Eigenfrequencies and Critical Speeds on a Beam due to Travelling Waves

Abstract

A dynamic load, suddenly applied at a point of a beam, produces a local disturbance that propagates or diffuses to the rest of the beam. This propagation takes place with a speed depending on the material and geometrical characteris- tics of the beam. It has been demonstrated that an impulsive disturbance involving shear and moment will result in two wave types, one that propagates with the shear wave velocity and a second that propagates with a moment-wave velocity. It is observed that tampering with the cross-section of the beam may result to equal shear wave and moment-wave veloci- ties and the two types of disturbances will travel together along with additionally interfering shear waves from beam's ends reflections. In this paper, the effect of the traveling waves on the dynamic characteristics of a beam is studied. A complete beam model is presented, which motion is governed by the Timoshenko equation. Two main cases are exam- ined, namely a simply supported beam, and a beam resting on a Winkler-type elastic foundation. Analytical results are presented in graphical form showing the influence of the traveling waves on the eigenfrequencies and critical speeds of such a beam and useful conclusions are drawn.