ISSN 2658–5782
DOI 10.21662
DOI 10.21662
Electronic Scientific Journal
Rods, beams, shafts, pipelines, round plates. membranes are parts of structures in which local defects such as cracks, dents, cavities, local corrosion can be formed. Provides an overview of the research A. G. Khakimov for the diagnosis of local defects. It is received: 1. The two eigenfrequencies of the longitudinal oscillations can determine the location and the notch parameter characterizing its size. 2. The three lower eigenfrequencies of the longitudinal oscillations can determine the initial coordinate and the value of the attached distributed mass to the stepped rod, as well as the ratio of the areas. 3. The solution of the inverse problem for extended rods allows us to determine the coordinate of the incision and the parameter containing its depth and length, according to the incident and reflected waves at the observation site. 4. The reflection from the air cavity and the passage of a longitudinal damped traveling wave in a pipeline immersed in a viscous liquid are determined, and the solution of the inverse problem allows to determine the coordinate of the air cavity and its length according to the reflected wave at the observation site. 5. The initial coordinate and the length of the longitudinal through radial section of the hollow shaft are determined by the two eigenfrequencies of torsional vibrations. 6. The coordinate, length and parameter of the drill string notch are determined by the three eigenfrequencies of the torsional vibrations. 7. The reflection from the distributed mass attached to the pipeline and the passage of the flexural traveling wave are considered. The dependence of the solution on the initial coordinate of the distributed mass and its magnitude is obtained, and the inverse problem of determining the initial coordinate of the distributed mass and its magnitude from the data of the reflected wave at the observation point is solved. 8. The radius and thickness of the thin central region of the membrane are determined by the two eigenfrequencies of the transverse vibrations. 9. The radius, thickness of the thinned central area of the plate and the value of the attached distributed mass are determined by the three natural frequencies of the bending oscillations. 10. By three frequencies of bending vibrations it is possible to determine the velocity parameter, the relative mass of the product per unit length of the pipeline and the relative mass of sediments on the walls of the pipeline and, as a consequence, the mass flow of liquid through the pipeline.
rod,
shaft,
beam,
membrane,
plate,
pipeline,
defect,
computational diagnostics
Problem: Review of works devoted to the identification of defects in distributed mechanical systems using natural oscillation frequencies and transmitted and reflected waves.
Methods: Eigenfrequencies are used to detect a defect in a finite length rod and its location. In the case of rods of large length in comparison with the wavelength, this method of determining defects is inconvenient. More appropriate is the method of determining defects by transmission and reflection of waves. Identification of these defects is made by means of natural frequencies of oscillations, and also by means of passing and reflected waves. Local defects are modeled by coupling conditions, and cavities and cracks are modeled by continuous sections of the rod with altered stiffness, cross-sectional area and density.
In a study was determined:
1. The two eigenfrequencies of the longitudinal oscillations can determine the location and the notch parameter characterizing its size.
2. The three lower eigenfrequencies of the longitudinal oscillations can determine the initial coordinate and the value of the attached distributed mass to the stepped rod, as well as the ratio of the areas.
3. The solution of the inverse problem for extended rods allows us to determine the coordinate of the incision and the parameter containing its depth and length, according to the incident and reflected waves at the observation site.
4. The reflection from the air cavity and the passage of a longitudinal damped traveling wave in a pipeline immersed in a viscous liquid are determined. The solution of the inverse problem allows to determine the coordinate of the air cavity and its length according to the reflected wave at the observation site.
5. The initial coordinate and the length of the longitudinal through radial section of the hollow shaft are determined by the two eigenfrequencies of torsional vibrations.
6. The coordinate, length and parameter of the drill string notch are determined by the three eigenfrequencies of the torsional vibrations.
7. The stiffness parameter, the polar moment of inertia of the shaft in the second section, the initial coordinate and the length of this section can be determined by the four frequencies of free torsional vibrations.
8. The reflection and passage of a torsional wave propagating along an infinite rod with an artificial defect are considered. The solution of the inverse problem allows us to determine the coordinate of the rod damage and the parameter containing the depth and length of the defect by the characteristics of the incident and reflected waves at the observation site.
9. The reflection from the distributed mass attached to the pipeline and the passage of the bending traveling wave are considered. The dependence of the solution on the initial coordinate of the distributed mass and its magnitude is obtained, and the inverse problem of determining the initial coordinate of the distributed mass and its magnitude from the data of the reflected wave at the observation point is solved.
10. The radius and thickness of the thin Central region of the membrane are determined by the two eigenfrequencies of the transverse vibrations.
11. The radius, thickness of the thinned Central area of the plate and the value of the attached distributed mass are determined by the three natural frequencies of the bending oscillations.
12. By three frequencies of bending vibrations it is possible to determine the velocity parameter, the relative mass of the product per unit length of the pipeline and the relative mass of sediments on the walls of the pipeline and, as a consequence, the mass flow of liquid through the pipeline. The obtained results can be used for the acoustic method of pipeline diagnostics.
