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Determination of bounding frequencies of cylindrical shells using a periodic structure wave approach with Rayleigh-Ritz method

Year 2024, Volume: 30 Issue: 5, 679 - 685, 30.10.2024

Chıtaranjan Pany

Abstract

Bu çalışmada, dalga yaklaşımı ile periyodik yapı teorisi, çevresel yönde
periyodik çizgi destekli silindirlerde yayılan dalga hareketlerini
karakterize etmek için basit bir yaklaşım çözüm tekniği sunmak için
kullanılmaktadır. Floquet'nin kavramına uygun yer değiştirme
fonksiyonları geliştirmek için, periyodik bir kirişin yayılma bantlarının
(PB) sınırlar modlarının (BM) basit kiriş fonksiyonlarının bir
kombinasyonu formüle edilmiştir. Bu çalışma düzlem dalga olarak
bilinen hareket türü için geliştirilmiştir. Sonuç olarak, yalnızca
zayıflama olmaksızın yayılan dalgalar dikkate alınmıştır.Tek bir
periyodik eğri panelin (birim hücre) çepeçevrgi modları, Floquet'in
dalga prensibini karşılayan klasik ışın fonksiyonları açısından
tanımlanmıştır, ancak eksenel modların sinüzoidal dalgalar olduğu
düşünülmektedir.Yer değiştirme fonksiyonları, gerinim enerjisi ve
kinetik enerji ifadelerini germek için kullanılır. Rayleigh-Ritz tekniği
daha sonra periyodik birim hücrenin sertlik ve kütle matrislerini
oluşturmak için kullanılır. Özdeğer denkleminin çözülmesiyle fazfrekans ilişkisi elde edilir. Belirli bir çepeçevrgi faz sabiti ile silindirik bir
kabuğun çeşitli eksenel modları için PB'nin sınırlar frekanslarını
tahmin etmek de mümkün olmuştur. Elde edilen bulgular daha sonra
literatürde belirtilenlerle karşılaştırılmıştır. Ayrıca, belirli bir silindirik
kabuk geometrisi için en düşük frekansı veren optimum periyodik
kavisli panel için sınırlar frekansı sonuçları da bulunmuştur. Periyodik
yapı (PS) dalga yaklaşımına sahip mevcut ışın fonksiyonunun sınırlar
frekansları (BF) ve sınırlar modları (BM) makul bir doğrulukla
bulabildiği tespit edilmiştir

Keywords

Silindirik kabuk Kavisli panel Dalga yayılımı Sınırlama frekansı Işın işlevi Rayleigh-Ritz yöntemi

