DYNAMIC ANALYSIS OF THICK FUNCTIONALLY GRADED BEAMS WITH ELASTIC BOUNDARY CONDITIONS USING A HIGHER-ORDER SHEAR DEFORMATION THEORY

This paper presents a unified solution for free and transient vibration analyses of thick functionally graded beams using a higher-order shear deformation theory. The variational principle in conjunction with modified Fourier series is employed to formulate the theoretical model. The material properties of the functionally graded beams are assumed to be continuous and smooth along the thickness direction according to the simple power-law distribution. The penalty method is used to deal to the boundary conditions and the arbitrary combinations of free, pinned, clamped and elastic restraints are examined. The convergence, accuracy and stability of the formulation are validated by comparing the presented solution with those available in literature. A comprehensive study concerning free vibration of functionally graded beam with different power-law exponents, slenderness ratios as well as boundary conditions is performed. As to the transient vibration analysis, functionally graded beams subjected to dynamic loads are examined. Furthermore, the effects of the power-law exponents, boundary conditions and load types on transient responses of the beams are also discussed.