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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Investigation of dynamic characteristics of shells with holes and added mass

Vestnik MGSU 4/2014
  • Seregin Sergey Valer’evich - Komsomolsk-na-Amure State Technical University postgraduate student, Department of Construction and Architecture, Komsomolsk-na-Amure State Technical University, 27 Lenin st., Komsomolsk-on-Amure, 681013, Russian Federation, (4217) 24-11-41; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 52-58

Thin cylindrical shells are widely used in construction, engineering and other industries. In case of designing a reservoir for the isothermal storage of liquefied gases such cases are inevitable, when housing requires various technical holes. A point wise added mass can appear into practice in the form of suspended spotlights, radar, architectural inclusions in buildings and structures of various purposes. It is known, that the dynamic asymmetry as an initial irregular geometric shape, including holes, and the added mass leads to specific effects in shells. In the paper the impact of a cut on the frequency and form of its own vibrations of thin circular cylindrical shells is theoretically examined with the help of the equations of linear shallow shell theory. For modal equations with Nav’e boundary conditions, we used the Bubnov - Galerkin method. The authors have expressed a formula for finding the lowest of the split-frequency vibrations of a shell with a cutout. It is stated, that in case of an appropriate choice of added mass value the lower frequencies are comparable with the case of vibrations of a shell with a hole. By numerical and experimental modeling and finite element method in the environment of MSC "Nastran" oscillation frequencies a shell supporting a concentrated mass and a shell with a cutout were compared. It is shown, that the results of the dynamic analysis of shells with holes with a suitable choice of the attached mass values are comparable with the results of the analysis of shells carrying a point mass. It was concluded that the edges in the holes, significantly affect the reduction in the lowest frequency, and need to be strengthened.

DOI: 10.22227/1997-0935.2014.4.52-58

References
  1. Dyshko A.L., Pavlenko I.D., Selivanov Yu. M. Issledovanie rezonansnykh kolebaniy obolochek s otverstiyami [Investigation of Resonant Vibrations of the Shells with Holes]. Smeshannye zadachi mekhaniki deformiruemykh sred. Sbornik nauchnykh trudov [Mixed Problems of Deformable Media Mechanics. Collection of Scientific Works]. Dnepropetrovsk, DDU Publ., 1995, pp. 58—66.
  2. Zarutskiy V.A., Telalov A.I. Kolebaniya tonkostennykh obolochek s konstruktivnymi osobennostyami. Obzor eksperimental'nykh issledovaniy [Vibrations of Thin-walled Shells with Constructive Features. Overview of Experimental Studies]. Prikladnaya Mekhanika [Applied Mechanics]. 1991, vol. 278, no. 4, pp. 3—9.
  3. Kubenko V.D., Koval'chuk P.S., Krasnopol'skaya T.S. Nelineynoe vzaimodeystvie form izgibnykh kolebaniy tsilindricheskikh obolochek [Nonlinear Interaction of Flexural Vibrations Forms of Cylindrical Shells]. Kiev, Moscow, Naukova dumka Publ., 1984, 220 p.
  4. Leyzerovich G.S., Taranukha N.A. Neochevidnye osobennosti dinamiki krugovykh tsilindricheskikh obolochek [Non-obvious Features of the Dynamics of Circular Cylindrical Shells]. Izvestiya RAN MTT [News of RAS Mechanics of Solids]. 2008, no. 2, pp. 96—105.
  5. Leyzerovich G.S., Prikhod'ko N.B., Seregin S.V. O vliyanii maloy prisoedinennoy massy na kolebaniya raznotolshchinnogo krugovogo kol'tsa [Effect of Small Added Mass on the Fluctuations of Gage Circular Ring]. Stroitel'stvo i rekonstruktsiya [Building and Reconstruction]. 2013, no. 4, pp. 38—41.
  6. 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 [Effect of Small Added Mass on Splitting of the Frequency Spectrum of a Circular Ring with Initial Irregularities]. Stroitel'naya mekhanika i raschet sooruzheniy [Structural Mechanics and Structures Calculation]. 2013, no. 6, pp. 49—51.
  7. Mikhlin S.G. Variatsionnye metody v matematicheskoy fizike [Variational Methods in Mathematical Physics]. Moscow, 1957, 440 p.
  8. Taranukha N.A., Leyzerovich G.S. O vliyanii nachal'nykh otkloneniy ot ideal'noy krugovoy formy tsilindricheskikh obolochek na sobstvennye izgibnye kolebaniya [On the Influence of Initial Deviations from the Perfectly Circular Shape of Cylindrical Shells on their Own Flexural Vibrations]. PMTF [Applied Mathematics and Technical Physics]. 2001, vol. 42, no. 2, pp. 180—187.
  9. Taranukha N. A., Leyzerovich. G.S. Novye resheniya v dinamike «nepravil'nykh» obolochek [New Solutions in the Dynamics of Imperfect shells]. Vladivostok, Dal'nauka Publ., 2007, 203 p.
  10. Amabili M., Garziera R., Carra S. The Effect of Rotary Inertia of Added Masses on Vibrations of Empty and Fluid-filled Circular Cylindrical Shells. Journal of Fluids and Structures. 2005, vol. 21, no. 5—7, pp. 449—458. DOI:10.1016/j.jfluidstructs.2005.07.018.
  11. Amabili M., Garziera R. Vibrations 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, pp. 795—809. DOI:10.1006/jfls.2002.0446.
  12. 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.
  13. 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, no. 45 (6), pp. 1587—1613. DOI: 10.1016/j.ijsolstr.2007.10.011.
  14. Mallon N.J., Fey R.H.B., Nijmeijer H. Dynamic Stability of a Base-excited Thin Orthotropic Cylindrical Shell with Top Mass: Simulations and Experiments. Journal of Sound and Vibration. 2010, vol. 329, no. 15, pp. 3149—3170. DOI: 10.1016/j.jsv.2010.02.007.
  15. Tobjas S. A. A Theory of Imperfection for the Vibration of Elastic Bodies of Revolution. Engineering. 1951, vol. 44, no. 70, pp. 409—420.

