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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Natural frequencies and forms of flexural vibrations of a beam with a crack

Vestnik MGSU 3/2014
  • Gordon Vladimir Aleksandrovich - State University - Education-Science-Production Complex (UNPK) Doctor of Technical Sciences, Professor, head, Department of Higher Mathematics, State University - Education-Science-Production Complex (UNPK), 29 Naugorskoe shosse, Orel, 302020, Russian Federation; +7(4862) 41-98-48; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Kravtsova El'vira Aleksandrovna - State University - Education-Science-Production Complex (UNPK) Senior Lecturer, Department of Information Systems, State University - Education-Science-Production Complex (UNPK), 29 Naugorskoe shosse, Orel, 302020, Russian Federation; +7(4862) 41-98-48; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 50-58

In view of providing durability of constructions, the urgent problem is studying dynamic processes in loaded rod structures occurring in the process of sudden local defects formation, such as breakage of support bonds, partial destruction, transverse and longitudinal cracks etc., which are united under general term "beyond design impacts". To date, a number of problems related to this topic are solved: the problem of dynamic loadings at sudden formation of transverse cracks, the problem of partial tie breaks in the bearings, partial destruction and longitudinal lamination of compound bars. In the paper the authors propose a method of determining the spectrum of natural frequencies of flexural vibrations of a rod system with this type of injury. The results are to be used for modal analysis of forced vibrations of a beam with a defect of longitudinal lamination, depending on its level.