References

  • [1] Senem S.“Case study for comparative analysis of BIMbased LEED building and non-LEED building”. Pamukkale University Journal of Engineering Sciences, 28(3), 418-426, 2022.
  • [2] Abd’gafar TT, Falade IK, Abdullahi SA. “Computational assessment of external force acting on beam elastic foundation”. Pamukkale University Journal of Engineering Sciences, 28(3), 401-407,2022.
  • [3] Mead DJ. “Wave propagation in continuous periodic structures: research contribution from Southampton, 1961-1995”. Journal of Sound and Vibration, 190(3), 495-524, 1996.
  • [4] Brillouin L. Wave Propagation in Periodic Structure.2nd ed. New York, USA, Dover Publications, 1953.
  • [5] Heckl M.“Investigation on the vibration of grillages and other simple beam structures”. Journal of Acoustic Society of America, 36(7), 1335-1343, 1964.
  • [6] Mead DJ.“Free wave propagation in periodically supported infinite periodic beams”. Journal of Sound and Vibration, 11(2), 181-197, 1970.
  • [7] Mead DJ. “A general theory of harmonic wave propagation in linear periodic systems with multiple coupling”. Journal of Sound and Vibration, 27(2), 235–260,1973.
  • [8] Saeed AA, Yousuf ZA.“Theoretical analysis of mechanical vibration for offshore platform structures”. World Journal of Mechanics, 4(1), 1-11, 2014.
  • [9] Mead DJ, Parthan S.“Free wave propagation in twodimensional periodic plates”. Journal of Sound and Vibration, 64(3), 325-348, 1979.
  • [10] Senagupta G.“Natural flexural waves and normal modes of periodically supported beams and plates”. Journal of Sound and Vibration, 13(1), 89-111, 1970.
  • [11] Mead DJ, Bardell NS. “Free vibration of a thin cylindrical shells with discrete axial stiffeners”. Journal of Sound and Vibration, 111(2), 229-250, 1986.
  • [12] Mead DJ, Bardell NS.“Free vibration of a thin cylindrical shell with periodic circumferential stiffeners”. Journal of Sound and Vibration, 115(3), 499-520, 1987.
  • [13] Bardell NS, Mead DJ.“Free Vibration of an orthogonally stiffened cylindrical shell, part I: discrete line simple supports”. Journal of Sound and Vibration, 134(1), 29-54, 1989.
  • [14] Bardell NS, Mead DJ. “Free vibration of an orthogonally stiffened cylindrical shell, part II: discrete general stiffeners”. Journal of Sound and Vibration, 134(1), 55-72, 1989.
  • [15] Accorsi ML, Bennett MS.“A finite element based method for the analysis of free wave propagation in stiffened cylinders”. Journal of Sound and Vibration, 148(2), 279-292, 1991.
  • [16] Laurent M, Oriol G, Valentin M, Mahmoud K.“Noise radiated from a periodically stiffened cylindrical shell excited by a turbulent boundary layer”. Journal of Sound and Vibration, 466(3), 1-32, 2020.
  • [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, 1-13, 2022.
  • [18] Pany C, Mukherjee S, Parthan S. “Study of circumferential wave propagation in an unstiffened circular cylindrical shell using periodic structure theory”. Journal of Institution Engineers (India): Aerospace Engineering Journal, 80(1), 18-24, 1999.
  • [19] Pany C, Parthan S, Mukherjee S.“Vibration analysis of multi-supported curved panel using the periodic structure approach”. International Journal of mechanical Science, 44(2),269-285,2002.
  • [20] Pany C, Parthan S.“Free vibration analysis of multi-span curved beam and circular ring using periodic structure concept”. Journal of Institution Engineers (India): Aerospace Engineering Journal, 83, 18-24, 2002.
  • [21] Pany C, Parthan S. “Axial wave propagation in infinitely long periodic curved panels”. Journal of Vibration and Acoustics, 125(1), 24-30, 2003.
  • [22] Pany C, Parthan S, Mukhopadhyay M.“Free vibration analysis of an orthogonally supported multi-span curved panel”. Journal of Sound and Vibration, 241(2), 315-318, 2001.
  • [23] Pany C, Parthan S, Mukhopadhyay M.“Wave propagation in orthogonally supported periodic curved panel”. Journal of Engineering Mechanics, 129(3), 342-349, 2003.
  • [24] Pany C. Vibration Analysis of Curved Panels and Shell Using Approximate Methods and Determination of Optimum Periodic Angle. Editors: Holm A, Alexander HD, Cheng XG, Аndrii K, Wladyslaw K, Piotr L, Viktor P, Andrii R, Stavros S. Lecture Notes in Mechanical Engineering of Advances in Mechanical and Power Engineering (CAMPE-2021), 354-365, Cham, Switzerland, Springer Nature, 2023.
  • [25] Pany C. “Panel flutter numerical study of thin isotropic flat plates and curved plates with various edge boundary conditions”. Journal of Polytechnic, 26(4), 1467-1473, 2023.
  • [26] Pany C, Parthan S. “Flutter analysis of periodically supported curved panels”. Journal of Sound and Vibration, 267(2), 267-278, 2003.
  • [27] Warburton GB. Dynamical Behaviour of Structures. 2nd ed. Great Britain, Pergamon Press, 1976.
  • [28] Bishop RED, Johnson DC. The Mechanics of Vibration. 1st ed. UK, Cambridge University Press, 2011.
  • [29] Cowper GR, Lindberg GM, Olson MD. “A shallow shell finite element of triangular shape”. International Journal of Solids and Structures, 6(8), 1133-1156, 1970.

