Free vibration analysis of sandwich plates with functionally graded face sheets and temperature-dependent material properties: A new approach

Improved high-order sandwich plate theory is used to analyze the free vibration of sandwich plates with functionally graded (FG) face sheets in various thermal environments. The material properties of FG face sheets are assumed to be temperature-dependent by a third-order function of temperature and vary continuously through the thickness according to a power-law distribution in terms of the volume fractions of the constituents. Also, the material properties of the core are assumed to be temperature-dependent by a third-order function of temperature. The governing equations of motion in free natural vibration are derived using Hamiltonʹs principle. A new approach is used to reduce the equations of motion and then solved them for both un-symmetric and symmetric sandwich plates. In-plane stresses of the core that usually are ignored in the vibration characteristics of the sandwich structures are considered in this formulation. The results show that the fundamental frequency parameter increases and decreases with increasing the volume fraction index for soft core and hard core sandwich plates, respectively. The results indicate that as the side-to-thickness ratio, the core-to-face sheet thickness ratio and the temperature are changed, a significant effect on the fundamental frequency parameter is observed. Good agreement is found between the theoretical predictions of the fundamental frequency parameters and the results obtained from other references for simply supported sandwich plates with functionally graded face sheets in the literature.