Energy analysis of axisymmetric vibrations of the cylindrical shell loaded by periodic concentrated masses
DOI:
https://doi.org/10.7242/1999-6691/2024.17.3.24Keywords:
propagation of the waves, cylindrical shell, vibrations of the shells, energy fluxAbstract
Cylindrical periodic shells are widely used in modeling various building structures, pipelines, offshore drilling rig supports, wind farms and other structures. Increasing their wear resistance and preventing the occurrence of risk-bearing operating modes is an urgent problem. In this paper, we investigate one of the potentially dangerous modes caused by axisymmetric vibrations of a circular cylindrical shell of Kirchhoff–Love type with additional inertia in the form of periodic "mass belts" of zero width. The shell is assumed to be infinite and its free harmonic vibrations are analyzed using a Floquet-type exact analytical solution. The dependence of pass bands and stop bands on the mass of the concentrated loads is investigated. At a certain combination of parameters, the points of intersection and quasi-intersection of the boundaries of these bands can coincide. The neighborhood of such a special point is considered in view of the fact that the boundaries of the pass and stop bands of an infinite periodic shell can be obtained and investigated by considering free vibrations of its separated symmetric segment of periodicity. This makes it possible to essentially reduce the volume of calculations, to simplify the determination of the coordinates of this special point, as well as to facilitate the analysis of the vibration field, the integral energy flux and its components. In such a way, the consideration of energy flows and its components not only significantly complements the picture of vibration fields, but also allows us to assess more adequately the nature of vibrations. It is shown that in the vicinity of a singular point there is a sharp change in the character of vibrations, which can lead to dangerous modes of operation of real structures.
Downloads
References
Cremer L., Heckl M., Petersson B.A. Structure-Borne Sound. Springer Berlin Heidelberg, 2005. 607 p. DOI: 10.1007/b137728
Novak P., Moffat A.I., Nalluri C., Narayanan R. Hydraulic Structures. CRC Press, 2007. 736 p. DOI: 10.1201/9781315274898
El-Reedy M. Offshore Structures: Design, Construction and Maintenance. Gulf Professional Publishing, 2012. 664 p.
Palmer A.C., King R.A. Subsea Pipeline Engineering. PennWell Corp., 2008. 624 p.
Gerwick Jr. B.C. Construction of Marine and Offshore Structures. CRC Press, 2007. 840 p. DOI: 10.1201/9780849330520
Yeliseyev V.V. Mekhanika uprugikh tel. St. Petersburg, Polytechnic University Press, 2003. 336 p.
Eliseev V.V., Vetyukov Y.M. Finite deformation of thin shells in the context of analytical mechanics of material surfaces. Acta Mechanica. 2010. Vol. 209, no. 1/2. P. 43–57. DOI: 10.1007/s00707-009-0154-7
Eliseev V., Vetyukov Y. Theory of shells as a product of analytical technologies in elastic body mechanics. Shell Structures: Theory and Applications. 2014. Vol. 3. P. 81–85. DOI: 10.1201/b15684-18
Eliseev V.V., Zinovieva T.V. Lagrangian mechanics of classical shells: Theory and calculation of shells of revolution. Shell Structures: Theory and Applications Volume 4 / ed. By W. Pietraszkiewicz, W. Witkowski. CRC Press, 2018. P. 73–76.
Zinov’yeva T.V. Vychislitel’naya mekhanika uprugikh obolochek vrashcheniya v mashinostroitel’nykh raschetakh. Sovremennoye mashinostroyeniye. Nauka i obrazovaniye. 2012. P. 335–343.
Zinovieva T.V. Calculation of Equivalent Stiffness of Corrugated Thin-Walled Tube. Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering / ed. by A.N. Evgrafov. Cham: Springer International Publishing, 2019. P. 211–220.
Zinovieva T.V., Smirnov K.K., Belyaev A.K. Stability of corrugated expansion bellows: shell and rod models. Acta Mechanica. 2019. Vol. 230. P. 4125–4135. DOI: 10.1007/s00707-019-02497-6
Zinov’eva T.V. Wave dispersion in cylindrical shell. Nauchno-tekhnicheskie vedomosti SPbGPU. 2007. No. 4–1. P. 53–58.
Zinovieva T.V. Calculation of Shells of Revolution with Arbitrary Meridian Oscillations. Advances in Mechanical Engineering, Lecture Notes in Mechanical Engineering / ed. by A.N. Evgrafov. Cham: Springer International Publishing, 2017. P. 165–176. DOI: 10.1007/978-3-319-53363-6_17
Filippenko G.V., Wilde M.V. Backwards waves in a fluid-filled cylindrical shell: comparison of 2D shell theories with 3D theory of elasticity. Proc. of the Int. Conf. “Days on Diffraction 2018”. 2018. P. 112–117. DOI: 10.1109/DD.2018.8553487
Filippenko G.V. Waves with the Negative Group Velocity in the Cylindrical Shell, Filled with Compressible Liquid. Advances in Mechanical Engineering / ed. by A.N. Evgrafov. Cham: Springer International Publishing, 2018. P. 93–104. DOI: 10.1007/978-3-319-72929-9_11
Ter-Akopyants G.L. Osesimmetrichnyye volnovyye protsessy v tsilindricheskikh obolochkakh, zapolnennykh zhidkost’yu. Natural and technical sciences. 2015. No. 7. P. 10–14.
