This work analysed the free vibration and stability of thick isotropic and orthotropic plates with SSSS and SSFS support conditions by applying the alternative II theory based on polynomial shape function. The total potential energy which was obtained by combining the strain energy and external work was reduced to three governing equations using Ritz method. Polynomial shape function which varies with Poisson’s ratio was substituted into the governing equation to obtain the fundamental natural frequency, linear frequency and critical buckling load. The values of frequencies of the first mode and critical loads obtained were compared with those obtained using first order shear deformation theory. For span depth ratio of 10, the fundamental linear frequency for orthotropic SSFS plate corresponding to modulus of elasticity ratios (E1/E2) of 10, 25 and 40 are 0.00156, 0.00219 and 0.00255Hz. The corresponding values using first order shear deformation theory are 0.00152, 0.00212 and 0.00245Hz. Keywords: Fundamental natural frequency, SSSS plate, SSFS plate, Ritz method, Orthotropic thick plate, Isotropic thick plate, Stability, Free vibration

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In this work, polynomial deflection expression was used in the free-vibration investigation of thick rectangular plates with two different boundary conditions; one with its four edges clamped denoted with the acronym (CCCC) and another with two adjacent edges fixed and having simple supports at the other two adjacent edges denoted with the acronym (CCSS). The edge conditions of the various plates were fulfilled and used in generating the stiffness coefficients which were substituted into the analytical equation to obtain the non-dimensional frequency functions for the plates at different span-depth ratio (a/t) and aspect ratio (b/a). It was observed that at the same value of (b/a), there is an increase in the value of the non-dimensional frequency parameter as (a/t) increases. Also, at the same value of (a/t), there is a decrease in the value of the non-dimensional frequency parameter as (b/a) increases. The results obtained for the all edges clamped plate were compared with similar works by other researchers in the literature and were found to follow similar pattern and trend and were quite close.

In this investigation, exact displacement functions were used to analyze thick anisotropic rectangular plates of two boundary conditions; simply supported on all edges (SSSS) and clamped on all edges (CCCC). Third order shear deformation model was employed in the formulation of the total potential energy functional for thick anisotropic rectangular plate. This total potential energy functional was reduced to the governing equation and compatibility equations for thick anisotropic plate. The governing equation and compatibility equations were solved to obtain the general displacement functions. By satisfying the boundary conditions for SSSS and CCCC plates their distinct displacement functions were obtained. These displacement functions were used to obtain the stiffness coefficients (kvalues) for the plates. Minimizing the total potential energy functional with respect to the coefficients of the displacement functions gives the formulas for calculating the values of the coefficients. At this point, the displacements and stresses of the plates were calculated at various angles fiber orientations (

This study applied polynomial expressions as displacement and shear deformation functions in the free-vibration study of thick and moderately thick isotropic rectangular plates. Rectangular plates with two different edge conditions investigated in this work are: one with simple supports at three of its edges and with no support at the other edge denoted with the acronym (SSFS) and a rectangular plate with simple supports at opposite edges while the other opposite edges has a fixed support at one edge and no support at the other edge, this is denoted with the acronym (CSFS). The total potential energy of the plate was derived using the general theory of elasticity. The general governing equation of the plate was derived by minimizing the total potential energy equation of the plate. Edge conditions of the SSFS and CSFS plates were met and substituted into the general governing equation to obtain a linear expression which was solved to generate fundamental natural frequency function for the plates with various span-depth proportion (m/t) and planar dimensions proportion (n/m). The results obtained from this research were found to agree favourably with the results of similar problems in the literature upon comparison.