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WİNKLER ZEMİN VE FONKSİYONEL DERECELENDİRİLMİŞ MALZEME ÖZELLİKLERİNİN KİRİŞİN FREKANS PARAMETRELERİNE ETKİLERİNİN İNCELENMESİ

Year 2017, Volume: 5 Issue: 3, 573 - 580, 19.12.2017
https://doi.org/10.21923/jesd.348875

Abstract



Bu
çalışmada, Winkler zemine oturan Fonksiyonel Derecelendirilmiş Malzemelerden
(FDM) oluşan kirişin serbest titreşimi incelenmiştir.  FDM’nin özelliklerinin kiriş kalınlığı
doğrultusunda kuvvet kuralına göre değiştiği varsayılmıştır. Bu amaçla, ilk
olarak Bernoulli-Euler kiriş teorisi çerçevesinde, Winkler zemine oturan FD
kirişin yönetici denklemi türetilmiştir. Yönetici denklem ankastre-basit
mesnetli sınır koşulu altında değişkenlerine ayrılarak çözülmüştür. Ayrıca,
ilgili sınır koşulu için ilk üç moda ait öz değerler Newton-Raphson yöntemi
uygulanarak elde edilmiştir. Daha sonra serbest boyutsuz frekans parametre değerleri
hesaplanmış ve bu değerlere malzeme özelliklerinin değişiminin ve Winkler
zeminin etkileri incelenmiştir. Ayrıca, elde edilen sonuçların doğruluğunu
göstermek için bir karşılaştırma çalışması yapılmıştır.


References

  • Akgöz, B., Civalek, Ö., 2013. Longitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM). Composites Part B: Engineering, 55, 263-268.
  • Avcar, M., 2010. Elastik zemin üzerinde bulunan her iki ucu ankastre mesnetli rastgele ve sürekli homojen olmayan kirişin serbest titreşimi. Süleyman Demirel Üniversitesi Mühendislik Bilimleri ve Tasarım Dergisi, 1, 33-38, (2010).
  • Çalım, F.F., Akkurt, F.G., 2011. Static and free vibration analysis of straight and circular beams on elastic foundation. Mechanics Research Communications, 38, 89-94.
  • Chakraverty, S., Pradhan, KK., 2016. Vibration of Functionally Graded Beams and Plates. Academic Press.
  • Civalek, Ö., Demir, Ç, 2009. Elastik zemine oturan kirişlerin ayrik tekil konvolüsyon ve harmonik diferansiyel quadrature yöntemleriyle analizi. Balıkesir Üniversitesi ,Fen Bilimleri Dergisi, 11, 56-71.
  • Coşkun, I., 2000. Non-linear vibrations of a beam resting on a tensionless Winkler foundation. Journal of Sound and Vibration, 236, 401-411.
  • Dimitoka, K., Yıldırım, B. 2003. Katmanlı ve Fonksiyonel Derecelendirilmiş Malzemelerden Yapılmış Termal Bariyer Kaplamalardaki Termal Gerilimlerin Sonlu Elemanlar Metodu ile Hesaplanması. Mühendis ve Makina, 525, 34-42.
  • Eisenberger, M., Clastornik, J., 1987. Vibration and buckling of beam on a variable Winkler elastic foundation. Journal of Sound and Vibration, 115: 233- 241.
  • Filonenko-Borodich, M.M., 1940. Some Approximate Theories of the Elastic Foundation. Uchenyie Zapiski Moskovskogo Gosudarstvennogo Universiteta, 46, 3-18.
  • Hetenyi, M., 1946. Beams on Elastic Foundation., The University of Michigan Press.
  • Issa, M.S., 1988. Natural frequencies of continuous curved beams on Winkler-type foundation. Journal of Sound and Vibration, 127, 291-301.
  • Kerr, A.D., 1964. Elastic and viscoelastic foundation models. Journal of Applied Mechanics, 31, 3491–3498.
  • Koizumi, M., 1993. The Concept of FGM. Ceramic transactions, Functionally Gradient Materials, 34, 3–10.
  • Obara, P., 2014. Vibrations and stability of Bernoulli-Euler and Timoshenko beams on two-parameter elastic foundation. Archives of Civil Engineering 60,421-440.
  • Ozturk, B., Coskun, S.B, 2013. Analytical solution for free vibration analysis of beam on elastic foundation with different support conditions. Mathematical Problems in Engineering, Article ID 470927.
  • Rao, S.S.. 2007. Vibration of Continuous Systems. John Wiley and Sons Ltd.
  • Ruge, P., Birk, C. (2007). A comparison of infinite Timoshenko and Euler–Bernoulli beam models on Winkler foundation in the frequency-and time-domain. Journal of Sound and Vibration, 304(3), 932-947.
  • Selvadurai, A.P.S., 1979. Elastic Analysis of Soil–Foundation Interaction. Amsterdam: Elsevier.
  • Suresh, S., Mortensen, A., 1998. Fundamentals of Functionally Graded Materials. IOM Communications, London.
  • Teodoru, I. B., Musat, V., 2008. Beam elements on linear variable two-parameter elastic foundation. Buletinul Institutului Politehnic din lasi. Sectia Constructii, Arhitectura, 5, 69-78.
  • Wakashima K., Hirano T., Niino M. ,1990. Space applications of advanced structural materials. ESA SP303-97.
  • Winkler, E., 1867. Die Lehre Vonder Elastizitat und Festigkeit, Prag
  • Yanık, F. ve Yaylı M.O., 2015. Rijit olmayan sinir koşullarinda elastik zemine oturan bir çubuğun eksenel titreşim analizi. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 2, 35-44.
  • Zhou, D., 1993. A general solution to vibrations of beams on variable Winkler elastic foundation. Computers & structures, 47, 83-90.

