DYNAMIC ANALYSIS OF ELASTICALLY SUPPORTED TIMOSHENKO BEAM

Abstract

The flexible beams carrying attachments and ends elastically restrained against rotational and translation inertia often appear in engineering structures, modal analysis of those structures is important and necessary in structural design. In case of structure with large aspect ratio of height and length the Timoshenko beam theory (TBT) is used, instead of the Euler-Bernoulli theory (EBT), since it takes both shear and rotary inertia into account. Shear effect is extremely large in higher vibration modes due to reduced mode half wave length. In this paper, the full development and analysis of TBT for transversely vibrations uniform beam are presented for elastically supported ends. A two-node beam element with two degree of freedom per node is obtained based upon Hamilton’s principle. The influence of stiffnesses of the supports on the free vibration characteristics is investigated. For this purpose, the eigenvalues of the Timoshenko beam are calculated for various rigidity values of translational and rotational springs. The results obtained are discussed and compared with results obtained by other researchers.