Application of alternative II theory to vibration and stability analysis of thick rectangular plates (Isotropic and orthotropic)
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