Modal characteristics of P- and S-FGM plates with temperature-dependent materials in thermal environment

ABSTRACT

The present article copes with the analysis of free vibration of functionally graded plates with temperature-dependent materials in thermal environment. The functionally graded material (FGM) can be produced by continuously varying the constituents of multiphase materials in a predetermined profile defined by the variation of the volume fraction. In the proposed study, two different volume fractions are considered: (i) power-law function (P-FGM) and (ii) sigmoid function (S-FGM). As the difference between the material properties of the FGM constituents used is relatively small, it is then possible to successfully apply the rule of mixture with no loss of accuracy with respect to the Mori–Tanaka method. The analysis is performed using advanced hierarchical higher order equivalent single-layer plate theories developed using the method of power series expansion of displacement components. The modal characteristics of the P- and S-FGM plates are investigated while subjected to a temperature gradient. More specifically, thermal loadings are induced by the through-the-thickness temperature distribution obtained as the solution of the one-dimensional Fourier's heat conduction equation. The governing equations are derived in their strong form using the principle of the virtual displacements and are solved in an exact sense by using the Navier-type closed form solution. The effect of length-to-thickness ratio, material temperature dependence, and volume fraction index on the natural frequencies is investigated.

KEYWORDS:

• FGMs
• free vibration
• hierarchical models
• temperature-dependent materials
• thermal effect

Notes

† = average percentage difference.

Diff. represents the average percentage difference of the first two dimensionless circular frequency parameters and .

P-FGM, power-law functionally graded materials.