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27.11.2021

Parametric Resonance of a Three-Layered Cylindrical Composite Rib-Stiffened Shell*

verfasst von: V. N. Bakulin, D. A. Boitsova, A. Ya. Nedbai

Erschienen in: Mechanics of Composite Materials | Ausgabe 5/2021

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Abstract

Equations for the parametric resonance of a three-layered cylindrical shell with composite layers stiffened with ribs and containing a hollow isotropic cylinder are obtained. The shell is loaded by axial forces and an external pressure varying harmonically in time. The influence of the cylinder is modeled as an elastic foundation whose modulus of subgrade reaction was determined from equations of 3D elasticity theory. Their solution is sought in the form of a trigonometric series in the axial coordinate. The infinite system of inhomogeneous differential equations of Mathieu–Hill type obtained is solved using a trigonometric series in time. Using a numerical example, the main regions of instability were obtained for the first time, and plots for the critical frequencies on the channel radius, the elastic modulus of cylinder material, and the number and height of ribs are found. The mathematical model proposed extends the range of relevant scientific and applied problems in studying three-layered stiffened shells.

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Literatur
1.
Zurück zum Zitat V. N. Bakulin, “Investigation of the influence of the cutout dimensions on the stress-strain state of three-layer shells with load-bearing layers of composite materials,” J. Phys. Conference Ser. Mater. Sci. Eng., 714, 012002 (2020). V. N. Bakulin, “Investigation of the influence of the cutout dimensions on the stress-strain state of three-layer shells with load-bearing layers of composite materials,” J. Phys. Conference Ser. Mater. Sci. Eng., 714, 012002 (2020).
2.
Zurück zum Zitat A. M. Lipanov, S. A. Karskanov, S. L. Cheernyshev, and I. I. Lipatov, “Theoretical investigation of conditions of the origination of high-speed buffeting,” Bulletin of Udmurt University, Mathematics, Mechanics, Computer Sciences, 29, No. 3, 382-395 (2019) [in Russian]. A. M. Lipanov, S. A. Karskanov, S. L. Cheernyshev, and I. I. Lipatov, “Theoretical investigation of conditions of the origination of high-speed buffeting,” Bulletin of Udmurt University, Mathematics, Mechanics, Computer Sciences, 29, No. 3, 382-395 (2019) [in Russian].
3.
Zurück zum Zitat A. S. Vol’mir, Shells in Flow of Liquid and Gas. Aeroelasticity Problems, Fizmatlit, Moscow (1976) [in Russian]. A. S. Vol’mir, Shells in Flow of Liquid and Gas. Aeroelasticity Problems, Fizmatlit, Moscow (1976) [in Russian].
4.
Zurück zum Zitat V. N. Bakulin, “An efficient model for layer-by-layer analysis of three-layered irregular cylindrical shells of revolution,” Doklady Akademii Nauk, 478, No. 2, 148-152 (2018). V. N. Bakulin, “An efficient model for layer-by-layer analysis of three-layered irregular cylindrical shells of revolution,” Doklady Akademii Nauk, 478, No. 2, 148-152 (2018).
5.
Zurück zum Zitat V. N. Bakulin, “Block-layer-by-layer approach for analyzing the stress-strain state of three-layered irregular cylindrical shells of revolution,” Prikladnaya Matematika I Mechanika, 85, No. 3, 383-395 (2021). V. N. Bakulin, “Block-layer-by-layer approach for analyzing the stress-strain state of three-layered irregular cylindrical shells of revolution,” Prikladnaya Matematika I Mechanika, 85, No. 3, 383-395 (2021).
6.
Zurück zum Zitat V. N. Paimushin, “Theory of moderately large deflections of sandwich shells having a transversely soft core and reinforced along their contour,” Mech. Compos. Mater., 53, No. 1, 1-16 (2017).CrossRef V. N. Paimushin, “Theory of moderately large deflections of sandwich shells having a transversely soft core and reinforced along their contour,” Mech. Compos. Mater., 53, No. 1, 1-16 (2017).CrossRef
7.
Zurück zum Zitat V. N. Bakulin, I. F. Obraztsov, and V. A. Potopakhin, Dynamic Problems of Nonlinear Theory of Multilayered Shells: Action of Intense Thermal Power Loads of Concentrated Energy Flows [in Russian], Fizmatlit, Moscow (1998). V. N. Bakulin, I. F. Obraztsov, and V. A. Potopakhin, Dynamic Problems of Nonlinear Theory of Multilayered Shells: Action of Intense Thermal Power Loads of Concentrated Energy Flows [in Russian], Fizmatlit, Moscow (1998).
