on free vibration of an exponentially varying thickness beam using a semi-analytical approach

In this paper, free vibration of a beam with exponentially varying thickness is analyzed. The solution is based on the Differential Transform Method (DTM), a semi-analytical technique, which is a strong and precise method in solving both ordinary and partial differential equations. In this study, an Euler-Bernoulli beam with a number of typical boundary conditions with different exponential rate in thickness is taken into account. Natural frequencies of the beam with exponentially varying thickness are derived in this contribution. In order to verify the results, small variation in thickness is considered and compared with a constant beam. In addition, convergence of the solution is investigated in different situations to ensure the reliability of the obtained results

کلیدواژه ها:

Differential Transform Method (DTM) ، Free vibration ، Exponential (tapered) beam ، semi-analytical solution