Abstract：Abstract：The general governing differential equation of the vibration of Euler-Bernoulli beams with multiple discontinuities subjected to axial force presented by using generalized functions. The equation is then solved based on Laplace transformation. Unlike the classical solutions of discontinuous beams, the proposed scheme is valid in arbitrary miscellaneous discontinuities conditions, the generalized solutions are expressed in the terms of a single expression on the entire beam. As the specified discontinuities type, eigenvalue matrices are simplified by the degenerated continuity conditions. Final, the accuracy and efficiency of the proposed method is verified with an example of the free vibration problems for a four-span simply supported beam with three spring-mass systems subject to compressive force.Final, the free vibration problems for (a) a beam with masses and their rotatory inertias, (b) a four-span pinned-pinned beam with three spring-mass systems subject to compressive force, (c) a multiple cracked beam with axial force and elastic foundation are studied. It is shown that the present method offers an accurate and effective method of free vibration analysis of beams with arbitrary discontinuities.
2014, Vol. 35 