EXAMINATION OF THE EFFECTS OF WINKLER FOUNDATION AND FUNCTIONALLY GRADED MATERIAL PROPERTIES ON THE FREQUENCY PARAMETERS OF BEAM

Year 2017, Volume: 5 Issue: 3, 573 - 580, 19.12.2017
https://doi.org/10.21923/jesd.348875

Abstract











In
the present study, free vibration of the beam composed of functionally graded
materials (FGM) resting on Winkler foundation is investigated. The material
properties are assumed to vary continuously through the thickness direction. The
governing equation of the free vibration of the FG beam resting on Winkler
foundation is derived in the framework of Bernoulli-Euler beam theory. The governing
equation is solved using separation of variables. The eigenvalues of the first
three modes for clamped-simply supported boundary conditions are found
employing Newton-Raphson Method. The effects of the Winkler foundation and varying
material properties on the values of dimensionless frequency parameters are examined.
Furthermore, to show the accuracy of the present results, a comparison study is
performed.
    

References

  • Akgöz, B., Civalek, Ö., 2013. Longitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM). Composites Part B: Engineering, 55, 263-268.
  • Avcar, M., 2010. Elastik zemin üzerinde bulunan her iki ucu ankastre mesnetli rastgele ve sürekli homojen olmayan kirişin serbest titreşimi. Süleyman Demirel Üniversitesi Mühendislik Bilimleri ve Tasarım Dergisi, 1, 33-38, (2010).
  • Çalım, F.F., Akkurt, F.G., 2011. Static and free vibration analysis of straight and circular beams on elastic foundation. Mechanics Research Communications, 38, 89-94.
  • Chakraverty, S., Pradhan, KK., 2016. Vibration of Functionally Graded Beams and Plates. Academic Press.
  • Civalek, Ö., Demir, Ç, 2009. Elastik zemine oturan kirişlerin ayrik tekil konvolüsyon ve harmonik diferansiyel quadrature yöntemleriyle analizi. Balıkesir Üniversitesi ,Fen Bilimleri Dergisi, 11, 56-71.
  • Coşkun, I., 2000. Non-linear vibrations of a beam resting on a tensionless Winkler foundation. Journal of Sound and Vibration, 236, 401-411.
  • Dimitoka, K., Yıldırım, B. 2003. Katmanlı ve Fonksiyonel Derecelendirilmiş Malzemelerden Yapılmış Termal Bariyer Kaplamalardaki Termal Gerilimlerin Sonlu Elemanlar Metodu ile Hesaplanması. Mühendis ve Makina, 525, 34-42.
  • Eisenberger, M., Clastornik, J., 1987. Vibration and buckling of beam on a variable Winkler elastic foundation. Journal of Sound and Vibration, 115: 233- 241.
  • Filonenko-Borodich, M.M., 1940. Some Approximate Theories of the Elastic Foundation. Uchenyie Zapiski Moskovskogo Gosudarstvennogo Universiteta, 46, 3-18.
