Free vibration analysis of general stepped circular plates with internal elastic ring support resting on Winkler foundation by green function method

Natural frequencies are important dynamic characteristics of a structure. Therefore, the exact solution pertaining to free vibration of stepped circular plate elastically restrained against rotation, translation, and internal elastic ring support resting on an arbitrary variable elastic foundation using Green Function is presented in this paper. Thus, an accurate and direct modeling technique is introduced for modeling stepped circular plate on an arbitrary variable elastic foundation with arbitrary boundary conditions and internal elastic ring support. The effect of the translational along with rotational support flexibilities, as well as, the elastic coefficient of Winkler foundation and other parameters are assessed. Finally, some numerical examples are shown in order to present the efficiency and simplicity of the Green Function in the new formulation.