Dynamic Analysis of Functionally Graded Euler Beam with Elastically Restrained Edges

Free vibration of functionally graded materials (FGMs) Euler beam with elastically restrained edges is investigated. The material properties of the FGMs beam vary continuously in the thickness direction according to the power law form. The neutral axis site of the FGMs beam is determined by the static equilibrium condition. The governing equation and boundary conditions are found by applying the Hamilton’s principle. The linear combination of a Fourier cosine series and auxiliary Legendre polynomial function is used to obtain the natural frequencies of the FGMs beam. The effects of the rotational spring stiffness, the translational spring stiffness and the gradient index on the natural frequencies are discussed and analyzed for different material properties and different boundary conditions, indicating that the frequencies are sensitive to the gradient variation of material properties and the spring stiffness.