical buckling load is a function of a coefficient, "K". The values of K from earlier and the present studies were compared within the range of aspect ratios from 0.1 to 2.0. A graph of critical buckling load against aspect ratio was plotted. It was discovered that for aspect ratios of 0.4, 0.5 and 1.0, the critical buckling loads coefficients were 26.94, 17.39 and 4.83. It was also observed from the behavior of the graph that as aspect ratio increases from 0.1 to 2.0, the critical buckling load decreases.