Year 2024, Volume: 30 Issue: 5, 679 - 685, 30.10.2024

Chıtaranjan Pany

Abstract

In this paper, periodic structure theory with the wave approximation is
used to present a simple approximate solution technique to characterize
wave motions propagating in periodic line-supported cylinders in the
circumferential direction. To develop displacement functions that
adhere to Floquet's concept, a combination of simple beam functions of
the bounding modes(BM)of propagation bands(PB) of a periodic beam
are formulated. This study is developed for the motion type known as a
plane wave. Consequently, only waves that are simply propagating
without attenuation are taken into account. The circumferential modes
of a single periodic curved panel (unit cell) have been defined in terms
of classical beam functions that satisfy Floquet's wave principle, but the
axial modes are thought to be sinusoidal waves. Displacement functions
are used to strain energy and kinetic energy expressions. The RayleighRitz technique is then used to generate the stiffness and mass matrices
of the periodic unit cell. By solving the eigenvalue equation, phasefrequency relation is obtained. It has also been possible to predict the
bounding frequencies of the PB for various axial modes of a cylindrical
shell with a certain circumferential phase constant. The findings are
then put through comparison with those outlined in the literature.
Further, the bounding frequency results for the optimum periodic
curved panel which gives lowest frequency for a given cylindrical shell
geometry are also found out. It has been found that the current beam
function with a periodic structure (PS) wave approach can find the
bounding frequencies (BF) and bounding modes (BM) with reasonable
accuracy.

Keywords

Cylindrical shell Curved panel Wave propagation Bounding frequency Beam function Rayleigh-Ritz method

References

  • [1] Senem S.“Case study for comparative analysis of BIMbased LEED building and non-LEED building”. Pamukkale University Journal of Engineering Sciences, 28(3), 418-426, 2022.
  • [2] Abd’gafar TT, Falade IK, Abdullahi SA. “Computational assessment of external force acting on beam elastic foundation”. Pamukkale University Journal of Engineering Sciences, 28(3), 401-407,2022.
  • [3] Mead DJ. “Wave propagation in continuous periodic structures: research contribution from Southampton, 1961-1995”. Journal of Sound and Vibration, 190(3), 495-524, 1996.
  • [4] Brillouin L. Wave Propagation in Periodic Structure.2nd ed. New York, USA, Dover Publications, 1953.
  • [5] Heckl M.“Investigation on the vibration of grillages and other simple beam structures”. Journal of Acoustic Society of America, 36(7), 1335-1343, 1964.
  • [6] Mead DJ.“Free wave propagation in periodically supported infinite periodic beams”. Journal of Sound and Vibration, 11(2), 181-197, 1970.
  • [7] Mead DJ. “A general theory of harmonic wave propagation in linear periodic systems with multiple coupling”. Journal of Sound and Vibration, 27(2), 235–260,1973.
  • [8] Saeed AA, Yousuf ZA.“Theoretical analysis of mechanical vibration for offshore platform structures”. World Journal of Mechanics, 4(1), 1-11, 2014.
  • [9] Mead DJ, Parthan S.“Free wave propagation in twodimensional periodic plates”. Journal of Sound and Vibration, 64(3), 325-348, 1979.
  • [10] Senagupta G.“Natural flexural waves and normal modes of periodically supported beams and plates”. Journal of Sound and Vibration, 13(1), 89-111, 1970.
  • [11] Mead DJ, Bardell NS. “Free vibration of a thin cylindrical shells with discrete axial stiffeners”. Journal of Sound and Vibration, 111(2), 229-250, 1986.
  • [12] Mead DJ, Bardell NS.“Free vibration of a thin cylindrical shell with periodic circumferential stiffeners”. Journal of Sound and Vibration, 115(3), 499-520, 1987.
  • [13] Bardell NS, Mead DJ.“Free Vibration of an orthogonally stiffened cylindrical shell, part I: discrete line simple supports”. Journal of Sound and Vibration, 134(1), 29-54, 1989.
  • [14] Bardell NS, Mead DJ. “Free vibration of an orthogonally stiffened cylindrical shell, part II: discrete general stiffeners”. Journal of Sound and Vibration, 134(1), 55-72, 1989.
  • [15] Accorsi ML, Bennett MS.“A finite element based method for the analysis of free wave propagation in stiffened cylinders”. Journal of Sound and Vibration, 148(2), 279-292, 1991.
  • [16] Laurent M, Oriol G, Valentin M, Mahmoud K.“Noise radiated from a periodically stiffened cylindrical shell excited by a turbulent boundary layer”. Journal of Sound and Vibration, 466(3), 1-32, 2020.
  • [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, 1-13, 2022.
  • [18] Pany C, Mukherjee S, Parthan S. “Study of circumferential wave propagation in an unstiffened circular cylindrical shell using periodic structure theory”. Journal of Institution Engineers (India): Aerospace Engineering Journal, 80(1), 18-24, 1999.
  • [19] Pany C, Parthan S, Mukherjee S.“Vibration analysis of multi-supported curved panel using the periodic structure approach”. International Journal of mechanical Science, 44(2),269-285,2002.
  • [20] Pany C, Parthan S.“Free vibration analysis of multi-span curved beam and circular ring using periodic structure concept”. Journal of Institution Engineers (India): Aerospace Engineering Journal, 83, 18-24, 2002.
  • [21] Pany C, Parthan S. “Axial wave propagation in infinitely long periodic curved panels”. Journal of Vibration and Acoustics, 125(1), 24-30, 2003.
  • [22] Pany C, Parthan S, Mukhopadhyay M.“Free vibration analysis of an orthogonally supported multi-span curved panel”. Journal of Sound and Vibration, 241(2), 315-318, 2001.
  • [23] Pany C, Parthan S, Mukhopadhyay M.“Wave propagation in orthogonally supported periodic curved panel”. Journal of Engineering Mechanics, 129(3), 342-349, 2003.
  • [24] Pany C. Vibration Analysis of Curved Panels and Shell Using Approximate Methods and Determination of Optimum Periodic Angle. Editors: Holm A, Alexander HD, Cheng XG, Аndrii K, Wladyslaw K, Piotr L, Viktor P, Andrii R, Stavros S. Lecture Notes in Mechanical Engineering of Advances in Mechanical and Power Engineering (CAMPE-2021), 354-365, Cham, Switzerland, Springer Nature, 2023.
  • [25] Pany C. “Panel flutter numerical study of thin isotropic flat plates and curved plates with various edge boundary conditions”. Journal of Polytechnic, 26(4), 1467-1473, 2023.
  • [26] Pany C, Parthan S. “Flutter analysis of periodically supported curved panels”. Journal of Sound and Vibration, 267(2), 267-278, 2003.
  • [27] Warburton GB. Dynamical Behaviour of Structures. 2nd ed. Great Britain, Pergamon Press, 1976.
  • [28] Bishop RED, Johnson DC. The Mechanics of Vibration. 1st ed. UK, Cambridge University Press, 2011.
  • [29] Cowper GR, Lindberg GM, Olson MD. “A shallow shell finite element of triangular shape”. International Journal of Solids and Structures, 6(8), 1133-1156, 1970.
There are 29 citations in total.

