Free Vibration Analysis of Sandwich Plates with FGM Face Sheets and Temperature-Dependent Properties of the Core Materials

In this paper, the free vibration of sandwich plates with power-law FGM face sheets in various thermal environments is performed by high-order sandwich plate theory. The material properties of the core, such as Young’s modulus, density, thermal expansion coefficient and Poisson’s ratio, are assumed to be temperature dependent by nonlinear function of temperature [۱]. The material properties of the FGM face sheets are assumed to vary continuously through the thickness according to a power law distribution in terms of volume fractions of the constituents [۲]. The governing equations of motion in free natural vibration are derived using Hamilton’s principle [۳]. A new approach is used to reduce the equations of motion from twenty three equations to eleven equations and then solve them. The new solution approach consists of isolating six of the unknowns in the displacements of the face sheets using the compatibility equations, followed by isolating the additional six Lagrange multipliers using the equations of the face sheets, finally, the isolated unknowns are substituted into the eleven equations of the core. Both un-symmetric and symmetric sandwich plates are considered in this analysis. Good agreement is found between theoretical predictions of the fundamental frequency parameters and the results obtained from other references for simply supported sandwich plates with functionally graded face sheets. The results show that the fundamental frequency parameters (ω ̅ ) increases by increasing the volume fraction index (κ). Also, the effect of temperature on the value of fundamental frequency parameters decreases with increases in the FGM face sheets thickness. The results also revealed that as the side-to-thickness ratio (b⁄h), the core-to-face sheet thickness ratio (h_c⁄h_t ) and temperature changes, have a significant effect on the fundamental frequency parameters.

Keywords:

Sandwich plates , FGM , Free vibration , Temperature Properties