DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

NATURAL TRANSVERSE VIBRATIONS OF A PRESTRESSED ORTHOTROPIC PLATE-STRIPE

Vestnik MGSU 2/2012
  • Egorychev Oleg Aleksandrovich - Moscow State University of Civil Engineering (MSUCE) Doctor of Technical Sciences, Professor 8 (495) 320-43-02, Moscow State University of Civil Engineering (MSUCE), 26 Jaroslavskoe shosse, Moscow, 129337, Russia.
  • Egorychev Oleg Olegovich - Moscow State University of Civil Engineering (MSUCE) Doctor of Technical Sciences, Professor 8 (495) 287-49-14, Moscow State University of Civil Engineering (MSUCE), 26 Jaroslavskoe shosse, Moscow, 129337, Russia; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Brendje Vladimir Vladislavovich - Moscow State University of Civil Engineering (MSUCE) Senior Lecturer 8 (499) 161-21-57, Moscow State University of Civil Engineering (MSUCE), 26 Jaroslavskoe shosse, Moscow, 129337, Russia; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 11 - 14

The article represents a new outlook at the boundary-value problem of natural vibrations of a homogeneous pre-stressed orthotropic plate-stripe. In the paper, the motion equation represents a new approximate hyperbolic equation (rather than a parabolic equation used in the majority of papers covering the same problem) describing the vibration of a homogeneous orthotropic plate-stripe. The proposed research is based on newly derived boundary conditions describing the pin-edge, rigid, and elastic (vertical) types of fixing, as well as the boundary conditions applicable to the unfixed edge of the plate. The paper contemplates the application of the Laplace transformation and a non-standard representation of a homogeneous differential equation with fixed factors. The article proposes a detailed representation of the problem of natural vibrations of a homogeneous orthotropic plate-stripe if rigidly fixed at opposite sides; besides, the article also provides frequency equations (no conclusions) describing the plate characterized by the following boundary conditions: rigid fixing at one side and pin-edge fixing at the opposite side; pin-edge fixing at one side and free (unfixed) other side; rigid fixing at one side and elastic fixing at the other side. The results described in the article may be helpful if applied in the construction sector whenever flat structural elements are considered. Moreover, specialists in solid mechanics and theory of elasticity may benefit from the ideas proposed in the article.

DOI: 10.22227/1997-0935.2012.2.11 - 14

References
  1. Egorychev O.O. Kolebanija ploskih elementov konstrukcij [Vibrations of Two-Dimensional Structural Elements]. Moscow, ASV, 2005, pp. 45—49.
  2. Arun K Gupta, Neeri Agarwal, Sanjay Kumar. Free transverse vibrations of orthotropic viscoelastic rectangular plate with continuously varying thickness and density// Institute of Thermomechanics AS CR, Prague, Czech Rep, 2010, Issue # 2.
  3. Filippov I.G., Cheban V.G. Matematicheskaja teorija kolebanij uprugih i vjazkouprugih plastin i sterzhnej [Mathematical Theory of Vibrations of Elastic and Viscoelastic Plates and Rods]. Kishinev, Shtinica, 1988, pp. 27—30.

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NATURAL TRANSVERSE VIBRATIONS OF AN ORTHOTROPIC PLATE-STRIP WITH FREE EDGES

Vestnik MGSU 7/2012
  • Egorychev Oleg Aleksandrovich - Moscow State University of Civil Engineering (MSUCE) Doctor of Technical Sciences, Professor, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Egorychev Oleg Olegovich - Moscow State University of Civil Engineering (MSUCE) Doctor of Technical Sciences, Professor 8 (495) 287-49-14, Moscow State University of Civil Engineering (MSUCE), 26 Jaroslavskoe shosse, Moscow, 129337, Russia; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Brende Vladimir Vladislavovich - Moscow State University of Civil Engineering (MSUCE) Senior Lecturer, +7 (499) 161-21-57, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 26 - 30

In the article, the authors present their new formulation of the problem of the boundary value of natural vibrations of a homogeneous pre-stressed orthotropic plate-strip in different boundary conditions. A new approximate hyperbolic (in contrast to most authors) equation of oscillations of a homogeneous orthotropic plate-strip is used in the paper in the capacity of an equation of motion. Besides, the authors propose their newly derived boundary conditions for a free edge of the plate. The authors employ the Laplace transformation and a non-standard representation of the general solution of homogeneous differential equations with constant coefficients. The authors also provide a detailed description of the problem of free vibrations of a homogeneous orthotropic plate-strip, if rigidly attached in the opposite sides. The results presented in this article may be applied in the areas of construction and machine building, wherever flat structural elements are used. In addition, professionals in mechanics of solid deformable body and elasticity theory may benefit from the findings presented in the article.

