An analysis of wave propagation in an infinite elastic beam on an elastic foundation is presented, considering the effect of the mass of a foundation. The foundation is represented as a base consisting of closely spaced, independent bars or linear springs. The frequency equation is derived and the spectrum of frequencies for real, imaginary, and complex wave numbers is investigated. The phase velocity and group velocity versus wave number are also calculated for various ratios of the mass of a foundation to that of a beam. Results from the present method of solution are compared with those obtained under the assumption that a beam is supported by a massless elastic foundation whose local restoring force per unit length depends only on the local deflection.
The Japan Society of Mechanical Engineers