Abstract
Analytical and finite-element solutions to the problem of a vibrating beam, fully or partly supported by an elastic foundation, are presented. An application example is the vertical (transverse) vibration of a concrete railway sleeper embedded in an elastic medium (the ballast). The sleeper is also elastically connected to the rails. Eigenfrequencies are calculated and vibration modes are discussed. The beam (sleeper) is divided into sections where each section may or may not be supported by the elastic foundation. Outside the voids (the non-supported parts of the sleeper) the sleeper is assumed fully attached to the support. Some conclusions are that the foundation stiffness influences the (almost) rigid-body vibration modes of the sleeper the most, whereas the lowest bending-mode eigenfrequencies are just slightly influenced by the foundation stiffness; higher eigenfrequencies are affected very little by the foundation. The influence of railpad (and rail) stiffness on the sleeper bending-mode eigenfrequencies is negligible.
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