DOI: 10.22227/1997-0935.2014.3.50-58

References
  1. Gordon V.A., Poturaeva T.V. Chastoty sobstvennykh izgibnykh kolebaniy svobodno opertoy balki s treshchinoy [Natural Flexural Vibrations of a freely supported beam with a crack]. Stroitel'naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 2009, no. 3 (224), pp. 19—23.
  2. Lin H.-P. Direct and Inverse Methods of Free Vibration Analysis of the Simply Supported Beams with Cracks. Engineering Structures. 2004, vol. 26, no. 4, pp. 427—436. DOI: 10.1016/j.engstruct.2003.10.014.
  3. Poturaeva T.V. Perekhodnye protsessy v balkakh pri vnezapnykh strukturnykh perestroykakh i treshchinoobrazovanii: dissertatsiya kandidata tekhnicheskikh nauk [Transition Processes in Beams in Case of Sudden Structural Reorganizations and Crack-formation. Thesis of the Candidate of Technical Sciences]. Orel, 2009, 143 p.
  4. Lin Hai-Ping. Dynamic Design of Beams Using Soft Tuning. Proceedings of the 15th International Congress on Sound and Vibration. Daejeon, Korea, 2008, pp. 215—222.
  5. Gordon V.A., Pavlova T.A. Dinamicheskie yavleniya v balke pri lavinoobraznom protsesse vyklyucheniya svyazey v oporakh [Dynamic Effects in a Beam in Case of Snowballing Process of Support Connections Shutting off]. Vibratsionnye mashiny i tekhnologii: sbornik nauchykh trudov v 2 chastyakh [Vibrating Machines and Technologies. Collection of Scientific Works. In 2 Parts]. Kursk, KurskGTU Publ., 2005, Part 1, pp. 166—169.
  6. Gordon V.A., Klyueva N.V., Bukhtiyarova A.S., Poturaeva T.V. Raschet dinamicheskikh usiliy v konstruktivno-nelineynykh elementakh sterzhnevykh sistem pri vnezapnykh strukturnykh izmeneniyakh [Calculating Dynamic Impact in Constructive Non-linear Elements of Bar Systems in Case of Sudden Structural Changes]. Stroitel'naya mekhanika i raschet sooruzheniy [Construction Mechanics and Calculation of Structures]. 2008, no. 6, pp. 23—26.
  7. Pavlova T.A. Razvitie metoda rascheta stroitel'nykh konstruktsiy na zhivuchest' pri vnezapnykh strukturnykh izmeneniyakh: dissertatsiya kandidata tekhnicheskikh nauk [Development of the Durability Calculating Method for Building Structures in Case of Sudden Structural Changes. Thesis of the Candidate of Technical Sciences]. Orel, 2006.
  8. Klyueva N.V., Gordon V.A. Raschet dinamicheskikh dogruzheniy v sterzhnevoy prostranstvennoy sisteme s vnezapno vyklyuchayushchimisya elementami [Calculating Dynamic Loads in a Space Bare Structure with Suddenly Shutting off Elements]. Stroitel'naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Structural Mechanics of Engineering Structures and Constructions]. 2008, no. 6, pp. 72—79.
  9. Gordon V.A., Brusova V.I., Volchkov A.A. Napryazhenno-deformirovannoe sostoyanie nagruzhennoy balki pri vnezapnom umen'shenii ploshchadi poperechnogo secheniya [Stressstrain State of a Loaded Beam in Case of Sudden Cross Section Area Decrease]. Izvestiya OrelGTU. Seriya Stroitel'stvo. Transport. [News of Orel Technical University. Series: Construction. Transport]. 2006, no. 3—4, pp. 20—27.
  10. Gordon V.A., Brusova V.I., Volchkov A.A. Analiz dinamicheskogo protsessa v nagruzhennoy balke pri ee chastichnom razrushenii [Dynamic Process Analysis in a Loaded Beam in Case of its Partial Destruction]. Sovremennye problemy matematiki, mekhaniki, informatiki: materialy Mezhdunarodnoy konferentsii [Current Issues of Mathematics, Mechanics, Computer Science: Works of International Conference]. Tula, TulGU Publ., 2007, pp. 136—137.
  11. Gordon V.A., Klyueva N.V., Bukhtiyarova A.S., Poturaeva T.V. Raschet dinamicheskikh usiliy v konstruktivno-nelineynykh elementakh sterzhnevykh sistem pri vnezapnykh strukturnykh izmeneniyakh [Dynamic Impact Calculation in Constructive Non-linear Elements of Bar Systems in Case of Sudden Structural Changes]. Stroitel'naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 2008, no. 6, pp. 23—26.
  12. Gordon V.A., Kravtsova E.A. Pereraspredelenie napryazheniy v nagruzhennoy sostavnoy balke pri degradatsii svyazey sdviga [Stress Redistribution in a Loaded Composite Beam in Case of Shift Connections Degradation]. Stroitel'naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 2010, no. 4, pp. 2—6.
  13. Gordon V., Anokhin P., Stepanov Y. Transitional Processes in the Constructions with the Sudden Structural Reconstructions. Proceedings of the 15th International Congress on Sound and Vibration. Daejeon, Korea, 2008, pp. 1544—1556.
  14. Gordon V.A., Kravtsova E.A. Vliyanie prodol'nogo rassloeniya sostavnogo sterzhnya na chastoty sobstvennykh izgibnykh kolebaniy [The Infl uence of Longitudinal Lamination of a Compound Bar on Natural Flexural Vibrations]. Stroitel'naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 2011, no. 1, pp. 19—24.

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Influence of the contact area and value of the linearly distributed and concentrated mass with a circular cylindrical shell on the frequency and modes of natural oscillations

Vestnik MGSU 7/2014
  • Seregin Sergey Valer'evich - Komsomolsk on Amur State Technical University (KnAGTU) postgraduate student, Department of Construction and Architecture, Komsomolsk on Amur State Technical University (KnAGTU), 27 Lenina st, Komsomolsk on Amur, 681013, Russian Federation; (4217) 24-11-41; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 64-74

Finite element method shows the influence of the joining area and the relative value of linearly distributed mass along the angular coordinate and concentrated mass on natural oscillations and forms of a closed, circular cylindrical shell. We defined the ranges of concentrated and linearly distributed mass, added to a shell. The variation of the concentrated mass contact area markedly affects the lower frequency of the "shell-mass" system, in this connection, reducing the area of the shell leads to a marked decrease of the lowest split natural frequencies. The greatest of split natural frequencies decreases markedly with the increasing of contact area. More complex (mixed) oscillation modes of the "shell-mass" are detected. Dependence of the geometric characteristics of the shell with a concentrated mass of the lower split natural frequencies lower tone of oscillations, thus, revealing the dependence of frequencies on the length of the sheath. Linear contact area variation of the added mass and the circular coordinate has little effect on the oscillation frequency of the "shell-mass" system.

