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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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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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