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Çatlak İçeren Bir Çerçeve Taşıyıcı Sistemin Zorlanmış Titreşim Analizi

Year 2020, Volume: 23 Issue: 4, 1059 - 1071, 01.12.2020
https://doi.org/10.2339/politeknik.606499

Abstract

Bu çalışmada,
kenarında çatlaklar bulunan tek açıklıklı bir çerçeve taşıyıcının sönümsüz ve
sönümlü zorlanmış titreşim cevapları incelenmiştir. Çatlaklı çerçevenin
titreşim analizleri, Euler-Bernoulli çubuk teorisi çerçevesinde incelenmiştir.
Çatlak etkisinden dolayı ortaya çıkan yerel esneklik, çatlak kesiti veya bölgesinde,
kütlesiz ve boyutsuz bir çubuk sonlu eleman ile modellenmiştir. Çatlaktan
dolayı ortaya çıkan yerel esneklik, lineer elastik kırılma mekaniği teorisi baz
alınarak açılma modu (Mod1) ile düzlem içi kayma modu (Mod2) kullanılmasıyla
birlikte elde edilen gerilme yığılma faktörü ve şekil değiştirme enerjisi
salıverininim oranlarına bağlı olarak elde edilmiştir. Çatlak esnekliğinin
tersi alınarak elde edilen çatlak rijitliğinin sonlu elemanlar modeline
eklenmesiyle birlikte birleştirilmiş sonlu elemanlar formülasyonları elde
edilmiştir.



 



Zorlanmış
titreşim çözümlerinde zaman tanım aralığında doğrudan integrasyon
yöntemlerinden biri olan merkezi farklar yöntemi kullanılmıştır. Çalışmada
farklı değerlerdeki çatlak derinliğinin, farklı çatlak konumunun ve farklı
değerlerdeki çerçeve yapının geometrik boyutlarına bağlı olarak dinamik
cevaplar elde edilmiş ve yorumlanmıştır. Elde edilen formülasyon ve sonuçların
doğruluğu için, literatürdeki benzer çalışmaların özel sonuçları ile kıyaslama
çalışmaları yapılmıştır.

Supporting Institution

Bursa Teknik Üniversitesi BAP Koordinatörlüğünce

Project Number

172L06

Thanks

Bu çalışma Bursa Teknik Üniversitesi BAP Koordinatörlüğünce desteklenmiştir. Proje Numarası: 172L06.