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Free flexural radial vibrations of a thin circular cylindrical shell bearing added mass

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

Pages 74-81

The author comes up with a refined mathematical model contemplating that added mass facilitates interaction between coupled flexural and radial vibrations in the linear setting. The author has identified a higher splitting of the flexural frequency spectrum due to the presence of the added mass and the wave generation parameters that characterize the relative length and thickness of the shell. Within the framework of the shallow-shell theory, the influence of the small concentrated mass onto natural dynamic properties of the shell is exposed to research. The refined mathematical model was employed to identify that the added mass binds the coupled flexural shape of the circular cylindrical shell and facilitates interaction between low-frequency flexural vibrations and high-frequency radial vibrations. Moreover, radial vibrations act as a supplementary inertial link between coupled flexural shapes. Due to the availability of the exciting load, non-resonant areas, identified through the application of the traditional mathematical model, can be resonant in essence. The findings of this research must be considered in the course of the assessment of the dynamic strength of any shell structures designed. This refined finite-dimensional model, capable of recognizing radial vibrations, has generated the results that comply with numerical analyses and experimental data both quantitatively and qualitatively. Therefore, dynamic problems that have already been resolved may need refinement.

DOI: 10.22227/1997-0935.2014.11.74-81

References
  1. Amabili M., Garziera R., Carra S. The Effect of Rotary Inertia of Added Masses on Vibrations of Empty and Fluid-filled Circular Cylindrical Shells. Journal of Fluids and Structures. 2005, vol. 21, no. 5—7, pp. 449—458. DOI: http://dx.doi.org/10.1016/j.jfluidstructs.2005.07.018.
  2. Seregin S.V. Vliyanie prisoedinennogo tela na chastoty i formy svobodnykh kolebaniy tsilindricheskikh obolochek [Influence of Attached Body on Natural Frequencies and their Forms]. Stroitel’naya mekhanika i raschet sooruzheniy [Building Mechanics and Calculation of Structures]. 2014, no. 3, pp. 35—38. (In Russian).
  3. Seregin S.V. Vliyanie ploshchadi kontakta i velichiny lineyno raspredelennoy i sosredotochennoy massy s krugovoy tsilindricheskoy obolochkoy na chastoty i formy svobodnykh kolebaniy [Influence of the Contact Area of Linearly Distributed and Concentrated Mass with a Circular Cylindrical Shell on the Frequency and Modes of Natural Oscillations]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2014, no. 7, pp. 64—74. (In Russian).
  4. Zarutskiy V.A., Telalov A.I. Kolebaniya tonkostennykh obolochek s konstruktivnymi osobennostyami. Obzor eksperimental’nykh issledovaniy [Frequencies of Thin-Walled Shells with Structiral Peculiarities]. Prikladnaya mekhanika [Applied mechanics]. 1991, vol. 278, no. 4, pp. 3—9. (In Russian).
  5. Trotsenko Yu.V. Frequencies and Modes of Vibration of a Cylindrical Shell with Attached Rigid Body. Journal of Sound and Vibration. 2006, vol. 292, no. 3—5, pp. 535—551. DOI: http://dx.doi.org/10.1016/j.jsv.2005.08.015.
  6. 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, no. 6, pp. 1587—1613. DOI: http://dx.doi.org/10.1016/j.ijsolstr.2007.10.011.
  7. Amabili M., Garziera R. Vibrations 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, pp. 795—809. DOI: http://dx.doi.org/10.1006/jfls.2002.0446.
  8. Khalili S.M.R., Tafazoli S., Malekzadeh Fard K. Free Vibrations of Laminated Composite Shells with Uniformly Distributed Attached Mass Using Higher Order Shell Theory Including Stiffness Effect. Journal of Sound and Vibration. 2011, vol. 330, no. 26, pp. 6355—6371. DOI: http://dx.doi.org/10.1016/j.jsv.2011.07.004.
