The coordinate of a notch and its depth and length are found from three eigenfrequencies of bending vibrations. The notch is a model of a flaw in a bar, in particular, of a transverse open crack. Taking into account that the crack propagates from a small nucleus and not necessarily from the most stressed cross section, it is assumed that the notch can be at any place in the bar.

The influence of the average value and amplitude of the transient internal pressure in the pipelines on the spatial vibrations of the latter has been assessed. The graphic dependences of the spatial vibrations, their phase patterns, Fourier spectra, and Poincare maps have been presented. The latter have been analyzed depending on the input parameters and time. Brief conclusions have been formulated.

The location and size of damage in the form of a transverse notch of a shaft were determined from three natural frequencies of its torsional vibrations.

Eigenfrequencies of bending oscillations are determined for a resonator with rectangular cross-sections mounted on hinged supports. Consideration is given to the surface effect caused by the interaction between gas pressure and the difference in the areas of the resonator’s convex and concave surfaces. Changes in the frequency spectrum are examined at the presence of both concentrated and uniformly distributed masses attached to the resonator’s surface. The solution of the inverse problem enables the identification of attached masses using changes of eigenfrequencies.

The spatial vibrations of a pipeline and the fluid inside it are considered with respect to the horizontal axis passing through supports under the action of internal shock pressure. The coupling...