Main Article Content
Vibration analysis of beams with an arbitrary number of intermediate elastic supports and concentrated masses at arbitrary positions under an axial force is of theoretical and practical importance. In this work, the mathematical model governing the vibrations of beams is reformulated by incorporating the Dirac’s delta function, which is solved by the proposed shape function method. The exact and explicit frequency and mode shape for the non-conventional and conventional boundary conditions are derived, which are determined by four shape functions and four unknown constants. The highest order of the frequency equation is four, which is independent of the number of intermediate supports or concentrated masses, making this method efficient. The validity is justified by comparing with the published literature and vibrations of beams under an axial force on an elastic foundation, and good agreements are achieved. A parametric study is carried out to show that the conventional boundary conditions can be represented by the non-conventional elastic boundary conditions. Besides, the vibrations of multi-span continuous beams can also be simulated with the proposed method by increasing the stiffnesses of the intermediate elastic supports. The results reported in this work are potentially useful in structural health monitoring, damage detection, and vehicle-bridge interaction study.
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