  9. 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, Mashinostroenie Publ., 1988, 200 p. (In Russian).
  10. Kubenko V.D., Koval’chuk P.S., Krasnopol’skaya T.S. Nelineynoe vzaimodeystvie form izgibnykh kolebaniy tsilindricheskikh obolochek [Nonlinear Interaction of Flexural Vibration Forms of Cylindrical Shells]. Kiev, Naukova dumka Publ., 1984, 220 p. (In Russian).
  11. Seregin S.V. Issledovanie dinamicheskikh kharakteristik obolochek s otverstiyami i prisoedinennoy massoy[Investigation of Dynamic Characteristics of Shells with Holes and Added Mass]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2014, no. 4, pp. 52—58. (In Russian).
  12. Sivak V.F., Sivak V.V. Experimental Investigation into the Vibrations of Shells of Revolution with Added Masses. International Applied Mechanics. 2002, vol. 38, no. 5, pp. 623—627. DOI: http://dx.doi.org/10.1023/A:1019770206949.
  13. 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.
  14. Vol’mir A.S. Nelineynaya dinamika plastinok i obolochek [Nonlinear Dynamics of Plates and Shells]. Moscow, Nauka Publ., 1972, 432 p. (In Russian).
  15. Amabili M. Nonlinear Vibrations and Stability of Shells and Plates. New York, USA, Cambridge university press, 2008, 392 p.
  16. Varadan T.K., Pratkhap Dzh., Ramani Kh.V. Nelineynye svobodnye izgibnye kolebaniya tonkostennykh krugovykh tsilindricheskikh obolochek [Nonlinear Free Frequencies of Thin-Walled Round Cylindrical Shells]. Aerokosmicheskaya tekh-nika [Aerospace Engineering]. 1990, no. 5, pp. 21—24. (In Russian).
  17. Seregin S.V. Svidetel’stvo o gosudarstvennoy registratsii programmy dlya EVM ¹ 2014617201. Svobodnye kolebaniya krugovoy tsilindricheskoy obolochki, nesushchey sosredotochennuyu massu [State Registration Certificate of a Computer Program no. 2014617201. Free vibrations of a circular cylindrical shell carrying a concentrated mass]. Programmy dlya EVM. Bazy dannykh. Topologii integral’nykh mikroskhem [Computer Programs. Databases. Typology of Integral Microchips]. Available at: http://www1.fips.ru/Archive/EVM/2014/2014.08.20/. Date of access: 28.08.2014. (In Russian).

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Body drop into a fluid tank and dynamic loads calculation

Vestnik MGSU 5/2014
  • Komarov Aleksandr Andreevich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Department of Hydraulics and Water Resources, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 261-48-04; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Kazennov Vyacheslav Vasil'evich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Head, Sector of Scientific and Technical Center «Blast Resistance», Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (499) 261-48-04; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 135-143

The theory of a body striking a fluid began intensively developing due to the tasks of hydroplanes landing. For the recent years the study of a stroke and submersion of bodies into fluid became even more current. We face them in the process of strength calculation of ship hulls and other structures in modern technology. These tasks solution represents great mathematical difficulty even in case of the mentioned simplifications. These difficulties emerge due to the unsteady character of fluid motion in case of body submersion, and also jet and spray phenomena, which lead to discontinuous motions. On the basis of G.V. Logvinovich’s concept the problem of loads determination with consideration for air gap is solved for both a body and reservoir enclosing structures when a body falls into a fluid. Numerical method is based on the decay of an arbitrary discontinuity.

