Study of non-homogeneity effects on natural frequencies and mode shapes of polar orthotropic annular plate of exponentially varying thickness rest on elastic foundation

Abstract

To analyze natural frequencies of vibrations of an orthotropic annular plate of exponentially varying thickness resting on Winkler type elastic foundation, a mathematical model is constructed using Hamilton’s energy principle. Numerical simulation is carried out using quintic spline method for three different combinations of edge conditions. Effect of non-homogeneity variation, together with elastic foundation and orthotropy, on the natural frequencies of vibration is illustrated for variety of thickness variation for the first three modes. To compare parametric effect on a specific plate, transverse displacements are presented in normalized form. Accuracy of the results and validity of numerical method are demonstrated by comparing the existing results in the literature.