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Çeşitli Kenar Sınır Koşullarına Sahip İnce İzotropik Düz Plakaların ve Eğri Plakaların Panel Çarpıntı Sayısal Çalışması

Year 2023, Volume: 26 Issue: 4, 1467 - 1473, 01.12.2023

Chıtaranjan Pany

https://doi.org/10.2339/politeknik.1139958

Abstract

Bu makale de, etkili, yüksek hassasiyetli üçgen sığ kabuk sonlu elemanlar kullanılarak, farklı kenar sınır koşullarına sahip düz plakaların ve eğri plakaların süpersonik panel çarpıntsı sayısal olarak incelenmiştir. Plakanın alt tarafındaki akışkanın durağan olduğu varsayılmıştır. Lineer piston teorisi, plakanın üst yüzeyine uygulanabilir. Aerodinamik yükleri değerlendirmek için doğrusallaştırılmış piston teorisi kullanılmıştır. Karmaşık bir özdeğer probleminin çözümü Hamilton ilkesine göre formüle edilir. Lagrange'ın hareket denklemi, özdeğerleri bulmak için standart yöntemler kullanılarak elde edilir. Mevcut sonlu eleman analizi, aerodinamik sönümlemeyi yok sayar. Geliştirilen sonlu elemanlar paneller için ince ve küçük deforme olmuş kabuklar teorisi dikkate alınır. Geliştirilen sonlu elemanlar kodunu doğrulamak için basitçe desteklenen kenarlı (S-S-S-S) kare ve dikdörtgen düz panellerin, dört sabit kenarlı kare plakanın (C-C-C-C) ve uzunluk yan kelepçeli kare plaka (C-S-C-S) sonuçları yayınlanmış veilerle karşılaştırılmıştır. Literatür verilerinin sınırlı olduğu kare ve dikdörtgen düz panel için diğer kenar sınır koşullarının (S-C-S-C, C-S-C-S ve C-C-C-C) flutter sonuçları değerlendirilmiştir. Çapraz akış yönündeki (S-C-S-C) sabit koşulun, kritik flutter basınç parametreleri ve flutter frekansları üzerinde önemli bir etkiye sahip olduğu bulunmuştur. Ayrıca, yukarıda bahsedilen etkiyi incelemek için, mevcut sonlu eleman (FE), çarpıntı sonuçlarını bulmak için S-C-S-C (çapraz akış yönünde kısıtlı ve süpersonik akışa maruz kalan), S-S-S-S sınır koşullarına sahip kavisli plakalara genişletildi.

Keywords

Panel çarpıntısı Sonlu eleman Kenar sınır koşulları Süpersonik akış Piston teorisi

