Rotary inertia effect in isotropic plates part I: Uniform thickness

This is the first of two companion papers which collectively present the effect of rotary inertia on dynamic behavior of rectangular plates. To the best of author’s knowledge, no such comprehensive comparison has been presented. A finite element code based on first-order shear deformation theory (FSDT) is developed to analyse the free vibration behaviour of rectangular isotropic plates of uniform thickness. Plates having different aspect ratios (b/a) and boundary condition are analysed. The analysis is performed considering plate thickness ratio, h/a = 0.001 to 0.2 i.e. thin as well as sufficiently thick plates. The fundamental frequency in non-dimensional forms is calculated by considering rotary inertia and without considering rotary inertia. The present solutions are compared with existing literature wherever possible and excellent agreement in the results is seen. The present formulation is robust and capable of producing highly accurate solutions. The variation in fundamental frequencies calculated with- and without- rotary inertia is presented here in graphical form. It is seen that natural frequencies obtained without rotary inertia are generally higher than those obtained with rotary inertia.