DOI: 10.22227/1997-0935.2014.7.64-74

References
  1. Zarutskiy V. A., Telalov A. I. Kolebaniya tonkostennykh obolochek s konstruktivnymi osobennostyami. Obzor eksperimental'nykh issledovaniy [Oscillations of Thin Shells with Design Features. Experimental Researches]. Prikladnaya mekhanika [Applied Mechanics]. 1991, vol. 278, no. 4, pp. 3—9.
  2. Avramov K.V., Pellicano F. Dynamical Instability of Cylindrical Shell with Big Mass at the End. Reports of the National Academy of Science of Ukraine. 2006, no. 5, pp. 41—46.
  3. Seregin S.V. Issledovanie dinamicheskikh kharakteristik obolochek s otverstiyami i prisoedinennoy massoy [Research of Dynamic Shell Properties with Holes and Added Mass]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2014, no. 4, pp. 52—58.
  4. Kubenko V.D., Koval'chuk P.S., Krasnopol'skaya T.S. Nelineynoe vzaimodeystvie form izgibnykh kolebaniy tsilindricheskikh obolochek [Nonlinear Interaction of Flexural Cylindrical Shell Oscillations]. Kiev, 1984, 220 p.
  5. Andreev L.V., Dyshko A.L., Pavlenko I.D. Dinamika plastin i obolochek s sosredotochennymi massami [Dynamics of Plates and Shells with Concentrated Masses]. Moscow, 1988, 200 p.
  6. Kubenko V.D., Koval’chuk P.S. Experimental Studies of the Oscillations and Dynamic Stability of Laminated Composite Shells. International Applied Mechanics. 2009, vol. 45, no. 5, pp. 514—533. DOI: http://dx.doi.org/10.1007/s10778-009-0209-4.
  7. Sivak V.F., Sivak V.V. Experimental Investigation into the Oscillations of Shells of Revolution with Added Masses. International Applied Mechanics. 2002, vol. 38, no. 5, pp. 623—627.
  8. Seregin S.V. Vliyanie prisoedinennogo tela na chastoty i formy svobodnykh kolebaniy tsilindricheskikh obolochek [Influence of Attached Body on Natural Oscillation Frequency Modes]. Stroitel'naya mekhanika i raschet sooruzheniy [Building Mechanics and Calculation Installations]. 2014, no. 3, pp. 35— 39.
  9. Trotsenko Yu.V. Frequencies and Modes of Cylindrical Shell Oscillation with Attached Stiff Body. Journal of Sound and Oscillation. 2006, vol. 292, no. 3—5, pp. 535—551.
  10. Amabili M., Garziera R., Carra S. The Effect Rotary Inertia of Added Masses on Oscillations of Empty and Fluid-filled Circular Cylindrical Shells. Journal of Fluids and Structures. 2005, vol. 21, no. 5—7, ðp. 449—458.
  11. Mallon N.J. Dynamic Stability of a Thin Cylindrical Shell with Top Mass Subjected to Harmonic Base-Acceleration. International Journal of Solids and Structures. 2008, vol. 45 (6), pp. 1587—1613.
  12. Amabili M., Garziera R., Carra S. The Effect of Rotary Inertia of Added Masses on Oscillations of Empty and Fluidfilled Circular Cylindrical Shells. Journal of Fluids and Structures. 2005, vol. 21, no. 5—7, pp. 449—458.
  13. Amabili M., Garziera R. Oscillations of Circular Cylindrical Shells with Nonuniform Constraints, Elastic Bed and Added Mass. Part III: Steady Viscous Effects on Shells Conveying Fluid. Journal of Fluids and Structures. 2002, vol. 16, no. 6, pð. 795—809.
  14. Leyzerovich G.S., Prikhod'ko N.B., Seregin S.V. O vliyanii maloy prisoedinennoy massy na kolebaniya raznotolshchinnogo krugovogo kol'tsa [Influence of Low Added Mass on Oscillations of Circular Spline with Varied Thickness]. Stroitel'stvo i rekonstruktsiya [Building and Reconstruction]. 2013, no. 4, pp. 38—41.
  15. Leyzerovich G.S., Prikhod'ko N.B. Seregin S.V. O vliyanii maloy prisoedinennoy massy na rasshcheplenie chastotnogo spektra krugovogo kol'tsa s nachal'nymi nepravil'nostyami [Influence of Low Added Mass on Frequency Spectrum of Circular Spline with Initial Imperfections]. Stroitel'naya mekhanika i raschet sooruzheniy [Structural Mechanics and Structural Analysis]. 2013, no. 6, pp. 49—51.
  16. Khalili S.M.R., Tafazoli S. Malekzadeh K. Fard. Natural Oscillations of Laminated Composite Shells with Uniformly Distributed Added Mass Using Higher Order Shell Theory Including Stiffness Effect. Journal of Sound and Oscillation. 2011, vol. 330, no. 26, ðð. 6355—6371.

