Application of the R‐functions in free vibration analysis of FGM plates and shallow shells with temperature dependent properties

Abstract

The free vibration of plates and shallow shells with/without cutouts made of functionally graded materials (FGM) is investigated using variational FG shallow shells with temperature dependent mechanical characteristics of the constituent materials. First‐order shear deformation theory of shallow shells is employed. It is supposed that material properties vary through thickness according to a power‐law distribution of the constituent's volume fraction. They depend on both the temperature and the thickness. Temperature field is modeled by one‐dimensional heat transfer equation, since the temperature is varied only in thickness direction. Solution of this equation is determined by a polynomial power series expansion. Corresponding software was developed to implement the proposed approach. The vibration analysis was carried out for FG plates and shallow shells with cutout and various boundary conditions.

Mechanical buckling analysis of functionally graded composite laminated plates reinforced with temperature dependent graphene sheets resting on elastic foundation

“…It was shown that the increment in foundation stiffness leads to the growth of the fundamental natural frequency of GRC laminated plates beside the decrement of their nonlinear to linear natural frequency ratios. Awrejcewicz et al [16] studied on the free vibrations of FG plates and shallow shells with cutout in thermal environment. Zhang et al [17] employed the finite Fourier integral transform technique to examine the buckling treatment of rectangular thin plates with two opposite edges free and the others rotationally restrained.…”

Mathematical modeling of planar physically nonlinear inhomogeneous plates with rectangular cuts in the three-dimensional formulation

“…Effects of varying material distributions, lamination schemes, curvatures, boundary conditions, and geometrical parameters on natural frequencies and backbone curves were reported. Awrejcewicz et al [40] employed the R-function theory in free vibration analysis of the FGM plates and shallow shells with temperature dependent properties. The temperature field was modeled as a 1D heat transfer equation, and its solution was obtained through a polynomial power series expansion.…”