Vibration analysis of a tapered beam with exponentially varying thickness resting on Winkler foundation using the differential transform method - Boreyri, Sayyad; Mohtat, Pouya; Ketabdari, Mohamad Javad; Moosavi, Ali (International Journal of Physical Research, 2014)
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).