Asymptotic two-dimensional elasticity approach for free vibration of FGM circular arches

Functionally graded materials (FGMs) have attracted intensive research and application as key components in smart designs. In this work, the free vibration of functionally graded circular arches composed of aluminum (Al) and silicon carbide (SiC) is investigated. Two models of the material properties of FGMs graded in the thickness direction are assumed: the Mori-Tanaka model and the self-consistent models. The analysis is carried out using the state space formulation and Fourier series expansion in the framework of two-dimensional theory of elasticity. Numerical examples are presented to assess the difference between these two micromechanical models and the effects of gradient index, and geometric parameters are analyzed and discussed. The new numerical results are verified by comparing, in specific cases, with published data in literature. The new solutions are possible to render a benchmark for functionally graded circular arches with arbitrary variation of material properties. © 2012 Copyright Taylor and Francis Group, LLC.