RIGOROUS DERIVATION OF A SYSTEM OF LINEAR INTEGRO-DIFFERENTIAL EQUATIONS FOR VIBRATIONS OF CURVED RODS
DOI:
https://doi.org/10.55640/Keywords:
curvilinear rod, vibration, viscoelasticity, hereditary nucleus, integro-differential equations, Hamilton's principle.Abstract
In this article, the problem of deriving a system of linear integro-differential equations describing small oscillations of curvilinear rods is considered. With a curvature along the axis of the rod, the viscoelastic properties of the material are described by the Boltzmann-Volterra hereditary model. Based on kinematic perceptions and stress-strain relationships, the equations of motion are derived using the Hamilton principle or the virtual work method. The obtained results show that in special cases (straight rod, pure elastic material) they are reduced to classical equations.
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References
1.Boltzmann, L. Fundamental works on the theory of viscoelastic media.
2.Volterra, V. Hereditary (integral) equations and their applications in mechanics.
3.Timoshenko, S. P. Theory of vibrations of rods and beams.
4.Goldenveizer, A. Theory of elasticity and methods of the calculus of variations.
5.Авлиякулов Н.Н., Сафаров И.И. Современные задачи статики и динамики подземных трубопроводов. Ташкент, Fan va texnologiya. 2007. 306 с.// Avliyaqulov N.N., Safarov I.I. Modern Problems of Statics and Dynamics of Underground Pipelines. Tashkent, Fan va texnologiya. 2007. 306 p.
6.Сафаров И.И., Тешаев М.Х.Эсанов Н.Қ., Ҳамроева З.Қ. “Математическое моделирование собственных и вынужденных колебаний криволинейных труб, взаимодействующих со средой. Тошкент, ФАН, 2009.-161б.// Safarov I.I., Teshayev M.Kh. Esanov N.K., Hamroyeva Z.K. "Mathematical modeling of natural and forced vibrations of curvilinear pipes interacting with the medium." Tashkent, FAN, 2009.-161p.
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