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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
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  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.
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  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.
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  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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