Analytic formulation on vibration of orthotropic clamped plate under in-plane forces

This paper is concerned with eigen values on buckling and vibration of orthotropic rectangular clamped plate. The present study attempts to achieve closed form solutions for orthotropic clamped plates resting on elastic base, in a novel way based on wide panel-transition matrix technique. Strip technique is employed with transition matrix method to develop the analytical solutions in series forms. Increasing the accuracy of the transition matrix is the main idea to reduce the number of strips of the decomposed plate domain. The buckling and natural frequency parameters of clamped plate are investigated under the effect of the un-axial and biaxial in-plane forces. Analytic results of vibration natural frequencies are obtained for orthotropic clamped plate under in-plane forces. Also the effects of the aspect ratios and coefficients of elastic foundation on the behavior of rectangular plates are discussed. The obtained analytical results may serve as benchmark solutions for such plates. Numerical results are obtained and discussed for a wide range of orthotropic properties and foundation coefficients. The validity of the present method is examined by means of several numerical examples compared with those available in the published papers. The obtained results proved accuracy and validity of the achieved technique.