References

  • [1] Tharp T.M., "A Finite Element for Edge‐Cracked Beam Columns", International Journal for Numerical Methods in Engineering, 24: 1941-1950, (1987).
  • [2] Ostachowicz W.M. and Krawczuk M., "Vibration Analysis of a Cracked Beam", Computers & Structures, 36: 245-250, (1990).
  • [3] Shen M. H. and Pierre C., "Free Vibrations of Veams with a Single-Edge Crack", Journal of Sound and Vibration, 170: 237-259, (1994).
  • [4] Nikolakopoulos P.G., Katsareas D.E. and Papadopoulos C.A., "Crack Identification in Frame Structures", Computers & structures, 64: 389-406, (1997).
  • [5] Krawczuk M., Ostachowicz W. and Zak A., "Dynamics of Cracked Composite Material Structures", Computational Mechanics, 20: 79-83, (1997).
  • [6] Yokoyama T. and Chen M. C., "Vibration Analysis of Edge-Cracked Beams Using a Line-Spring Model", Engineering Fracture Mechanics, 59: 403-409, (1998).
  • [7] Saavedra P.N. and Cuitino L.A., "Crack Detection and Vibration Behavior of Cracked Beams", Computers & Structures, 79:1451-1459, (2001).
  • [8] Kuntiyawichai K. and Burdekin F.M., "Engineering Assessment of Cracked Structures Subjected to Dynamic Loads Using Fracture Mechanics Assessment", Engineering Fracture Mechanics, 70:1991-2014, (2003).
  • [9] Zheng D.Y. and Kessissoglou N. J., "Free Vibration Analysis of a Cracked Beam by Finite Element Method", Journal of Sound and vibration, 273:457-475, (2004).
  • [10] Gürel M.A. and Kısa M., "Buckling of Slender Prismatic Columns with a Single Edge Crack Under Concentric Vertical Loads", Turkish Journal of Engineering and Environmental Sciences, 29:185- 193, (2005).
  • [11] Gürel M. A., "Buckling of Slender Prismatic Circular Columns Weakened by Multiple Edge Cracks", Acta Mechanica, 188:1-19, (2007).
  • [12] Caddemi S. and Caliò' I., “Exact Solution of the Multi-Cracked Euler- Bernoulli Column”, International Journal of Solids and Structures,45:1332-1351, (2008).
  • [13] Caddemi S., Caliò' I. and Cannizzaro F., “The Influence of Multiple Cracks on Tensile and Compressive Buckling of Shear Deformable Beams”, International Journal of Solids and Structures, 50:3166-3183, (2013).
  • [14] Challamel N. and Xiang Y., "On the Influence of the Unilateral Damage Behaviour in the Stability of Cracked Beam/Columns", Engineering Fracture Mechanics, 77:1467-1478, (2010).
  • [15] Ibrahem A.M., Öztürk H. And Sabuncu M., "Vibration Analysis of Cracked Frame Structures", Structural Engineering and Mechanics, 45: 33-52, (2013).
  • [16] Chatterjee A., "Nonlinear Dynamics and Damage Assessment of a Cantilever Beam with Breathing Edge Crack", Journal of Vibration and Acoustics, 133: 051004, (2011).
  • [17] Akbaş Ş.D., "Free Vibration Characteristics of Edge Cracked Functionally Graded Beams by Using Finite Element Method", International Journal of Engineering Trends and Technology, 4:4590-4597, (2013).
  • [18] Labib A., Kennedy D. and Featherston C., "Free Vibration Analysis of Beams and Frames with Multiple Cracks for Damage Detection", Journal of Sound and Vibration, 333: 4991-5003, (2014).
  • [19] Akbaş Ş.D., "Wave Propagation Analysis of Edge Cracked Circular Beams under Impact Force", Plos One, 9: 1-8, (2014).
  • [20] Akbaş Ş.D., "Wave Propagation in Edge Cracked Functionally Graded Beams Under Impact Force", Journal of Vibration and Control, 22: 2443-2457, (2014).
  • [21] Öztürk H., Yashar A. and Sabuncu M., "Dynamic Stability of Cracked Multi-Bay Frame Structures", Mechanics of Advanced Materials and Structures, 23:715-726, (2016).
  • [22] Tan G., Liu Z., Shan J. and Wu C., "Direct and Inverse Problems on Free Vibration Analysis of Cracked Non-Uniform Beams Carrying Spring-Mass Systems by Finite Element Method", Journal of Vibroengineering, 14:7-12, (2017).

Forced Vibration Analysis of a Cracked Frame

Year 2020, Volume: 23 Issue: 4, 1059 - 1071, 01.12.2020
https://doi.org/10.2339/politeknik.606499

Abstract

In this study, undamped and damped forced vibration responses of a
single span frame with cracks are investigated. The vibration analysis of the
cracked frame is examined by using the Euler -Bernoulli beam theory. The local
flexibility resulting from the crack effect is modeled with a massless and
dimensionless finite element beam in the crack section. The local flexibility
is obtained by using the stress intensity factor and strain energy release
rates according to the opening mode (Mode 1) and the in-plane shear mode (Mode
2) based on the linear elastic fracture mechanics theory. The crack stiffness
is obtained by taking the inverse of the flexibility of the crack. Assembly of
global finite element matrices are obtained by adding the crack stiffness to the
finite element model.

