Eigenfrequencies of generally restrained Timoshenko beams with an internal hinge

Abstract

This paper deals with the free transverse vibration of a Timoshenko beam with endselastically restrained against rotation and translation, and an arbitrarily located internal hingeincluding intermediate elastic constraints. A combination of the Ritz method and the Lagrangemultiplier 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 beamare expressed in polynomial forms. In order to obtain an indication of the accuracy of the developed mathematical model, some casesavailable in the literature have been considered. New results are presented for different end conditionsand restraint conditions in the intermediate elastic constraints. Also a comparison with a crack modelis included.