DOI: 10.22227/1997-0935.2014.5.135-143

References
  1. Ionina M.F. Chislennoe issledovanie zadachi ob udare uprugikh tsilindricheskikh obolochek o vodu [Numerical Study of Water Impact on Cylindrical Shells in Case of Stroke]. Vychislitel'nye tekhnologii [Calculative Technologies]. 1999, vol. 4, no. 3, pp. 84—94.
  2. Ryabchenko V.P. Metod integral'nykh uravneniy v ploskoy i prostranstvennoy zadachakh ob udare plastiny o zhidkost' konechnoy glubiny [Method of Integral Equations in 2D and 3D Problems of Plate Impacting a Fluid of Finite Depth]. Prikladnaya mekhanika i tekhnicheskaya fizika [Journal of Applied Mechanics and Technical Physics]. 2001, vol. 42, no. 4, pp. 98—111.
  3. Taranukha N.A., Chizhumov S.D. Chislennoe modelirovanie padeniya na vodu tela s gofrirovannym dnishchem [Numerical Simulation of a Body with Corrugated Bottom Falling on Water]. Prikladnaya mekhanika i tekhnicheskaya fizika [Journal of Applied Mechanics and Technical Physics]. 2001, vol. 42, no. 4, pp. 112—118.
  4. Korobkin A.A. Ploskaya zadacha o simmetrichnom udare volnoy po balke Eylera [The problem of a symmetric wave impaction on the Euler beam]. Prikladnaya mekhanika i tekhnicheskaya fizika [Journal of Applied Mechanics and Technical Physics]. 1998, vol. 39, no. 5, рp. 134—147.
  5. Malenica S. Modified Logvinovich Model for Hydrodynamic Loads on Asymmetric Contours Entering Water. UEA Repository, 2005.
  6. Scolan Y., Korobkin A. Energy Distribution from Vertical Impact of a Three-Dimensional Solid Body onto the Flat Free Surface of an Ideal Fluid. Journal of Fluids and Structures. 2003, vol. 17, no. 2, pp. 275—286. DOI: 10.1016/S0889-9746(02)00118-4.
  7. Logvinovich G.V. Gidrodinamika techeniy so svobodnymi granitsami [Hydrodynamics of Free-Boundary Flows]. Kiev, 1969, 215 p.
  8. Shibue T., Ito A., Nakayama E. Structural Response Analysis of Cylinders under Water Impact. Hydroelasticity in Marine Technology. 1994, pр. 221—228.
  9. Arai M., Miyauchi T. Numerical Study of the Impact of Water on Cylindrical Shells, Considering Fluid-structure Interactions. PRADS’98, the Hague, September, 1998.
  10. Stow C.D., Hadfield M.G. An Experimental Investigation of Fluid Flow Resulting from the Impact of a Water Drop with an Unyielding Dry Surface. Proc. R. Soc. London Ser. 1981, vol. 373, no. 1755, pp. 419—441. DOI: 10.1098/rspa.1981.0002.
  11. Iafrati A., Korobkin A. Asymptotic Estimates of Hydrodynamic Loads in the Early Stage of Water Entry of a Circular Disk. Journal of Engineering Mathematics. 2011, vol. 69, no. 2-3, pp. 199—224. DOI: 10.1007/s10665-010-9411-y.
  12. Scolan Y., Korobkin A. Mixed Boundary Value Problem in Potential Theory: Application to the Hydrodynamic Impact (Wagner) Problem. Comptes Rendus Mecanique. 2012, vol. 340, no. 10, pp. 702—705. DOI: 10.1016/j.crme.2012.09.006.
  13. Chau S.-W., Lu C.-Y., Chou S.-K. Numerical Simulation of Nonlinear Slamming for a High-speed Planning Vessel. TEAM-2000: Proc. Of the 14th Asian Technical Exchange and Advisory Meeting on Marine Structures, Vladivostok, 18—21 Sept. 2000. Vladivostok, Far East. State Tech. Univ., 2000, pp. 224—232.
  14. Godunov S.K., editor. Chislennoe reshenie mnogomernykh zadach gazovoy dinamiki [Numerical Solution of Multidimensional Problems of Gas Dynamics]. Moscow, Nauka Publ., 1976, 400 p.
  15. Grigolyuk E.I., Gorshkov A.G. Vzaimodeystvie uprugikh konstruktsiy s zhidkost'yu (udar i pogruzhenie) [Interaction of Elastic Structures with a Liquid (Impact and Immersion)]. Leningrad, Sudostroenie Publ., 1976, 200 p.

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