8.
Zurück zum Zitat E. I. Grigolyuk and P. P. Chulkov, Stability and Vibrations of Three-layered Shells [in Russian], Mashinostroenie, Moscow (1973) . E. I. Grigolyuk and P. P. Chulkov, Stability and Vibrations of Three-layered Shells [in Russian], Mashinostroenie, Moscow (1973) .
9.
Zurück zum Zitat E. I. Starovoitov and D. and V. Leonenko, “Resonance vibrations of a three-layered cylindrical shell with elastic core,” Mech. Compos. Mater. and Struct., 22, No. 1, 60-68 (2016). E. I. Starovoitov and D. and V. Leonenko, “Resonance vibrations of a three-layered cylindrical shell with elastic core,” Mech. Compos. Mater. and Struct., 22, No. 1, 60-68 (2016).
10.
Zurück zum Zitat V. N. Bakulin, E. N.Volkov, and A. Ya. Nedbai, “Dynamic stability of a cylindrical shell reinforced by longitudinal ribs and a hollow cylinder under the action of axial forces,” J. Eng. Phys. Thermophys., 89, No. 3, 747-753 (2016).CrossRef V. N. Bakulin, E. N.Volkov, and A. Ya. Nedbai, “Dynamic stability of a cylindrical shell reinforced by longitudinal ribs and a hollow cylinder under the action of axial forces,” J. Eng. Phys. Thermophys., 89, No. 3, 747-753 (2016).CrossRef
11.
Zurück zum Zitat V. N. Bakulin and A. Ya Nedbai, “Dynamic stability of a cylindrical shell stiffened with longitidunal ribs of of piecewise constant thickness under action of axial load,” Doklady Akademii Nauk, Physics, Tekhn. Nauki, 495, 43-49 (2020). V. N. Bakulin and A. Ya Nedbai, “Dynamic stability of a cylindrical shell stiffened with longitidunal ribs of of piecewise constant thickness under action of axial load,” Doklady Akademii Nauk, Physics, Tekhn. Nauki, 495, 43-49 (2020).
12.
Zurück zum Zitat A. A. Mailybaev and A. P. Seiranyan, Multiparameter Stability Problems. Theory and Applications in Mechanics [in Russian], Fizmatlit, Moscow (2009). A. A. Mailybaev and A. P. Seiranyan, Multiparameter Stability Problems. Theory and Applications in Mechanics [in Russian], Fizmatlit, Moscow (2009).
13.
Zurück zum Zitat Jin-Yih Kao, Chun-Sheng Chen, and Wei-Ren Chen, “Parametric vibration response of foam-filled sandwich plates under periodic loads,” Mech. Compos. Mater., 48, No. 5, 525-538 (2012).CrossRef Jin-Yih Kao, Chun-Sheng Chen, and Wei-Ren Chen, “Parametric vibration response of foam-filled sandwich plates under periodic loads,” Mech. Compos. Mater., 48, No. 5, 525-538 (2012).CrossRef
14.
Zurück zum Zitat P. M. Ogibalov and M. A. Koltunov, Shells and Plates [in Russian], GITTL, Moscow, (1956). P. M. Ogibalov and M. A. Koltunov, Shells and Plates [in Russian], GITTL, Moscow, (1956).
15.
Zurück zum Zitat S. A. Vol’mir, Nonlinear Dynamics of Plates and Shells [in Russian], Nauka, Moscow (1972). S. A. Vol’mir, Nonlinear Dynamics of Plates and Shells [in Russian], Nauka, Moscow (1972).
16.
Zurück zum Zitat S. D. Algazin and I. A. Kijko, Flutter of Plates and Shells [in Russian], Nauka, Moscow (2006). S. D. Algazin and I. A. Kijko, Flutter of Plates and Shells [in Russian], Nauka, Moscow (2006).
17.
Zurück zum Zitat V. N. Bakulin, E. N. Volkov, and A. Ya. Nedbai, “Flutter of a layered cylindrical shell stiffened with annular ribs and loaded with axial forces,” Doklady Akademii Nauk, 463, No. 4, 414-417 (2015). V. N. Bakulin, E. N. Volkov, and A. Ya. Nedbai, “Flutter of a layered cylindrical shell stiffened with annular ribs and loaded with axial forces,” Doklady Akademii Nauk, 463, No. 4, 414-417 (2015).
18.
Zurück zum Zitat V. N. Bakulin, M. A. Konopel’chev, and A. Ya. Nedbai, “Flutter of a laminated cantilever cylindrical shell with a ringstiffened edge,” Russ. Aeronautika, 61, No. 4, 517-523 (2018).CrossRef V. N. Bakulin, M. A. Konopel’chev, and A. Ya. Nedbai, “Flutter of a laminated cantilever cylindrical shell with a ringstiffened edge,” Russ. Aeronautika, 61, No. 4, 517-523 (2018).CrossRef
19.
Zurück zum Zitat V. G. Moskvin, “Stability of circular cylindrical shell made from linear viscoelastic material in a supersonic gas flow,” Proc. 8th All-Union Conf. on Theory of Shells and Plates, Nauka, Moscow, (1962), 527-531. V. G. Moskvin, “Stability of circular cylindrical shell made from linear viscoelastic material in a supersonic gas flow,” Proc. 8th All-Union Conf. on Theory of Shells and Plates, Nauka, Moscow, (1962), 527-531.
