ISSN 1991-2927

ACP № 3 (65) 2021

Author: "Sergei Anatolevich Kashkirov"

Sergei Anatolevich Kashkirov, Deputy Head of the Design Engineering Department of Sosny R&D Company, Post-graduate Student; graduated from the Dimitrovgrad Institute of Technology, Management, and Design at Ulyanovsk State Technical University; Deputy Head of the Design Engineering Department of Sosny R&D Company; an author of articles in the field of analysis of alternating structure mechanisms. [e-mail:]S. Kashkirov,

Vladimir Kuzmich Manzhosov, Ulyanovsk State Technical University, Doctor of Engineering, Professor; graduated from the Machine-Building Faculty of Frunze Polytechnic Institute; Head of the Department of Theoretical and Applied Mechanics at Ulyanovsk State Technical University; an author of articles, monographs, and inventions in the field of dynamics of machines, modeling of shock processes. [e-mail:]V. Manzhosov

The Wave Model of Hauling Member (locomotive), Elastic Rod, and Transported Object Motion  37_9.pdf

A wave model was developed to simulate motion of the rod rigidly connected to a driving member (locomotive) and towing a driven member. The motion of the driving member is set cinematically. The motion of the rod cross-sections is described by a wave equation. The equation is solved by the traveling wave method. The functions of forward and backward waves on different motion intervals are determined from the conditions of their development in the rod cross-sections interfacing the driving member and the transported object. Characteristics of the forward and backward waves are linear functions. Their view in the coordinate plane allows preparation of the field of wave states for the mechanical system. The nature and time of the wave state experienced by a random cross-section of the rod on any motion interval can be assessed by the vertical slice method for the field of wave states. The computing scheme for solving motion equations is based on representation of the rod as a multitude of successively connected sections, as well as on the pattern of the forward wave development in the cross-section х = 0, the pattern of the forward and backward wave development on the “rod end - driving member (locomotive)” boundary, and the properties of the forward and backward wave functions to maintain their parameters during propagation throughout a homogeneous section at the velocity of sound. The wave model of the rod motion allows taking into account the rod distributed mass, analyzing the wave processes that determine the nature of the motion of the transported object, and determining the unilateral constraint point.

Rod, wave equation, traveling wave method, strain wave, rod cross-section rate, longitudinal strain in rod cross-sections, field of wave states, computing scheme.

2014_ 3

Sections: Mathematical modeling

Subjects: Mathematical modeling.

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