Periodic vibrations of reservoir shell with the real shape imperfections under pressure
DOI:
https://doi.org/10.32347/2410-2547.2022.108.255-266Keywords:
reservoir, cylinder shell, shape imperfections, finite-element method, periodic vibrationsAbstract
The numeral approach to analysis of influence the real shape imperfections on natural and forced periodic vibrations of reservoir shell under pressure was presented. The approach was based on a theory and the methods of structural mechanics and calculable procedures of finite-element software complex NASTRAN. The welded steel reservoir with a variable thickness along its height was investigated. On the manufacted stage, transporting and exploitating the defects of wall shape were formed. The actual radial and angular deviations of the reservoir belts as a result measurements by theodolite were got. Geometry of shell with the real shape imperfections by spline curves and spline surfaces with adding of factual radial and angular rejections to the proper coordinates of points formative shells with an ideal surface was built. Model of reservoir in the form of a cylindrical shell with a three-cornered finite-element net was presented. The limits on the radial and tangential displacements of top edge nodes were entered, the nodes of lower edge were fastened. The periodic loading as external pressure was given. The modal analysis of shell without and with real shape imperfections by the decision of task on natural vibrations (Normal Modes) by the Lanczos method was executed. It was discovered that the natural forms of shell with real shape imperfections had local deformations in the places of maximal radial deviations from a vertical line unlike regular deformations in all natural forms of ideal shell. Natural frequencies were decreased and were slit and there wasn’t influence on its dense distribution due to the presence of shell shape imperfections. A transient and forced periodic vibrations of shell under pressure were investigated. Analysis of transient was executed by the method of direct integration (Direct Transient). The presence of shape imperfections in the shell wall influenced the increase of the transient duration and the dynamic coefficient The direct frequency analysis of shell response on periodic loading (Direct Frequency) was executed taking into account the proper ten first forms and frequencies of natural vibrations. Significant influence of the shell shape imperfections on the resonant frequencies of the forced periodic vibrations and corresponding form of deformation was discovered.
References
Hunt G.M. Imperfection and near-coincidence for symmetric bifurcations // New York Academy of Sciences. Bifurcation theory and applications in scientific disciplines. Ann. N. Y. Acad. Sci., 1977. – Vol. 316. – P. 572-589.
Rikards R.B. Metod konechnykh elementov v teoryy obolochek y plastyn [The Finite Element Method in the theory of shells and plates]. − Ryha: Zynatne, 1988. − 284 s.(rus).
Grigorenko Ya.M., Guliaev V.I. Nelyneinye zadachy teoryy obolochek y metody ykh reshenyia (obzor) [Nonlinear tasks of theory of shells and methods of their decision (review)] // Prykladnaia mekhanyka, 1991. − T. 27, №10. − S. 3-23 s.(rus).
Gudramovych V.S. Osobennosty nelyneinoho deformyrovanyia y krytycheskye sostoianyia obolochechnykh system s heometrycheskymy nesovershenstvamy [Features of nonlinear deformation and critical conditions of the оболочечных systems with geometrical imperfections] // Prykladnaia mekhanyka, 2006. – T. 42, № 12. – S. 32-47 (rus).
Gavrilenko H.D. Nesushchaia sposobnost nesovershennykh obolochek [Bearing strength of imperfect shells]. Monohr. Yn-t mekhanyky ym. S.P.Tymoshenko NAN Ukrayny, 2007. – 294s.(rus).
Nguyen Dinh Duc, Hoang Thi Thiem. Dynamic Analisys of Imperfect FGM Circular Cylindrical Shells Reinforced by Stiffener System Using Third Order Shear Deformation Theory in Term of Displacement Components // Latin American Journal of Solids and Structures, 2017, Vol. 14. P. 2534-2570.