 





In solution of the forced vibration problem, the central difference
method is used in the time history. In the numerical results, the effects of
the crack depth, the crack location and dimension of the frame on the undamped
and damped forced vibration responses of the cracked frame are investigated.
Also, the validation studies are performed in order to accuracy of the
presented method.

Project Number

172L06

References

  • [1] Tharp T.M., "A Finite Element for Edge‐Cracked Beam Columns", International Journal for Numerical Methods in Engineering, 24: 1941-1950, (1987).
  • [2] Ostachowicz W.M. and Krawczuk M., "Vibration Analysis of a Cracked Beam", Computers & Structures, 36: 245-250, (1990).
  • [3] Shen M. H. and Pierre C., "Free Vibrations of Veams with a Single-Edge Crack", Journal of Sound and Vibration, 170: 237-259, (1994).
  • [4] Nikolakopoulos P.G., Katsareas D.E. and Papadopoulos C.A., "Crack Identification in Frame Structures", Computers & structures, 64: 389-406, (1997).
  • [5] Krawczuk M., Ostachowicz W. and Zak A., "Dynamics of Cracked Composite Material Structures", Computational Mechanics, 20: 79-83, (1997).
  • [6] Yokoyama T. and Chen M. C., "Vibration Analysis of Edge-Cracked Beams Using a Line-Spring Model", Engineering Fracture Mechanics, 59: 403-409, (1998).
  • [7] Saavedra P.N. and Cuitino L.A., "Crack Detection and Vibration Behavior of Cracked Beams", Computers & Structures, 79:1451-1459, (2001).
  • [8] Kuntiyawichai K. and Burdekin F.M., "Engineering Assessment of Cracked Structures Subjected to Dynamic Loads Using Fracture Mechanics Assessment", Engineering Fracture Mechanics, 70:1991-2014, (2003).
  • [9] Zheng D.Y. and Kessissoglou N. J., "Free Vibration Analysis of a Cracked Beam by Finite Element Method", Journal of Sound and vibration, 273:457-475, (2004).
  • [10] Gürel M.A. and Kısa M., "Buckling of Slender Prismatic Columns with a Single Edge Crack Under Concentric Vertical Loads", Turkish Journal of Engineering and Environmental Sciences, 29:185- 193, (2005).
  • [11] Gürel M. A., "Buckling of Slender Prismatic Circular Columns Weakened by Multiple Edge Cracks", Acta Mechanica, 188:1-19, (2007).
  • [12] Caddemi S. and Caliò' I., “Exact Solution of the Multi-Cracked Euler- Bernoulli Column”, International Journal of Solids and Structures,45:1332-1351, (2008).
  • [13] Caddemi S., Caliò' I. and Cannizzaro F., “The Influence of Multiple Cracks on Tensile and Compressive Buckling of Shear Deformable Beams”, International Journal of Solids and Structures, 50:3166-3183, (2013).
  • [14] Challamel N. and Xiang Y., "On the Influence of the Unilateral Damage Behaviour in the Stability of Cracked Beam/Columns", Engineering Fracture Mechanics, 77:1467-1478, (2010).
  • [15] Ibrahem A.M., Öztürk H. And Sabuncu M., "Vibration Analysis of Cracked Frame Structures", Structural Engineering and Mechanics, 45: 33-52, (2013).
  • [16] Chatterjee A., "Nonlinear Dynamics and Damage Assessment of a Cantilever Beam with Breathing Edge Crack", Journal of Vibration and Acoustics, 133: 051004, (2011).
  • [17] Akbaş Ş.D., "Free Vibration Characteristics of Edge Cracked Functionally Graded Beams by Using Finite Element Method", International Journal of Engineering Trends and Technology, 4:4590-4597, (2013).
  • [18] Labib A., Kennedy D. and Featherston C., "Free Vibration Analysis of Beams and Frames with Multiple Cracks for Damage Detection", Journal of Sound and Vibration, 333: 4991-5003, (2014).
  • [19] Akbaş Ş.D., "Wave Propagation Analysis of Edge Cracked Circular Beams under Impact Force", Plos One, 9: 1-8, (2014).
  • [20] Akbaş Ş.D., "Wave Propagation in Edge Cracked Functionally Graded Beams Under Impact Force", Journal of Vibration and Control, 22: 2443-2457, (2014).
  • [21] Öztürk H., Yashar A. and Sabuncu M., "Dynamic Stability of Cracked Multi-Bay Frame Structures", Mechanics of Advanced Materials and Structures, 23:715-726, (2016).
  • [22] Tan G., Liu Z., Shan J. and Wu C., "Direct and Inverse Problems on Free Vibration Analysis of Cracked Non-Uniform Beams Carrying Spring-Mass Systems by Finite Element Method", Journal of Vibroengineering, 14:7-12, (2017).
There are 22 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Research Article
Authors