Sorokin S.V., Ershova O.A. Analysis of the energy transmission in compound cylindrical shells with and without internal heavy fluid loading by boundary integral equations and by Floquet theory. Journal of Sound and Vibration. 2006. Vol. 291, no. 1/2. P. 81–99. DOI: 10.1016/j.jsv.2005.05.031
Sorokin S.V., Nielsen J.B., Olhoff N. Green’s matrix and the boundary integral equation method for the analysis of vibration and energy flow in cylindrical shells with and without internal fluid loading. Journal of Sound and Vibration. 2004. Vol. 271, no. 3–5. P. 815–847. DOI: 10.1016/S0022-460X(03)00755-7
Erofeev V.I., Lenin A.O., Lisenkova E.E., Tsarev I.S. Dispersional dependences and peculiarities of energy transfer by flexible waves in a beam lying on a generalized elastic base. PNRPU Mechanics Bulletin. 2023. No. 2. P. 118–125. DOI: 10.15593/perm.mech/2023.2.11
Filippenko G.V. Energy Flux Analysis of Axisymmetric Vibrations of Circular Cylindrical Shell on an Elastic Foundation. Advances in Mechanical Engineering / ed. by A.N. Evgrafov. Cham: Springer International Publishing, 2020. P. 83–91. DOI: 10.1007/978-3-030-39500-1_9
Filippenko G.V., Zinovieva T.V. Axially Symmetric Oscillations of Circular Cylindrical Shell with Localized Mass on Winkler Foundation. Advanced Problem in Mechanics II / ed. by D.A. Indeitsev, A. Krivtsov. Springer International Publishing, 2022. P. 245–257. DOI: 10.1007/978-3-030-92144-6_19
Filippenko G.V., Zinovieva T.V. Axisymmetric Vibrations of the Cylindrical Shell Loaded with Pointed Masses. Advances in Mechanical Engineering / ed. by A.N. Evgrafov. Cham: Springer International Publishing, 2021. P. 80–91. DOI: 10.1007/978-3-030-62062-2_9
Filippenko G. The location of pass and stop bands of an infinite periodic structure versus the eigenfrequencies of its finite segment consisting of several ‘periodicity cells’. Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2013). 2013. P. 2220–2231. DOI: 10.7712/120113.4660.C1690
Filippenko G.V. The banding waves in the beam with periodically located point masses. Computational Continuum Mechanics. 2015. Vol. 8, no. 2. P. 153–163. DOI: 10.7242/1999-6691/2015.8.2.13
Filippenko G.V. Wave Processes in the Periodically Loaded Infinite Shell. Advances in Mechanical Engineering / ed. By A.N. Evgrafov. Cham: Springer International Publishing, 2019. P. 11–20. DOI: 10.1007/978-3-030-11981-2_2
Hvatov A., Sorokin S. Assessment of reduced-order models in analysis of Floquet modes in an infinite periodic elastic layer. Journal of Sound and Vibration. 2019. Vol. 440, no. 3. P. 332–345. DOI: 10.1016/j.jsv.2018.10.034
Filippenko G.V. HarmonicVibrations of the Simplest Shell Models Loaded with a Periodic System of Localised Masses.Advances in Mechanical Engineering / ed. by A. Evgrafov. Springer Nature Switzerland, 2024. P. 93–102. DOI: 10.1007/978-3-031-48851-1_9
Hvatov A., Sorokin S. Free vibrations of finite periodic structures in pass- and stop-bands of the counterpart infinite waveguides. Journal of Sound and Vibration. 2015. Vol. 347. P. 200–217. DOI: 10.1016/j.jsv.2015.03.003
Tomczyk B., Bagdasaryan V., Gołąbczak M., Litawska A. On the modelling of stability problems for thin cylindrical shells with two-directional micro-periodic structure. Composite Structures. 2021. Vol. 275. 114495. DOI: 10.1016/j.compstruct.2021.114495
Kumar A., Das S.L., Wahi P., Żur K.K. On the stability of thin-walled circular cylindrical shells under static and periodic radial loading. Journal of Sound and Vibration. 2022. Vol. 527. 116872. DOI: 10.1016/j.jsv.2022.116872
Zheng D., Du J., Liu Y. Bandgap mechanism analysis of elastically restrained periodic cylindrical shells with arbitrary periodic thickness. International Journal of Mechanical Sciences. 2023. Vol. 237. 107803. DOI: 10.1016/j.ijmecsci.2022.107803
Deng J., Guasch O., Maxit L., Zheng L. Reduction of Bloch-Floquet bending waves via annular acoustic black holes in periodically supported cylindrical shell structures. Applied Acoustics. 2020. Vol. 169. 107424. DOI: 10.1016/j.apacoust.2020.107424
Tian K., Lai P., Sun Y., Sun W., Cheng Z., Wang B. Efficient buckling analysis and optimization method for rotationally periodic stiffened shells accelerated by Bloch wave method. Engineering Structures. 2023. Vol. 276. 115395. DOI: 10.1016/j.engstruct.2022.115395
Sorokin S.V. On propagation of plane symmetric waves in a periodically corrugated straight elastic layer. Journal of Sound and Vibration. 2015. Vol. 349. P. 348–360. DOI: 10.1016/j.jsv.2015.03047
Chapra S.C., Canale R.P. Numerical Methods for Engineers. McGraw-Hill Education, 2015. 970 p.
Mikhasev G.I., Tovstik P.E. Lokalizovannyye kolebaniya i volny v tonkikh obolochkakh. Asimptoticheskiye metody. Fizmatlit, 2009. 290 p.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.