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IDENTIFICATION OF NATURAL FREQUENCIES OF MULTISTORIED BUILDINGS OF PERIODIC STRUCTURE

Vestnik MGSU 2/2012
  • Dashevskij Mihail Aronovich - VIBROSEJSMOZASCHITA Limited Liability Company (VIBROSEJSMOZASCHITA LLC) Doctor of Technical Sciences, Senior Researcher, Director of Technology 8 (495) 650-41-52, VIBROSEJSMOZASCHITA Limited Liability Company (VIBROSEJSMOZASCHITA LLC), Building 1, 20/2 Kominterna Str., Moscow, 129327, Russia; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Mondrus Vladimir L'vovich - Moscow State University of Civil Engineering (MSUCE) Doctor of Technical Sciences, Professor, Head of Department of Structural Mechanics 8 (495) 287-49-14, ext. 3141, 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 .
  • Shutovskij Stanislav Nikolaevich - Moscow State University of Civil Engineering (MSUCE) postgraduate student, Department of Structural Mechanics 8 (495) 287-49-14, ext. 3141, 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 35 - 40

Periodic two- and three-dimensional structural models designated for rectangular-plan buildings are considered in the article. Expressions for identification of natural frequencies designated for unloaded and loaded two-dimensional structural models, as well as non-free three-dimensional structural models of multistoried buildings are provided in the article.

DOI: 10.22227/1997-0935.2012.2.35 - 40

References
  1. Vol'fson B.P. O rasprostranenii voln v modeljah zdanij i sooruzhenij s vnutrennim treniem [On propagation of Waves in Models of Buildings and Structures That Feature Internal Friction]. Stroitel'naja mehanika i raschet sooruzhenij [Structural Mechanics and Analysis of Structures]. 1971, Issue # 5, pp. 105—112.
  2. Nikiforov A.F., Uvarov V.B. Special'nye funkcii matematicheskoj fiziki [Special Functions of Mathematical Physics]. Moscow, Intellect, 2007.
  3. Szeg? G. Ortogonal'nye mnogochleny [Orthogonal Polynomials]. Moscow, Gosudarstvennoe izdatel'stvo fiziko-matematicheskoj literatury [State Publishing House of Physical and Mathematical Literature], 1962.
  4. Brillouin L., Parodi M. Rasprostranenie voln v periodicheskih strukturah [Propagation of Waves in Periodic Structures]. Moscow, Inostrannaja literatura, 1959.
  5. Banakh L., Kempner M. Vibrations of Mechanical Systems with Regular Structure. Springer, 2010.
  6. Mead D. J. Wave Propagation in Continuous Periodic Structures: Research Contributions from Southampton, 1964—1995. Journal of Sound and Vibration (1996) 190(3), pp. 495—524.