References

  • [1] Aytaç Z., and Aktaş F., “Utilization of CFD for the aerodynamic analysis of a subsonic rocket”, Politeknik Dergisi, 23(3): 879-887, (2020).
  • [2] Bismarck-Nasr M.N., “Finite elements in aeroelasticity of plates and shells”, Applied Mechanics Review, 49: 17–24, (1996).
  • [3] Dowell E. H., “Nonlinear flutter of curved plates-II”, AIAA Journal, 8: 259-261,(1970).
  • [4] Olson M.D., “Some flutter solutions using finite element”, AIAA Journal, 4:747-752,(1970).
  • [5] Pany C., and Parthan S., “Flutter analysis of periodically supported curved panels, Journal of Sound and Vibration, 267: 267-278,(2003).
  • [6] Avramov K., Uspensky B., “Nonlinear supersonic flutter of sandwich truncated conical shell with flexible honeycomb core manufactured by fused deposition modeling”, International Journal of Non-Linear Mechanics, 143:104039, (2022).
  • [7] Sabri F., and Lakis A. A., “Hybrid finite element method applied to supersonic flutter of an empty or partially liquid-filled truncated conical shell”, Journal of Sound and Vibration,329:302–316,(2010).
  • [8] Chowdary T.V.R., Parthan S., and Sinha P. K.,”Finite element flutter analysis of laminated composite panels”, Computer and Structures, 53: 245-251,(1994).
  • [9] Hassan A., Yusef A., Seyed S.R.K., Hossein A., and Mostafa O.B., “Supersonic flutter behavior of a polymeric truncated conical shell reinforced with agglomerated CNTs”, Waves in Random and Complex Media, (2022), DOI: 10.1080/17455030.2022.2082581.
  • [10] Farukoğlu Ö.C., and Korkut İ., “Analytical solutions for transversely isotropic fiber-reinforced composite cylinders under internal or external pressure”, Politeknik Dergisi, 24(2): 663-672, (2021).
  • [11] Çağdaş İ. U.,“The influence of axial compression on the free vibration frequencies of cross-ply laminated and moderately thick cylinders”, Politeknik Dergisi, 23(1): 45-52, (2020).
  • [12] Muc A., and Flis J., “Free vibrations and supersonic flutter of multilayered laminated cylindrical Panels”, Composite Structures, 246:112400, (2020).
  • [13] Kouchakzadeh M.A., Rasekh M., Haddadpour H., “Panel flutter analysis of general laminated composite plates”,Composite Structures, 92(12):2906-2915, (2010).
  • [14] Pany C., Parthan S., and Mukherjee S., “Vibration analysis of multi-supported curved panel using the periodic structure approach”, International Journal of mechanical Sciences, 44: 269-285,(2002).
  • [15] Cowper G.R., Lindberg G.M., and Olson M.D.,“A shallow shell finite element of triangular shape”, International Journal of Solids and Structures, 6:1133-1156,(1970).
  • [16] Lindberg G.M., and Olson M.D., “A high precision triangular cylindrical shell finite element”, AIAA Journal,9:530-532,(1971).
  • [17] Pany C., “An insight on the estimation of wave propagation constants in an orthogonal grid of a simple line-supported periodic plate using a finite element mathematical model”, Frontier Mechanical Engineering, 8:926559,(2022).
  • [18] Pany C., Parthan S., and Mukhopadhyay M., ”Free vibration analysis of orthogonally supported curved panels”, Journal of Sound and Vibration, 24: 315-318,(2001).
  • [19] Pany C., Parthan S., and Mukhopadhyay M., “Wave propagation in orthogonally supported periodic curved panel”, Journal of Engineering Mechanics (ASCE),129: 342-349,(2003).
  • [20] Pany C., Parthan S., “Axial wave propagation in infinitely long periodic curved panels”, Journal of Vibration and Acoustics (ASME), 125: 24-30,(2003).
  • [21] Zhi-Guang S., and Feng-Ming L., “Investigations on the flutter properties of supersonic panels with different boundary conditions”, International Journal Dynamics and Control 2: 346-353,(2014).
  • [22] Ashley H., and Zartarian G., “Piston Theory- A new aerodynamic tool for the aeroelastician”, Journal of Aeronautical Sciences,23:1109-1118,(1956).

Panel Flutter Numerical Study of Thin Isotropic Flat Plates and Curved Plates with Various Edge Boundary Conditions

