In one scenario, the development of a defect in the attachment of the rod (Journal of Mathematics Mechanics and Computer Science, 2024)
This article discusses the issue of the origin of a rod fastening defect. At the beginning of operation, the rod is rigidly fixed at the edges. During operation, over time, certain defects may appear at the ends of the rod. We need to find out what defects may occur? Then it is necessary to trace the further behavior of the emerging defects at the ends of the rod. This paper discusses the diagnostics of types of fastening of a structure made of interconnected rods. In this work, the state of fastening types in individual parts of the structure is determined and a number of results are obtained using mathematical analysis. Most of them assume how failures begin at the end connections of the rods, and then the scenario for their further development. Mathematical models are presented to determine the state of the rod attachments relative to the proposed scenario, and then the state in which they are in is carefully examined. Defects in fastening objects made from a system of rods are investigated using identification problems. The difference between this article and other works is that instead of the shape of the area, the size of the object, or the state of its location, defects that occur in fasteners are studied. This work is devoted to the search for types of fastening that provide the required range of vibration frequencies.
Keywords: Euler-Bernoulli equation; rod; defect; Taylor formula