On some features of the spectrum of longitudinal vibrations and sound emission of a rod

This study is devoted to the correlation of theoretical models of the impact and post-impact longitudinal vibrations of a rod with the corresponding experimental data. A solution to the problem of longitudinal vibrations of a cylindrical rod is obtained using the Saint-Venant wave model with free ends in the presence of friction. The friction coefficient is determined by a set of multi-frequency damped vibrations of the rod after impact. The amplitude-frequency dependences of the displacements and velocities of the rod ends for free post-shock vibrations are determined and analyzed together with their relationship with the acoustic pressure emitted by the ends at different ratios between the masses of the striker and rod. The shift of the amplitude maximum of acoustic pressure from the frequency of the fundamental tone to the overtone is shown to depend on the parameters determining the oscillation period and the mass ratio of the striker and rod. This is inconsistent with the longitudinal vibration spectrum of the rod, whose maximum corresponds to the frequency of the fundamental tone at any mass ratio of the striking pair. The obtained data are experimentally validated.