Chapter 7 - Vibration Problems of Functionally Graded Triangular Plates

Abstract

This chapter deals with free vibration of functionally graded (FG) thin triangular plates subject to various classical boundary conditions at the three edges. Here, four different types of triangular plates are considered, viz. two right-angled, an equilateral, and an isosceles. The power-law variation of FG material properties is also considered. The plate displacement components are expressed as the linear combination of simple algebraic polynomials (generated from Pascal’s triangle) and the Rayleigh-Ritz procedure is applied to generate the generalized eigenvalue problem. The triangular plate generally considers coordinate transformation to standard triangle and leads to a slight modification in the energy expressions in the Rayleigh-Ritz method. Corresponding natural frequencies are incorporated after test of convergence and verification with existing results in special cases. Three-dimensional mode shapes for clamped-clamped-clamped (C-C-C) and clamped-free-free (C-F-F) triangular plates are also depicted corresponding to the first six non-dimensional frequencies.