Details

Primary Language English
Subjects Civil Engineering (Other)
Journal Section Research Article
Authors

Chıtaranjan Pany

Publication Date October 30, 2024
Published in Issue Year 2024 Volume: 30 Issue: 5

Cite

APA Pany, C. (2024). Determination of bounding frequencies of cylindrical shells using a periodic structure wave approach with Rayleigh-Ritz method. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 30(5), 679-685.
AMA Pany C. Determination of bounding frequencies of cylindrical shells using a periodic structure wave approach with Rayleigh-Ritz method. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. October 2024;30(5):679-685.
Chicago Pany, Chıtaranjan. “Determination of Bounding Frequencies of Cylindrical Shells Using a Periodic Structure Wave Approach With Rayleigh-Ritz Method”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 30, no. 5 (October 2024): 679-85.
EndNote Pany C (October 1, 2024) Determination of bounding frequencies of cylindrical shells using a periodic structure wave approach with Rayleigh-Ritz method. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 30 5 679–685.
IEEE C. Pany, “Determination of bounding frequencies of cylindrical shells using a periodic structure wave approach with Rayleigh-Ritz method”, Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, vol. 30, no. 5, pp. 679–685, 2024.
ISNAD Pany, Chıtaranjan. “Determination of Bounding Frequencies of Cylindrical Shells Using a Periodic Structure Wave Approach With Rayleigh-Ritz Method”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 30/5 (October 2024), 679-685.
JAMA Pany C. Determination of bounding frequencies of cylindrical shells using a periodic structure wave approach with Rayleigh-Ritz method. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. 2024;30:679–685.
MLA Pany, Chıtaranjan. “Determination of Bounding Frequencies of Cylindrical Shells Using a Periodic Structure Wave Approach With Rayleigh-Ritz Method”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, vol. 30, no. 5, 2024, pp. 679-85.
Vancouver Pany C. Determination of bounding frequencies of cylindrical shells using a periodic structure wave approach with Rayleigh-Ritz method. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. 2024;30(5):679-85.

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