WAVE PROPAGATION IN AND VIBRATION OF A TRAVELLING BEAM WITH AND WITHOUT NON-LINEAR EFFECTS, PART I: FREE VIBRATION

The relation between the wave propagation and the free vibration in a travelling beam with simple supports has been thoroughly investigated. The frequency equation of such a beam has been derived using the phase-closure principle. Since the characters of the waves change drastically as the axial speed is increased beyond a certain value, the phase-closure principle has been applied differently in these two speed regimes. The justifications for some approximate methods of obtaining the natural frequencies are also discussed. Lastly, the non-linear normal modes are derived again using the phase-closure principle. The computation of the forced response using the wave propagation approach is discussed in Part II.