20.
Zurück zum Zitat S. A. Bochkarev and S. V. Lekomtsev, “ Study of panel flutter of circular cylindrical shells made of functional-gradient material,” PNRPU Mechanikha Bulet, No. 1, 57-75 (2014). S. A. Bochkarev and S. V. Lekomtsev, “ Study of panel flutter of circular cylindrical shells made of functional-gradient material,” PNRPU Mechanikha Bulet, No. 1, 57-75 (2014).
21.
Zurück zum Zitat V. N. Bakulin, E. N. Volkov, and A. I. Simonov, “Dynamic stability of a cylindrical shell under alternating axial external pressure,” Russian Aeronautika, 60, No. 4, 508-513 (2017).CrossRef V. N. Bakulin, E. N. Volkov, and A. I. Simonov, “Dynamic stability of a cylindrical shell under alternating axial external pressure,” Russian Aeronautika, 60, No. 4, 508-513 (2017).CrossRef
22.
Zurück zum Zitat V. N. Bakulin, V. N. Bokov, and A. Ya. Nedbai, “Aeroelastic stability of a cylindrical composite shell at a bilateral flow,” 53, No. 6, 801-808 (2018). V. N. Bakulin, V. N. Bokov, and A. Ya. Nedbai, “Aeroelastic stability of a cylindrical composite shell at a bilateral flow,” 53, No. 6, 801-808 (2018).
23.
Zurück zum Zitat Yu. S. Solomonov, V. P. Georgievskii, A. Ya. Nedbai, and E. N. Volkov, “Dynamic stability of layered cylindrical shell stiffened with circular ribs and cylinder under external pressure,” Mech. Compos. Mater. and Struct., 19, No.4, 61-623 (2013). Yu. S. Solomonov, V. P. Georgievskii, A. Ya. Nedbai, and E. N. Volkov, “Dynamic stability of layered cylindrical shell stiffened with circular ribs and cylinder under external pressure,” Mech. Compos. Mater. and Struct., 19, No.4, 61-623 (2013).
24.
Zurück zum Zitat V. V. Bagdasaryan, O. V. Kuznetsov, and I. S. Malyutin, ‘On parametric resonance of cylindrical shell stiffened with longitudinal ribs,” Vopr. Mat. Fiz. Vibration Teor. Issue 3, 89-96 (1975). V. V. Bagdasaryan, O. V. Kuznetsov, and I. S. Malyutin, ‘On parametric resonance of cylindrical shell stiffened with longitudinal ribs,” Vopr. Mat. Fiz. Vibration Teor. Issue 3, 89-96 (1975).
25.
Zurück zum Zitat V. N. Bakulin, E. V. Danilkin, and A. Ya. Nedbai, “Dynamic stability of a cylindrical shell stiffened with a cylinder and longitudinal diaphragms at external pressure,” J. Eng. Phys. Thermophys., 91, No. 2, 537–543 (2018).CrossRef V. N. Bakulin, E. V. Danilkin, and A. Ya. Nedbai, “Dynamic stability of a cylindrical shell stiffened with a cylinder and longitudinal diaphragms at external pressure,” J. Eng. Phys. Thermophys., 91, No. 2, 537–543 (2018).CrossRef
26.
Zurück zum Zitat Yu. S. Solomonov, V. P. Georgievskii, A. Ya. Nedbai, and V. A. Andryushin, Applied Problems of Mechanics of Composite Cylindrical Sheels [in Russian], Fizmatgiz, Moscow (2014). Yu. S. Solomonov, V. P. Georgievskii, A. Ya. Nedbai, and V. A. Andryushin, Applied Problems of Mechanics of Composite Cylindrical Sheels [in Russian], Fizmatgiz, Moscow (2014).
27.
Zurück zum Zitat I. S. Malyutin, “Stability of three-layered orthotropic cylindrical shells directly stiffened by ribs,” Applied Mech., 15, No. 7, 20-26 (1979). I. S. Malyutin, “Stability of three-layered orthotropic cylindrical shells directly stiffened by ribs,” Applied Mech., 15, No. 7, 20-26 (1979).
28.
Zurück zum Zitat V. V. Bolotin, Dynamic Stability of Elastic Systems [in Russian], GITTL, Moscow (1956). V. V. Bolotin, Dynamic Stability of Elastic Systems [in Russian], GITTL, Moscow (1956).
29.
Zurück zum Zitat V. N. Bakulin and A. Ya. Nedbai, “Dynamic stability of composite cylindrical shell of linear-variable thickness under the action pulsed external pressure,” J. Eng. Phys. Thermophys, 94, No. 2, 525-533 (2021).CrossRef V. N. Bakulin and A. Ya. Nedbai, “Dynamic stability of composite cylindrical shell of linear-variable thickness under the action pulsed external pressure,” J. Eng. Phys. Thermophys, 94, No. 2, 525-533 (2021).CrossRef
Metadaten
Titel
Parametric Resonance of a Three-Layered Cylindrical Composite Rib-Stiffened Shell*
verfasst von
V. N. Bakulin
D. A. Boitsova
A. Ya. Nedbai
Publikationsdatum
27.11.2021
Verlag
Springer US
Erschienen in
Mechanics of Composite Materials / Ausgabe 5/2021
Print ISSN: 0191-5665
Elektronische ISSN: 1573-8922
DOI
https://doi.org/10.1007/s11029-021-09984-9

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