Eigenfrequencies of Generally Restrained Timoshenko Beams with an Internal Hinge

Abstract

This paper deals with the free transverse vibration of a Timoshenko beam with ends elastically restrained against rotation and translation, and an arbitrarily located internal hinge including intermediate elastic constraints. A combination of the Ritz method and the Lagrange multiplier method is used to determine free vibrations 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 model, some cases available in the literature have been considered. New results are presented for different end conditions and restraint conditions in the intermediate elastic constraints. Also a comparison with a crack model is included.