Eliseev S.V., Eliseev A.V., Kashuba V.B. Features of gap estimation in model problem of flipping particle with unilateral constraints
Features of gap estimation in model problem of flipping particle with unilateral constraints
Eliseev S.V., Eliseev A.V., Kashuba V.B.
The article presents the research results of mechanical systems with unilateral constraints. The model problem of flipping a particle on a horizontal surface with unilateral constraints under gravitation is considered. The re-search deals with the time and height of the particle reaching the surface in accordance with the surface frequency and vibration amplitude. The estimation of the gap between the material particle and the vibration surface is obtained. The paper presents analytical ratios of frequency and the surface vibration amplitude that provide a predetermined height or the reaching time of the material particle. A number of maximum flipping characteristics are given. The paper discusses restrictions on the mathematical model parameters, based on the surface physical characteristics and the ways to modify the original mathematical model. The methodological framework can be used in the research of continuous flipping mode, taking into consideration some additional constant force.
Keywords: unilateral constraints, the interaction of a particle with the vibrating surface, one-touch flipping mode, multiple flipping mode, the gap between particle and surface, flipping height, flipping time, the particle take-off.
References
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- Lurie A.I. Analytical Mechanics. – Moscow: Nauka, 1986. – 516 p.
- Artobolevskiy I.I. Theory of mechanisms and machines. – Moscow: Nauka, 1978. – 640 p.
- Blechman I.I., Dzhanalidze G.Y. Vibratory movement. – Moscow: Nauka, 1968. – 316 p.
- Selvinskiy V.V. The dynamics of the contact interaction of solids. – Blagoveshchensk: Publishing House of the Amur State University. 2009. – 164 p.
- Eliseev S.V., Markov K.K. Some aspects of the dynamics of the oscillatory process with unilateral constraints // Mechanics and Control. – Irkutsk: IPI, 1971. – P. 71-83.
- Eliseev S.V., Lotkin O.I. The conditions of existence and loss of contact for systems with unilateral constraints // Proceedings of the OMIITa. Vol. 69. – Omsk OMIIT, 1966. – P. 93-99.
- Gorbikov S.P., Neumark Y.I. The main modes of motion in vibro-tossing // Math. Academy of Sciences of the USSR, Mechanics of Solids, № 4, 1981. – P. 39-50.
- Eliseev S.V., Eliseev A.V. Modes flip of a particle on a vibrating surface in the model problem with unilateral constraints // Modern technology. System analysis. Modeling. 2012, № 3 (35). – P. 64-75.
- Serebrenitskiy P.P. General Technical Reference. – St. Petersburg: Polytechnic. 2004. – 445 p.
«Engineering industry and life safety» №1 (15), 2013. Pages: 50-56
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Eliseev Sergey Viktorovich – Professor, Irkutsk State University of Railway Transport, Irkutsk, Russia. E-mail: eliseev_s@inbox.ru
Eliseev Andrey Vladimirovich – Graduate student, Irkutsk State University of Railway Engineering, Irkutsk, Russia. E-mail: andrey.marketer@gmail.com
Kashuba Vladimir Bogdanovich – Ph.D., Bratsk State University, Bratsk, Russia. E-mail: plemja@rambler.ru
Eliseev S.V., Sitov I.S., Eliseev A.V. Motion of material particle with tossing in model problem with «not holding» ties
Motion of material particle with tossing in model problem with «not holding» ties
Eliseev S.V., Sitov I.S., Eliseev A.V.
The purpose of this work is to establish research methods mechanical systems with «not holding» ties. The problems of determining the mode of continuous flying up of a material particle from surface oscillations with the force of gravity are considered. The graphical-analytical method for determination of the mode parameters is realized. The analytical characteristics of the relations between the basic modes of continuous flying up of a particle as a function of the parameters of the surface vibrations are identified. The proposed methodological framework can be used to research the mode of continuous flipping with additional constant force which operate from the external environment in free flight phase.
Keywords: not holding ties, interaction of a material particle with a vibrating surface, a mode of a material particle tossing with one contact.
References
- Loitsyansky L.G. Course of Theoretical Mechanics. Vol. 2. Dynamics / L.G. Loitsyansky, A.I. Lurie. – Moscow: Nauka. 1968. – 638 p.
- Lurie A.I. Analytical Mechanics / A.I. Lurie. – M: Nauka. 1986. – 516 p.
- Artobolevsky I.I. Theory of mechanisms and machines – M: Nauka. 1978. – 640 p.
- Blekhman I.I., Dzhanalidze G.Y. Vibrational displacement. – M: Nauka. 1968. -316 p.
- Selvinsky V.V. The dynamics of the contact interaction of solids. – Blagoveshchensk: Publishing House of Amur of public university, 2009. – 164 p.
- Eliseev S.V., Markov K.K. Some aspects of the dynamics-rye oscillatory process with unilateral constraints // Mechanics and Control. – Irkutsk: IPI, 1971. – P. 71-83.
- Eliseev S.V., Lotkin O.I. Conditions of existence and breach of contact for systems with unilateral constraints // Proceedings OMIIT. – Omsk: OMIIT, 1966, Vol. 69. – P. 93-99.
- Gorbikov S.P., Neimark Y.I. The major modes of motion in vibro tossing // Math. USSR “Mechanics of rigid body”, 1981, № 4. – P. 39-50.
- Eliseev S.V., Eliseev A.V. Modes flip of a particle on a vibrating surface in the model problem with unilateral constraints. // Modern technologies. Systems analysis. Modeling, 2012, № 3 (35). – P. 64-75.
«Engineering industry and life safety» №3 (13), 2012. Pages: 53-58
Download full text:
Eliseev Sergey Viktorovich – Professor, Irkutsk State University of Railway Transport, Irkutsk, Russia. E-mail: eliseev_s@inbox.ru
Sitov Ilya Sergeevich – Docent, Bratsk State University, Irkutsk, Russia. E-mail: sitov@yandex.ru
Eliseev Andrey Vladimirovich – Student, Irkutsk State University of Railway Engineering, Irkutsk, Russia. E-mail: andrey.marketer@gmail.com