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Dynamic characteristics investigations of nuclear power plants containment shells using physicaland mathematical models and real projects

Vestnik MGSU 11/2013
  • Andreeva Peraskovya Ivanovna - Moscow State University of Civil Engineering (MGSU) postgraduate student, Department of Strength of Materials, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shоsse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Zavalishin Sergey Iosifovich - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Professor, Senior Research Worker, Head, Research Institute of Experimental Mechanics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shоsse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Shablinskiy Georgiy Eduardovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Senior Research Worker, Research Institute of Experimental Mechanics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shоsse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 114-122

The article reveals comparative results of experimental model studies of the dynamical characteristics of containment shells used for their calculation and construction as well as actual calculation of dynamic characteristics and the results of actual full-scale investigations executed after 40 years of their operation. This comparison of present-day calculations and full-scale researches showed their agreement with the previous investigations performed on physical models of containment shells.The dynamic analysis of the facilities on the base of physical models were widely used in the 70's of the 20th century, when the computers were still in the initial level of development. The results of these model studies were used to justify the strength of critical structures, including nuclear power plants (NPPs), some of which have already worked for over 40 years. The current investigation gives the opportunity to compare the results of the previous model studies with the present calculations of NPP protective containments (shells) and the field studies results. The field investigations were carried out on the reactor containment of VVER-1000 reactor for the 1st unit of Kalinin NPP.1. Model studies of the dynamic characteristics on the physical model base. In order to provide dynamic model studies in the laboratory it is necessary to solve the following problems: 1) to fulfill certain similarity conditions, which provide unambiguous recalculation of the results to the full-scale structures; 2) to determine the scale of the model and its production material, which is related to the structure and characteristics of the vibration-testing machine (shaker), the transitional fixing devices for the model, special vibrators for dynamic loads, etc. The particular attention should be paid to the registration, processing and analysis of dynamic parameters, taking into account quality changes, which have recently occurred in the measurement technique. The model studies were carried out on a series of geometrically similar models of the protective containments fabricated under special technology of gypsum (1:100 scale) and plexiglas (1:200 scale). The models were mounted on a specially designed shaker. Harmonic oscillations with continuous frequency scanning were set up to the testers and resonant vibration frequency was recorded. Then the shell vibration mode was defined at these frequencies using small-sized mobile vibrometer. The frequencies of natural oscillations were recounted for correlation on similarity conditions.2. The study (investigation) of the dynamic characteristics of the protective containment on the base of mathematical model. The model is built in ANSYS calculation software complex and is structurally similar to the physical model, but without built elements and elastic foundation (i.e, the adopted conditions are similar to the physical model). The problem is solved in three-dimensional setting, all elements are made of three-dimensional elements (of solid type). The comparison of the experiment results on physical models and field studies is given in the Table.

DOI: 10.22227/1997-0935.2013.11.114-122

References
  1. Jeong S.-H., Mwafy A.M., Elnashai A.S. Probabilistic Seismic Performance Assessment of Code-compliant Multi-story RC Buildings. Engineering Structures. 2012, vol. 34, pp. 527—537.
  2. Fardis M. N. Seismic Design Assessment and Retrofitting of Concrete Buildings. 2009, pp. 25—33.
  3. Kirillov A.P., Krylov V.V., Sargsyan A.E. Vzaimodeystvie fundamentov sooruzheniy elektrostantsiy s osnovaniem pri dinamicheskikh nagruzkakh [Interaction of Power Plant Foundations with the Base under Dynamic Loads]. Moscow, Energoatomizdat Publ., 1984, 125 p.
  4. Kirillov A.P., Sargsyan A. E. Dinamika i seysmostoykost' AES s uchetom podatlivosti osnovaniya [Dynamics and Earthquake Resistanse of Nuclear Power Plants with Account for the Foundation Yielding]. Moscow, Informenergo Publ., 1988, p. 86.
  5. Chernov Yu.T. Prikladnyye metody dinamiki sooruzheniy [Applied Methods of Structural Dynamics]. Moscow, ASV Publ. 2001, p. 282.
  6. Shablinsky G., Zoubkov D., Isaikin A. Frequency Response Analysis of NPP Containment with WWER – 1000 Type Reactor. 18th International Conference on Structural Mechanics in Reactor Technology (SMIRT 18). Beijing, China, 2005, pp. 83—88.
  7. Liel A.B., Haselton C.B., Deierlein G.G., Baker J. W. Incorporating Modeling Uncertainties in the Assessment of Seismic Collapse Risk of Buildings. Structural Safety. 2009, vol. 31, no. 2, p. 134.

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