Abstract
The wave processes in the infinite and finite periodic shells (cylinder shell, beam, and rod) are explored. Look-alike systems can model different elements of buildings, hydro-technical constructions, bridges, oil rigs, different pipes, etc. The statement of the problem is considered the rigorous statement. In the infinite systems, Floquet solution is founded. The comparison of the wave processes in the rod and beam is fulfilled. The energy fluxes in them are calculated. The main effects are explored with the attraction of the analysis of vibrations, corresponding to different pass- and stopbands. The dependence of character and «heterogeneity degree» of wave process in the finite systems via the position of corresponding wave number in relation to passbands is considered. The modes of free vibrations of a periodic cell in the case of its asymmetry are analyzed with special attention to edge effects via the parameters of the problem.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Mead DJ (1996) Wave propagation in continuous periodic structures: research contribution from Southampton, 1964–1995. J Sound and Vibr 190(3):495–524
Olhoff N, Niu B, Cheng G (2012) Optimum design of band-gap beam structures. Int J Solids Struct 49:3158–3169
Sorokin SV, Ershova OA (2004) Plane wave propagation and frequency band gaps in periodic plates and cylindrical shells with and without heavy fluid loading. J Sound Vibr 278(3):501–526. https://doi.org/10.1016/j.jsv.2003.10.042
Jensen JS (2003) Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures. J Sound Vibr 266(5):1053–1078
Du J, Olhoff N (2007) Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multi Optim 34(2):91–110. Editors Erratum in 34:91. https://doi.org/10.1007/s00158-007-0101-y
Filippenko GV (2013) The location of pass and stop bands of an infinite periodic structure versus the eigenfrequencies of its finite segment consisting of several ‘periodicity cells’. In: 4th ECCOMAS thematic conference on computational methods in structural dynamics and earthquake engineering COMPDYN 2013, Kos Island, Greece, 12–14 June 2013. CD format. Paper №1690, 12 pages. https://files.eccomasproceedia.org/papers/compdyn-2013/C1690.pdf, http://www.eccomasproceedings.org/cs2013/pdf/1690.pdf
Hvatov A, Sorokin S (2015) Free vibrations of finite periodic structures in pass-and stop-bands of the counterpart infinite waveguides. J Sound Vibr 347:200–217. http://dx.doi.org/10.1016/j.jsv.2015.03.003
Zhuchkova MG (2016) Wave propagation in a floating elastic plate with a periodic support. In: Proceedings of the international conference “Days on diffraction 2016”, 27 June–1 July 2016, St. Petersburg, Russia, pp 455–460
Filippenko GV (2015) The banding waves in the beam with periodically located point masses. Vycisl. meh. splos. sred—Comput Continuum Mech 8(2):153–163. http://dx.doi.org/10.7242/1999-6691/2015.8.2.13
Eliseev VV, Zinovieva TV (2018) Lagrangian mechanics of classical shells: theory and calculation of shells of revolution. In: Shell structures: theory and applications, vol 4, Proceedings of the 11th international conference, Published by Taylor & Francis Group, London, pp 73–76
Zinovieva TV (2017) Calculation of shells of revolution with arbitrary meridian oscillations. In: Evgrafov A (ed) Advances in mechanical engineering. Selected contributions from the conference “Modern Engineering: science and education”, Saint Petersburg, Russia, June 2016, Springer International Publishing, Switzerland, Lecture notes in mechanical engineering, 2017, pp 165–176. ISSN 2195-4356. https://doi.org/10.1007/978-3-319-53363-6
Filippenko GV (2016) The vibrations of reservoirs and cylindrical supports of hydro technical constructions partially submerged into the liquid. Evgrafov A (ed) Advances in mechanical engineering. Selected contributions from the conference “Modern engineering: science and education”, Saint Petersburg, Russia, June 2014, Springer International Publishing, Switzerland, Lecture notes in mechanical engineering, 2016, pp 115–126. ISSN 2195-4356. https://doi.org/10.1007/978-3-319-29574-4
Veshev VA, Kouzov DP, Mirolyubova NA (1999) Energy flows and dispersion of the normal bending waves in the X-shaped beam. Acoust Phys 45(3):331–337
Kouzov DP, Mirolubova NA (2012) Local energy fluxes of forced vibrations of a thin elastic band. Vycisl. meh. splos. sred—Comput Continuum Mech 5(4):397–404. http://dx.doi.org/10.7242/1999-6691/2012.5.4.47
Sorokin SV (2002) Analysis of vibrations and energy flows in sandwich plates bearing concentrated masses and springlike inclusions in heavy fluid loading conditions. J Sound Vibr 253:485–505. https://doi.org/10.1006/jsvi.2001.4065
Sorokin SV, Nielsen JB, Olhoff N (2004) Green’s matrix and the boundary integral equations method for analysis of vibrations and energy flows in cylindrical shells with and without internal fluid loading. J. Sound Vibr 271(3–5):815–847
Filippenko GV (2017) Energy-flux analysis of the bending waves in an infinite cylindrical shell filled with acoustical fluid. In: Evgrafov A (ed) Advances in mechanical engineering. Selected contributions from the conference “Modern engineering: science and education”, Saint Petersburg, Russia, June 2016, Springer International Publishing, Switzerland, Lecture notes in mechanical engineering, 2017, pp 57–64. ISSN 2195-4356. https://doi.org/10.1007/978-3-319-53363-6
Filippenko GV (2017) Waves with the negative group velocity in the cylindrical shell, filled with compressible liquid. In: Evgrafov A (ed) Advances in mechanical engineering. Selected contributions from the conference “Modern engineering: science and education”, Saint Petersburg, Russia, June 2017, Springer International Publishing, Switzerland, Lecture notes in mechanical engineering, 2018, pp 93–104. ISSN 2195-4356. https://doi.org/10.1007/978-3-319-72929-9
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Filippenko, G.V. (2019). Wave Processes in the Periodically Loaded Infinite Shell. In: Evgrafov, A. (eds) Advances in Mechanical Engineering. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-11981-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-11981-2_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-11980-5
Online ISBN: 978-3-030-11981-2
eBook Packages: EngineeringEngineering (R0)