Free Vibration Analysis of Rotating Euler–Bernoulli Beam with Exponentially Varying Cross-Section by Differential Transform Method

Abstract

In this paper, the free vibration analysis of non-uniform rotating Euler–Bernoulli beam is<br><br>carried out. It is assumed that the beam has exponentially decaying circular cross-section.<br><br>In order to solve the problem, the differential transform method (DTM) is utilized. Based on our<br><br>knowledge, we claim that the recurrence relation presented herein is an elaborate recurrence<br><br>relation which has been obtained for ordinary differential equations. Non-dimensional natural<br><br>frequencies of the beam are obtained and tabulated for different values of the beam parameters<br><br>such as taper ratio and rotating speed. Furthermore, the finite element method (FEM) is<br><br>employed to solve the problem. Comparison of the results obtained by DTM and FEM indicates<br><br>the accuracy of proposed solutions.