Thermal Effect on the Natural Frequency of FGM Nano Circular Plate Based on Modified Couple Stress Theory

In this research, thermal effect on the natural frequency of axisymmetric free vibration of a thin nano circular plate made of functionally graded material will be studied. Thermal distribution has been assumed uniform and properties of the materials are changing through the thickness of the plate. The modified couple stress theory has been used for considering the length scale parameter and the governing equation of motion and boundary conditions are obtained using the Hamilton’s principle and based on the classical plate theory. The analytical solution for the clamped and simply supported boundary conditions are established utilizing the Bessel functions. The results show that by increasing the temperature changes, ratio of the thickness to length scale parameter, ratio of radius to thickness and power-law index, the natural frequency decreases at both boundary conditions. The effect of increasing ratio of the thickness to length scale parameter in clamped boundary condition is more than simply supported boundary condition but for higher ratios, this effect decreases at both boundary conditions. The effect of increasing temperature changes in simply supported boundary condition is more than clamped boundary condition such a way that the lower temperature changes lead to the nonlinear behavior of the plate.