Vibration analysis of a tapered beam with exponentially varying thickness resting on Winkler foundation using the differential transform method

  • Authors

    • Sayyad Boreyri Department of Marine Technology Amirkabir University of Technology,Hafez Ave., Tehran, Iran
    • Pouya Mohtat Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
    • Mohamad Javad Ketabdari Department of Marine Technology, Amirkabir University of Technology, Hafez Ave., Tehran, Iran
    • Ali Moosavi Department of Mathematics, Sharif University of Technology, Tehran, Iran
    2014-04-07
    https://doi.org/10.14419/ijpr.v2i1.2152

  • In this paper, free vibration of a new type of tapered beam, with exponentially varying thickness, resting on a linear foundation is analyzed. The solution is based on a semi-analytical technique, the differential transform method (DTM). Applying DTM, nonlinear partial differential equations of the varying thickness beam are transformed into algebraic equations, which are then solved to obtain the solution. An Euler-Bernoulli beam with a number of boundary conditions and different exponential factor is taken into account. Results have been compared to the 4th order Runge-Kutta, and where possible with DQEM and analytical solution. These comparisons prove the preciseness of this method, based on which DTM can be considered as a powerful framework for eigenvalue analysis of new type of tapered beams.

     

    Keywords: Free Vibration, Exponential (Tapered) Beam, Winkler Foundation, Differential Transform Method (DTM).

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    Boreyri, S., Mohtat, P., Ketabdari, M. J., & Moosavi, A. (2014). Vibration analysis of a tapered beam with exponentially varying thickness resting on Winkler foundation using the differential transform method. International Journal of Physical Research, 2(1), 10-15. https://doi.org/10.14419/ijpr.v2i1.2152