IDENTIFICATION OF SECOND SPECTRUM OF A TIMOSHENKO BEAM USING DIFFERENTIAL TRANSFORM METHOD

Abstract

In the present work, the vibration characteristics of a Timoshenko beam are examined using Differential Transform Method (DTM) with the end conditions hinge-hinge, fix-hinge, fix-fix and fix-free. The frequencies are computed for the beam with the length to depth ratio (L/H) of 2, 3, 5, 10 and 20. The results obtained from the DTM are compared with exact values and finite element results. DTM analysis shows that the second spectrum of frequency is observed in beams which are comparatively thick (L/H  10), with hinge-hinge end condition. Eigenfunctions for both frequency spectra are derived using this method. The convergence analysis of frequencies of a Timoshenko beam obtained using DTM is also presented. The second set of frequencies are not reflected in the vibration of beams with end conditions other than hinge-hinge. The mode shapes are presented for the pure shear mode and the first three bending and shear modes of hinge-hinge supported Timoshenko beam.

Keywords

• Timoshenko beam
• Second spectrum
• Differential transform method
• Bending spectrum
• Shear spectrum