DOI: 10.22227/1997-0935.2012.7.26 - 30

References
  1. Uflyand Ya.S. Rasprostranenie voln pri poperechnykh kolebaniyakh sterzhney i plastin [Wave Propagation in the Event of Transverse Vibrations of Rods and Plates]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 1948, vol. 12, no. 33, pp. 287—300.
  2. Lyav A. Matematicheskaya teoriya uprugosti [Mathematical Theory of Elasticity]. Moscow-Leningrad, ONTI Publ., 1935, 674 p.
  3. Egorychev O.O. Kolebaniya ploskikh elementov konstruktsiy [Vibrations of Flat Elements of Structures]. Moscow, ASV Publ., 2005, pp. 45—49.
  4. Egorychev O.A., Egorychev O.O., Brende V.V. Vyvod chastotnogo uravneniya sobstvennykh poperechnykh kolebaniy predvaritel’no napryazhennoy plastiny uprugo zakreplennoy po odnomu krayu i zhestko zakreplennoy po-drugomu [Derivation of a Frequency Equation of Natural Transverse Vibrations of a Pre-stressed Elastic Plate, If One Edge Is Fixed Rigidly and the Other One is Fixed Elastically]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2010, no. 4, vol. 3, pp. 246—251.
  5. Filippov I.G., Cheban V.G. Matematicheskaya teoriya kolebaniy uprugikh i vyazkouprugikh plastin i sterzhney [Mathematical Theory of Vibrations of Elastic and Viscoelastic Plates and Rods]. Kishinev, Shtiintsa Publ., 1988, pp. 27—30.
  6. Gupta A.K., Aragval N., Kumar S. Svobodnye kolebaniya ortotropnoy vyazkouprugoy plastiny s postoyanno menyayushcheysya tolshchinoy i plotnost’yu [Free Transverse Vibrations of an Orthotropic Visco-Elastic Plate with Continuously Varying Thickness and Density]. Institute of Thermal Dynamics, Prague, Czech Republic, 2010, no. 2.
  7. Egorychev O.A., Egorychev O.O., Brende V.V. Sobstvennye poperechnye kolebaniya predvaritel’no napryazhennoy ortotropnoy plastinki-polosy uprugo zakreplennoy po odnomu krayu i svobodnoy po drugomu [Natural Transverse Vibrations of a Pre-stressed Orthotropic Plate, If One Edge Is Fixed Elastically and the Other One Is Free]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2010, no. 4, vol. 3, pp. 252—258.
  8. Lol R. Poperechnye kolebaniya ortotropnykh neodnorodnykh pryamougol’nykh plastin s nepreryvno menyayushcheysya plotnost’yu [Transverse Vibrations of Orthotropic Non-homogeneous Rectangular Plates with Continuously Varying Density]. Indian University of Technology, 2002, no. 5.
  9. Egorychev O.A., Brende V.V. Sobstvennye kolebaniya odnorodnoy ortotropnoy plastiny [Natural Vibrations of a Homogeneous Orthotropic Plate]. Department of Industrial and Civil Engineering, 2010, no. 6, pp.
  10. Lekhnitskiy S.G. Teoriya uprugosti anizotropnogo tela [Theory of Elasticity of an Anisotropic Body]. Moscow, Nauka. Fizmatlit Publ., 1977.

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MODELING OF RAILWAY TRACK OPERATION AS A SYSTEM OF QUASI-ELASTIC ORTHOTROPIC LAYERS

Vestnik MGSU 3/2016
  • Sycheva Anna Vyacheslavovna - Moscow State University of Railway Engineering (MIIT) Candidate of Technical Sciences, Associate Professor, Department of Buildings and Structures on the Transport, Moscow State University of Railway Engineering (MIIT), 22/2 Chasovaya str., Moscow, 125993, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Sychev Vyacheslav Petrovich - Moscow State University of Railway Engineering (MIIT) Doctor of Technical Sciences, Professor, Department of Transport Construction, Moscow State University of Railway Engineering (MIIT), 22/2 Chasovaya str., Moscow, 125993, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Buchkin Vitaliy Alekseevich - Moscow State University of Railway Engineering (MIIT) Doctor of Technical Sciences, Professor, Department of Railway Design and Construction, Moscow State University of Railway Engineering (MIIT), 22/2 Chasovaya str., Moscow, 125993, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Bykov Yuriy Aleksandrovich - Moscow State University of Railway Engineering (MIIT) Doctor of Technical Sciences, Professor, Department of Railway and Track Economy, Moscow State University of Railway Engineering (MIIT), 22/2 Chasovaya str., Moscow, 125993, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 37-46

In this paper the authors give a solution to the problem of the impact of a rolling stock on the rail track on the basis of modeling a railway track as a multi-layered space, introducing each of the layers is a quasi-elastic orthotropic layer with cylindrical anisotropy in the polar coordinate system. The article describes wave equations, taking into account the rotational inertia of cross sectional and transverse shear strains. From the point of view of classical structural mechanics train path can be represented as a multilayer system comprising separate layers with different stiffness, lying on the foundation being the elastic-isotropic space. Winkler model provides that the basis is linearly deformable space, there are loads influencing its surface. These loads are transferred through a layered deformable half-space. This representation is used in this study as an initial approximation. For more accurate results of the deformation of a railway track because of rolling dynamic loads it is proposed to present a railway track in the form of a layered structure, where each element (assembled rails and sleepers, ballast section, the soil in the embankment, basement soils) is modeled as a planar quasi-elastic orthotropic layer with cylindrical anisotropy. The equations describing the dynamic behaviour of flat element in a polar coordinate system are hyperbolic in nature and take into account the rotational inertia of the cross sectional and the transverse shear strains. This allows identifying the impact on the final characteristics of the blade wave effects, and oscillatory processes. In order to determine the unknown functions included in the constitutive equations it is proposed to use decomposition in power series in spatial coordinate and time. In order to determine the coefficients of ray series for the required functions, it is necessary to differentiate the defining wave equations k times on time, to take their difference on the different sides of the wave surface, and apply the consistency condition for the transition from the jump of the derivative of a function in the coordinate to the jump of the derivative of a sought function in time of higher order. The proposed approach allows considering the whole structure of the railway track in the form of a set of layers, making for each layer (rail - sleeper; sleeper - ballast; ballast - ballast bed) a system of equations and solving them. Therefore it is possible to vary the characteristics of different layers and their modules of elasticity, determining the optimal thickness of the ballast layer or oversleeper and undersleeper strips.

DOI: 10.22227/1997-0935.2016.3.37-46

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