Differential Transformation Method for Free Vibration Analysis of Rotating Timoshenko Beams with Elastic Boundary Conditions

Abstract

This study proposes an efficient method for free vibration analysis of rotating beams under elastic boundary conditions. The existing literature widely used the Rayleigh–Ritz (R–R) method to study the free vibration of beams under elastic boundary conditions, but the computational efficiency of this method is not satisfactory. In view of this, we introduce the differential transformation method (DTM) to solve this problem. The influence of the Coriolis force on the natural frequency of rotating beams is considered. The artificial spring attachment technique is implemented to represent the elastic boundary constraints. Based on the Timoshenko beam theory, governing equations and general boundary conditions of rotating beams are obtained by using Hamilton’s principle. The accuracy, computational efficiency, and convergence of the present method are in contrast with those of the R–R method. The results show that the present method has a higher accuracy and efficiency than the R–R method.