Two-dimensional elasticity solutions for temperature-dependent in-plane vibration of FGM circular arches

Temperature-dependent in-plane vibration of functionally graded (FGM) circular arches based on the two-dimensional theory of elasticity is investigated. An analytical solution using the state space formulation and Fourier series expansion is obtained for a simply supported circular arch. For such functionally graded arches, the state equation has variable coefficients. Because a definite, continuously varying FG model through the thickness is impractical if not impossible, an approximate laminate model is constructed to derive an asymptotic solution through the thickness direction. The transfer relationship between the state vectors at the inner and outer surfaces is ultimately obtained by considering the continuity conditions at the artificial interfaces. The new formulation is validated by comparing some numerical solutions with established results in open literature, such as functionally graded straight beams, curved sandwich beams and laminated thick circular arches. Effective material properties are predicted using the Mori–Tanaka model and taken as temperature-dependent. Effects of the gradient index, temperature and geometric parameters, i.e. the curvature, length-to-thickness ratio, subtended angle, on the vibration frequency are analyzed and discussed.