Abstract: In this paper, an energy flow model is developed to analyze
transverse vibration including the effects of rotatory inertia as well as shear
distortion, which are very important in the Timoshenko beam transversely
vibrating in the medium-to-high frequency ranges. The energy governing
equations for this energy flow model are newly derived by using classical
displacement solutions of the flexural motion for the Timoshenko beam, in
detail. The derived energy governing equations are in the general form
incorporating not only the Euler-Bernoulli beam theory used for the
conventional energy flow model but also the Rayleigh, shear, and Timoshenko
beam theories. Finally, to verify the validity and accuracy of the derived
model, numerical analyses for simple finite Timoshenko beams were performed.
The results obtained by the derived energy flow model for simple finite
Timoshenko beams are compared with those of the classical solutions for the
Timoshenko beam, the energy flow solution, and the classical solution for the
Euler-Bernoulli beam with various excitation frequencies and damping loss
factors of the beam. In addition, the vibrational energy flow analyses of
coupled Timoshenko beams are described in the other companion paper.