  • Hetenyi, M., 1946. Beams on Elastic Foundation., The University of Michigan Press.
  • Issa, M.S., 1988. Natural frequencies of continuous curved beams on Winkler-type foundation. Journal of Sound and Vibration, 127, 291-301.
  • Kerr, A.D., 1964. Elastic and viscoelastic foundation models. Journal of Applied Mechanics, 31, 3491–3498.
  • Koizumi, M., 1993. The Concept of FGM. Ceramic transactions, Functionally Gradient Materials, 34, 3–10.
  • Obara, P., 2014. Vibrations and stability of Bernoulli-Euler and Timoshenko beams on two-parameter elastic foundation. Archives of Civil Engineering 60,421-440.
  • Ozturk, B., Coskun, S.B, 2013. Analytical solution for free vibration analysis of beam on elastic foundation with different support conditions. Mathematical Problems in Engineering, Article ID 470927.
  • Rao, S.S.. 2007. Vibration of Continuous Systems. John Wiley and Sons Ltd.
  • Ruge, P., Birk, C. (2007). A comparison of infinite Timoshenko and Euler–Bernoulli beam models on Winkler foundation in the frequency-and time-domain. Journal of Sound and Vibration, 304(3), 932-947.
  • Selvadurai, A.P.S., 1979. Elastic Analysis of Soil–Foundation Interaction. Amsterdam: Elsevier.
  • Suresh, S., Mortensen, A., 1998. Fundamentals of Functionally Graded Materials. IOM Communications, London.
  • Teodoru, I. B., Musat, V., 2008. Beam elements on linear variable two-parameter elastic foundation. Buletinul Institutului Politehnic din lasi. Sectia Constructii, Arhitectura, 5, 69-78.
  • Wakashima K., Hirano T., Niino M. ,1990. Space applications of advanced structural materials. ESA SP303-97.
  • Winkler, E., 1867. Die Lehre Vonder Elastizitat und Festigkeit, Prag
  • Yanık, F. ve Yaylı M.O., 2015. Rijit olmayan sinir koşullarinda elastik zemine oturan bir çubuğun eksenel titreşim analizi. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 2, 35-44.
  • Zhou, D., 1993. A general solution to vibrations of beams on variable Winkler elastic foundation. Computers & structures, 47, 83-90.
There are 24 citations in total.

Details

Subjects Engineering
Journal Section Research Articles
Authors

MEHMET Avcar 0000-0002-0689-0601

Waleed Khalid Mohammed Mohammed This is me

Publication Date December 19, 2017
Submission Date November 2, 2017
Acceptance Date November 30, 2017
Published in Issue Year 2017 Volume: 5 Issue: 3

Cite

APA Avcar, M., & Mohammed, W. K. M. (2017). WİNKLER ZEMİN VE FONKSİYONEL DERECELENDİRİLMİŞ MALZEME ÖZELLİKLERİNİN KİRİŞİN FREKANS PARAMETRELERİNE ETKİLERİNİN İNCELENMESİ. Mühendislik Bilimleri Ve Tasarım Dergisi, 5(3), 573-580. https://doi.org/10.21923/jesd.348875