Eigenfrequencies of generally restrained Timoshenko beams

This article deals with the free transverse vibration of a Timoshenko beam with intermediate elastic constraints and ends elastically restrained against rotation and translation. A combination of the Ritz method and the Lagrange multiplier method and also the standard Ritz method are used to examine the free vibration characteristics of the mentioned beam. Trial functions denoting the transverse deflections and the normal rotations of the cross-section of the beam are expressed in polynomial forms. In order to obtain an indication of the accuracy of the developed mathematical models, some cases available in the literature have been considered. New results are presented for different end conditions and intermediate elastic restraints.