Natural Frequencies of Functionally Graded Plate Composed of a Mixture of Titanium (Ti-6Al-4V) and Zirconia (ZrO2)

Abstract

In the present paper, the higher order shear deformation theory is used to analyze the natural frequencies of simply supported functionally graded plate composed of a mixture of Titanium (Ti-6Al-4 V) and zirconia (ZrO2) resting on elastic foundation. This theory accounts for adequate distribution of the transverse shear strains in the thickness of the plate and satisfies the traction free boundary conditions on the top and bottom surface of the plates, thus a shear correction factor is not required. The material properties change within the plate thickness according to the power law distribution of the volume fraction of the constituents (Titanium and zirconia). The equations of motion are derived employing the principle of Hamilton. Navier type solutions are proposed to obtain the natural frequencies of functionally graded plate and efficiency of the theory is ensured by comparing the results with the existing results. Numerical results are computed to examine the effects of different geometrical parameters such the power-law index, aspect ratio, elastic foundation parameters, and side-to-thickness ratio, on the natural frequencies of simply supported functionally graded plate. It can be concluded that the presence of the elastic foundation increases the non dimensional natural frequencies. It can be found also that the normalized natural frequencies of the plate decrease with increasing the volume fraction exponent and slenderness ratio.