Free Vibrational Analysis of A Rotating Tapered Timoshenko Beam with Bending-Torsion Coupling

摘要

In this study, free vibration analysis of a double tapered Timoshenko beam mounted on the periphery of a rotating rigid hub is performed. The governing differential equations of motion are derived for an elastic beam by using the Hamilton's principle. The bending-torsion coupling of practical interest is also included in the formulations and the equations are solved by using the Differential Transform Method, DTM. During the derivation of the equations, effects of rotary inertia, shear deformation and hub radius are included. A code is written using the computer package Mathematica to calculate the natural frequencies and to plot the mode shapes. Since the results that are related to the trapezoidal cross-section are not present in literature, the beam is modeled by using a commercial FEM program, ABAQUS and the results obtained using DTM are compared with the ones taken from ABAQUS.