DOI: https://doi.org/10.36719/2789-6919/50/114-122
Tahir Mammadov
Ganja State University
PhD in Mathematics
https://orcid.org/0009-0002-9546-3683
tahir.mammadov@gdu.edu.az
Elchin Javadov
Ganja State University
PhD in Technique
https://orcid.org/0009-0002-8868-9617
elcin.cavadov@gdu.edu.az
Irada Seyidova
Ganja State University
https://orcid.org/0009-0008-0633-4868
irada.seyidova@gdu.edu.az
The Problem of Impact on a Flexibly Deformable Shaft
Abstract
In addition to elasticity, materials with viscous properties are also widely used in various fields of industry. Therefore, it is important to determine the physical state of these materials, in the form of fibers, when they are hit by an object of a given shape. One of the current and important problems in the theory of transverse impact is the classification of boundary conditions at the turning point and the reflection of the obtained solution to physical reality. For the first time in the theory of transverse impact, Sh.M.Mutallimov showed that for cases greater than the speed of sound, the stress of flexible structures behind the turning point (behind the sharp shear wave) does not take a negative value and the rod (membrane) "wrinkles" in this section. He gave a classification of boundary conditions at the sharp shear wave front depending on the speed of the striking object, the geometric shape of the object, the friction coefficient and the mechanical properties of the material.
The article provides information on the basic concepts used in the theory of transverse impact on flexible structures. The equation of motion in the bending region of a flexible rod is given for the variable-velocity case of impact. The boundary conditions in the transverse impact on a linear viscoelastic (Maxwell model) rod, at the sharp shear wave front, are investigated. The solution of such problems can be used in addition to the development of wave mechanics, in the solution of various engineering problems, and in the solution of various technological problems.
Keywords: transverse impact, flexible thread, viscoelastic thread, supersonic mode, subsonic mode, wedge, inflection point, symmetrical wedge