Vibration of Timoshenko Beams with Internal Hinge

This paper is concerned with the free vibration problem of Timoshenko beams with an internal hinge. Exact vibration frequencies for axially loaded, clamped-clamped beams and clamped-simply supported beams are determined. The effects of axial force, transverse shear deformation, rotary inertia, and the location of the internal hinge on the fundamental frequency of vibration are investigated. A necessary condition for the optimal location of internal hinge that maximizes the fundamental frequency is also presented. We establish that (a) the optimal location of the hinge is at the point of inflection of an equivalent beam and (b) the maximum frequency value possible for a beam with an optimally positioned internal hinge is equal to the frequency of an equivalent beam without a hinge.