Vibration of a beam on continuous elastic foundation with nonhomogeneous stiffness and damping under a harmonically excited mass

Abstract

In this paper, a method of analysis of a beam that is continuously supported on a linear nonhomogeneous elastic foundation and subjected to a harmonically excited mass is presented. The solution is obtained by decomposing the nonhomogeneous foundation properties and the beam displacement response into double Fourier summations which are solved in the frequency–wavenumber domain, from which the space–time domain response can be obtained. The method is applied to railway tracks with step variation in foundation properties. The validity of this method is checked, through examples, against existing methods for both homogeneous and nonhomogeneous foundation parameters. The effect of inhomogeneity and the magnitude of the mass are also investigated. It is found that a step variation in foundation properties leads to a reduction in the beam displacement and an increase in the resonance frequency for increasing step change, with the reverse occurring for decreasing step change. Furthermore, a beam on nonhomogeneous foundation may exhibit multiple resonances corresponding to the foundation stiffness of individual sections, as the mass moves through the respective sections along the beam.