A Mathematical Model of Rod Lateral Oscillations Considering an External Tangential Load

A mathematical model has been developed for lateral oscillations of a rod fixed at one end, taking into account internal friction and external tangential harmonic loading. Analysis of the results of numerical calculations has shown that when the natural oscillation of the rod coincide with the external load frequency, resonant oscillations occur, accompanied by significant increase in the amplitude of rod oscillations, limited by the friction coefficient. At load frequencies approaching to the natural oscillation frequency, the amplitude of oscillations at each point of the rod is accompanied by periodic increase and decrease, qualifying them as bifurcation-flutter oscillations (beats). When the amplitude and frequency of the load oscillation change, the rod oscillations occur in the form of wave packets with amplitude-frequency modulation. In general, rod oscillations occur with an infinitely large number of amplitudes and frequencies. The maximum frequency at minimum amplitude is observed in sections of the rod close to the fixed end.