مرکز منطقه ای اطلاع رساني علوم و فناوري - Investigation of the Influences of Shear Deformation and Rotary Inertia on the Dynamic Response of Functionally Graded Orthotropic Plates

Abstract :

In this study, the free vibration problem of plates composed of functional graded (FG) orthotropic materials, considering combined effects of shear deformations and rotary inertia is investigated. It is assumed that the materials properties of the orthotropic plate changes exponentially in the thickness direction. The basic equations for FG orthotropic plate are derived based on first order shear deformation plate theory (SDPT). By using Galerkin method, the resulting equations are reduced to a sixth order algebraic equation and solved numerically and found the values of the fundamental frequency. Then, ignoring the effects of forces of rotary inertia, the values of frequencies of FG orthotropic plate based on the SDPT and classical plate theory (CPT) are obtained. Finally, the influences of FG orthotropic material properties, variations of plate geometry parameters, shear deformations and rotary inertia on the non-dimensional frequency parameter are investigated numerically. According to the analysis, despite the change the effects of shear stresses functions on the values of dimensionless frequency parameters of rectangular plates, these effects are very significant for different sizes of plates. It is observed that the effect of heterogeneity and orthotropy are very significant and can not be ignored and taking into account the effects of the rotary inertia provides more realistic results for the various sizes of plates. For the reliability of the results obtained in this thesis are compared with the solutions presented in the literature.