Year 2023, Volume: 26 Issue: 4, 1467 - 1473, 01.12.2023

Chıtaranjan Pany

https://doi.org/10.2339/politeknik.1139958

Abstract

In this article, supersonic panel flutter analysis of flat plates and curved plates with different edge boundary conditions are studied, using efficient, high precision triangular shallow shell finite elements. The fluid on the underside of the plate was is assumed to be stationary. The linear piston theory can be applied to the top surface of the plate. The linear piston theory was used to evaluate the aerodynamic loads. The solution of a complex eigenvalue problem was formulated according to Hamilton’s principle. Lagrange’s equation of motion was obtained using standard methods for finding eigenvalues. Current finite element analysis ignores aerodynamic damping. For panels, the theory of thin and small deformed shells was taken into account. To validate the developed finite element code, the results of a square and rectangular flat-panels with simply supported edges (S-S-S-S), a square plate with four fixed edges (C-C-C-C), and a square plate with the length side clamps (C-S-C-S) were compared with the published data. The flutter results of other edge boundary conditions (S-C-S-C, C-S-C-S, and C-C-C-C) for square and rectangular flat panels are evaluated for which literature data is limited. It has been found that the fixed condition in the cross-flow direction (S-C-S-C) has a significant effect on the critical flutter pressure parameters and flutter frequencies. Further, to study the aforementioned effect, the current finite element (FE) has been extended to curved plates with S-C-S-C(constrained in the cross-flow direction and exposed to supersonic flow), SS-S-S boundary conditions to find flutter results.

Keywords

Panel flutter Finite element Edge boundary conditions Supersonic flow Piston theory

References

  • [1] Aytaç Z., and Aktaş F., “Utilization of CFD for the aerodynamic analysis of a subsonic rocket”, Politeknik Dergisi, 23(3): 879-887, (2020).
  • [2] Bismarck-Nasr M.N., “Finite elements in aeroelasticity of plates and shells”, Applied Mechanics Review, 49: 17–24, (1996).
  • [3] Dowell E. H., “Nonlinear flutter of curved plates-II”, AIAA Journal, 8: 259-261,(1970).
  • [4] Olson M.D., “Some flutter solutions using finite element”, AIAA Journal, 4:747-752,(1970).
  • [5] Pany C., and Parthan S., “Flutter analysis of periodically supported curved panels, Journal of Sound and Vibration, 267: 267-278,(2003).
  • [6] Avramov K., Uspensky B., “Nonlinear supersonic flutter of sandwich truncated conical shell with flexible honeycomb core manufactured by fused deposition modeling”, International Journal of Non-Linear Mechanics, 143:104039, (2022).
  • [7] Sabri F., and Lakis A. A., “Hybrid finite element method applied to supersonic flutter of an empty or partially liquid-filled truncated conical shell”, Journal of Sound and Vibration,329:302–316,(2010).
  • [8] Chowdary T.V.R., Parthan S., and Sinha P. K.,”Finite element flutter analysis of laminated composite panels”, Computer and Structures, 53: 245-251,(1994).
  • [9] Hassan A., Yusef A., Seyed S.R.K., Hossein A., and Mostafa O.B., “Supersonic flutter behavior of a polymeric truncated conical shell reinforced with agglomerated CNTs”, Waves in Random and Complex Media, (2022), DOI: 10.1080/17455030.2022.2082581.
  • [10] Farukoğlu Ö.C., and Korkut İ., “Analytical solutions for transversely isotropic fiber-reinforced composite cylinders under internal or external pressure”, Politeknik Dergisi, 24(2): 663-672, (2021).
  • [11] Çağdaş İ. U.,“The influence of axial compression on the free vibration frequencies of cross-ply laminated and moderately thick cylinders”, Politeknik Dergisi, 23(1): 45-52, (2020).
  • [12] Muc A., and Flis J., “Free vibrations and supersonic flutter of multilayered laminated cylindrical Panels”, Composite Structures, 246:112400, (2020).
  • [13] Kouchakzadeh M.A., Rasekh M., Haddadpour H., “Panel flutter analysis of general laminated composite plates”,Composite Structures, 92(12):2906-2915, (2010).
  • [14] Pany C., Parthan S., and Mukherjee S., “Vibration analysis of multi-supported curved panel using the periodic structure approach”, International Journal of mechanical Sciences, 44: 269-285,(2002).
  • [15] Cowper G.R., Lindberg G.M., and Olson M.D.,“A shallow shell finite element of triangular shape”, International Journal of Solids and Structures, 6:1133-1156,(1970).
  • [16] Lindberg G.M., and Olson M.D., “A high precision triangular cylindrical shell finite element”, AIAA Journal,9:530-532,(1971).
  • [17] Pany C., “An insight on the estimation of wave propagation constants in an orthogonal grid of a simple line-supported periodic plate using a finite element mathematical model”, Frontier Mechanical Engineering, 8:926559,(2022).
  • [18] Pany C., Parthan S., and Mukhopadhyay M., ”Free vibration analysis of orthogonally supported curved panels”, Journal of Sound and Vibration, 24: 315-318,(2001).
  • [19] Pany C., Parthan S., and Mukhopadhyay M., “Wave propagation in orthogonally supported periodic curved panel”, Journal of Engineering Mechanics (ASCE),129: 342-349,(2003).
  • [20] Pany C., Parthan S., “Axial wave propagation in infinitely long periodic curved panels”, Journal of Vibration and Acoustics (ASME), 125: 24-30,(2003).
  • [21] Zhi-Guang S., and Feng-Ming L., “Investigations on the flutter properties of supersonic panels with different boundary conditions”, International Journal Dynamics and Control 2: 346-353,(2014).
  • [22] Ashley H., and Zartarian G., “Piston Theory- A new aerodynamic tool for the aeroelastician”, Journal of Aeronautical Sciences,23:1109-1118,(1956).
There are 22 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Chıtaranjan Pany 0000-0001-8617-2134

