Transverse vibration of axially moving beam made of functionally graded materials

Abstract

As a new type of heterogeneous composite materials, the functionally gradient materials with preventing the delaminating and slowing down the heat stress are applied to the engineering structure of the beams, which has an important engineering value. Based on Euler-Bernoulli beam theory and the Hamilton's principle, the differential equations of motion of the transverse free vibration of the axially moving beam made of functionally gradient materials is derived, where the materials properties of the functionally gradient beam are assumed to vary continuously follows a power law distribution of the volume fraction of the constituents along the thickness of the beam. Dimensionless parametrization is carried out for the differential equations and boundary conditions, and the nondimensional differential equations are discretized by differential quadrature method, and then the system complex characteristic equation is derived. With the change of the dimensionless axial movement speed and gradient index, the complex frequencies of transverse vibration of the axially moving beam made of functionally gradient materials with simply supported are analyzed, and the influences of the dimensionless axial movement speed and gradient index on the transverse vibration characteristics and instability forms of the axially moving beam made of functionally gradient materials are discussed. © 2013 Journal of Mechanical Engineering.