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

Abstract

In the present chapter, the free vibration of sandwich plates with power-law functionally graded face sheets in different thermal environments is performed. 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 a nonlinear function of temperature and the material properties of the face sheets are assumed to vary continuously through the thickness according to a power-law distribution in terms of the volume fractions of the constituents. Both un-symmetric and symmetric sandwich plates are considered in this analysis. 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. 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 FG face sheets. The results also reveal that as the side-to-thickness ratio, the core-to-face sheet thickness ratio and temperature changes, affect the fundamental frequency parameters significantly.