Transverse Vibration of Beams with Internal Damping, Rotary Inertia, and Shear

The manner in which the Timoshenko equation may be extended to predict the response to vibration of beams with internal damping has been discussed in detail. The conventional form of the Timoshenko equation describes how the presence of rotary inertia and shear displacement influences the vibrational response of beams when the bending wavelength is not large as compared with the beam thickness. Analysis has been developed in general terms, although, when considering the specific examples of center‐driven “free‐free” and simply clamped beams, it has sometimes been assumed that equal damping factors are associated with the complex shear and Young' moduli. This is normally realistic assumption for plastic and rubberlike materials, which possess relatively high internal damping. Representative computations of beam response have been performed and contrasted with results obtained from the simpler Bernoulli Euler theory, which assumes that the influence of rotary inertia and shear displacement may be disregarded.