Kemal Koçyiğit 0000-0001-5430-0701

Şeref Doğuşcan Akbaş 0000-0001-5327-3406

Project Number 172L06
Publication Date December 1, 2020
Submission Date August 19, 2019
Published in Issue Year 2020 Volume: 23 Issue: 4

Cite

APA Koçyiğit, K., & Akbaş, Ş. D. (2020). Çatlak İçeren Bir Çerçeve Taşıyıcı Sistemin Zorlanmış Titreşim Analizi. Politeknik Dergisi, 23(4), 1059-1071. https://doi.org/10.2339/politeknik.606499
AMA Koçyiğit K, Akbaş ŞD. Çatlak İçeren Bir Çerçeve Taşıyıcı Sistemin Zorlanmış Titreşim Analizi. Politeknik Dergisi. December 2020;23(4):1059-1071. doi:10.2339/politeknik.606499
Chicago Koçyiğit, Kemal, and Şeref Doğuşcan Akbaş. “Çatlak İçeren Bir Çerçeve Taşıyıcı Sistemin Zorlanmış Titreşim Analizi”. Politeknik Dergisi 23, no. 4 (December 2020): 1059-71. https://doi.org/10.2339/politeknik.606499.
EndNote Koçyiğit K, Akbaş ŞD (December 1, 2020) Çatlak İçeren Bir Çerçeve Taşıyıcı Sistemin Zorlanmış Titreşim Analizi. Politeknik Dergisi 23 4 1059–1071.
IEEE K. Koçyiğit and Ş. D. Akbaş, “Çatlak İçeren Bir Çerçeve Taşıyıcı Sistemin Zorlanmış Titreşim Analizi”, Politeknik Dergisi, vol. 23, no. 4, pp. 1059–1071, 2020, doi: 10.2339/politeknik.606499.
ISNAD Koçyiğit, Kemal - Akbaş, Şeref Doğuşcan. “Çatlak İçeren Bir Çerçeve Taşıyıcı Sistemin Zorlanmış Titreşim Analizi”. Politeknik Dergisi 23/4 (December 2020), 1059-1071. https://doi.org/10.2339/politeknik.606499.
JAMA Koçyiğit K, Akbaş ŞD. Çatlak İçeren Bir Çerçeve Taşıyıcı Sistemin Zorlanmış Titreşim Analizi. Politeknik Dergisi. 2020;23:1059–1071.
MLA Koçyiğit, Kemal and Şeref Doğuşcan Akbaş. “Çatlak İçeren Bir Çerçeve Taşıyıcı Sistemin Zorlanmış Titreşim Analizi”. Politeknik Dergisi, vol. 23, no. 4, 2020, pp. 1059-71, doi:10.2339/politeknik.606499.
Vancouver Koçyiğit K, Akbaş ŞD. Çatlak İçeren Bir Çerçeve Taşıyıcı Sistemin Zorlanmış Titreşim Analizi. Politeknik Dergisi. 2020;23(4):1059-71.