Distribution of cross travel in a bar at the sudden longitudinal load
DOI:
https://doi.org/10.15587/1729-4061.2012.4160Keywords:
asymptotic-group, cross travel, longitudinal stress, longitudinal wave.Abstract
The article is devoted to the disturbed region of the bar during the action of constant longitudinal load. The dynamics of the construction is described by new specified univariate dynamical equations of longitudinal strain. These equations are derived from asymptotic-group analysis of three-dimensional dynamical equations of the elasticity theory and they make it possible to study the averaged three-dimensional picture along the disturbed region, from the wave front to loaded butt. New equations also take into account the deformation of the bar cross-section. The method of asymptotic-group analysis made it possible to solve the specified equations, which allow obtaining and studying the distribution pattern of cross travel, according to construction near the front. As opposed to the classical pattern of a step change of a bar cross-section under the sudden load, the picture of a slow cross-section resizing was obtained.References
- Шамровский А.Д., Егармина Л.Н. Вывод динамических уравнений продольной деформации стержня при помощи двойного упрощения уравнений теории упругости // Нові матеріали і технології в металургії та машинобудуванні, 2009. – №2. –111-115 с.
- Шамровский А.Д., Егармина Л.Н. Моделирование распространения продольной волны в стержне с помощью уточненных динамических уравнений // Нові матеріали і технології в металургії та машинобудуванні, 2010. – №2. –139-145 с.
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Copyright (c) 2014 Александр Дмитриевич Шамровский, Лариса Николаевна Егармина
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