Lukianchenko O.О. Rozviazannia problemy nadiinosti i bezpeky obolonkovykh struktur z nedoskonalostiamy formy metodamy obchysliuvalnoi mekhaniky [Decision of problem of reliability and safety of shell structures with shape imperfections by the methods of calculable mechanics]. − Kyiv: Vyd-vo „Karavela”, 2019. − 197 s (ukr).
Bazhenov V.A., Lukianchenko O.A., Kostina E.V., Geraschenko O.V. Probabilistic Approach to Determination of Reliability of an Imperfect Supporting Shell // Strength of Materials, 2014. Vol. 46, №4. – Р. 567-574.
Bazhenov V.A., Lukianchenko O.O., Kostina O.V. Investigation of Static and Dynamic Characteristics of Complex Thin-Walled Shell Structure with Cracks // Strength of Materials, 2016. Vol. 48, №3. – Р. 401-410.
Bazhenov V.A., Lukianchenko O.A., Vorona Yu.V., Kostina E.V. Stability of the parametric vibrations of a shell in the form of a hyperbolic paraboloid // Internat. Appl. Mech., 2018. Vol. 54, №3. – P. 274-286.
Bazhenov V.А., Lukianchenko O.О., Kostina О.V. Definition of the failure region of the oil tank with wall imperfections in combined loading // Strength of Materials and Theory of Structures, 2018. – Issue 100, C. 27-39.
Lukianchenko O.О., Paliy О.М. Chyselne modeliuvannia stiikosti parametrychnykh kolyvan tonkostinnoi obolonky vidiemnoi hausovoi kryvyzny [Numeral design of vibrations stability of the thin-walled shell with negative гаусової curvature] // Opir materialiv i teoriia sporud: nauk.-tekh. zbirn., K.: KNUBA, 2018. – Vyp. 101, S. 45-59 (ukr).
Lukianchenko O., Kostina O. The finite Element Method in Problems of the Thin Shells Theory, LAP LAMBERT Academic Publishing, 2019. − 134 p.(ukr).
Lukianchenko O.О., Vorona Yu.V., Kostina О.V., Vabyshchevych M.O., Paliy О.М. Nadiinist tonkykh obolonok z realnymy nedoskonalostiamy formy [Reliability of thin shells with real shape imperfections] // Visnyk KPI. Seriia Pryladobuduvannia, 2019. − Vyp. 58(2). − S. 34-40 (ukr).
Paliy О.М., Lukianchenko O.О. Chastotnyi analiz vidhuku hiperbolichnoho paraboloida na periodychne povzdovzhnie navantazhennia [Frequency analysis of response of hyperbolical paraboloid on the periodic longitudinal loading] // Opir materialiv i teoriia sporud: nauk.-tekh. zbirn. – K.: KNUBA, 2019. – Vyp. 102, S. 199-206 (ukr).
Lukianchenko O.O. Application of stiffness rings for improving of operating reliability of the tank with shape imperfections // Strength of Materials and Theory of Structures: Scientificand-technical collected articles. − K.: KNUBA, 2020. − Issue 104. − P. 244-256.
Bazhenov V.A., Lukianchenko O.О., Vorona Yu.V., Vabyshchevych M.O. The influence of shape imperfections on the stability of thin spherical shells // Strengh of Materials, 2021. – Vol. 53, №6. – Р. 842-850.
Rudakov K.N. FEMAP 10.2.0. Heometrycheskoe y konechno-еlementnoe modelyrovanye konstruktsyi [Geometrical and finite-element design of constructions]. – K: NTTU KPY, 2011. – 317 s.(rus).
Lukianchenko O.О., Bourau N.І., Geraschenko O.V., Kostina О.V. Chastoty i formy vlasnykh kolyvan zakhysnoi yemnosti rezervuara z defektamy zvarnykh shviv pry statychnii dii osovoho navantazhennia [Natural frequencies and forms of protective capacity of reservoir with the weld defects under the static action of axial loading] // Opir materialiv i teoriia sporud: nauk.-tekh. zbirn. – K.: KNUBA, 2021. – Vyp. 107. – S. 103-119 (ukr).
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