Publication Date December 1, 2023
Submission Date July 3, 2022
Published in Issue Year 2023 Volume: 26 Issue: 4

Cite

APA Pany, C. (2023). Panel Flutter Numerical Study of Thin Isotropic Flat Plates and Curved Plates with Various Edge Boundary Conditions. Politeknik Dergisi, 26(4), 1467-1473. https://doi.org/10.2339/politeknik.1139958
AMA Pany C. Panel Flutter Numerical Study of Thin Isotropic Flat Plates and Curved Plates with Various Edge Boundary Conditions. Politeknik Dergisi. December 2023;26(4):1467-1473. doi:10.2339/politeknik.1139958
Chicago Pany, Chıtaranjan. “Panel Flutter Numerical Study of Thin Isotropic Flat Plates and Curved Plates With Various Edge Boundary Conditions”. Politeknik Dergisi 26, no. 4 (December 2023): 1467-73. https://doi.org/10.2339/politeknik.1139958.
EndNote Pany C (December 1, 2023) Panel Flutter Numerical Study of Thin Isotropic Flat Plates and Curved Plates with Various Edge Boundary Conditions. Politeknik Dergisi 26 4 1467–1473.
IEEE C. Pany, “Panel Flutter Numerical Study of Thin Isotropic Flat Plates and Curved Plates with Various Edge Boundary Conditions”, Politeknik Dergisi, vol. 26, no. 4, pp. 1467–1473, 2023, doi: 10.2339/politeknik.1139958.
ISNAD Pany, Chıtaranjan. “Panel Flutter Numerical Study of Thin Isotropic Flat Plates and Curved Plates With Various Edge Boundary Conditions”. Politeknik Dergisi 26/4 (December 2023), 1467-1473. https://doi.org/10.2339/politeknik.1139958.
JAMA Pany C. Panel Flutter Numerical Study of Thin Isotropic Flat Plates and Curved Plates with Various Edge Boundary Conditions. Politeknik Dergisi. 2023;26:1467–1473.
MLA Pany, Chıtaranjan. “Panel Flutter Numerical Study of Thin Isotropic Flat Plates and Curved Plates With Various Edge Boundary Conditions”. Politeknik Dergisi, vol. 26, no. 4, 2023, pp. 1467-73, doi:10.2339/politeknik.1139958.
Vancouver Pany C. Panel Flutter Numerical Study of Thin Isotropic Flat Plates and Curved Plates with Various Edge Boundary Conditions. Politeknik Dergisi. 2023;26(4):1467-73.

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