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VIBRATION ANALYSIS OF ROTATING TIMOSHENKO BEAMS WITH DIFFERENT MATERIAL DISTRIBUTION PROPERTIES

Yıl 2019, Cilt: 7 Sayı: 2, 272 - 286, 01.06.2019
https://doi.org/10.15317/Scitech.2019.198

Öz

In
this study, vibration characteristics of functionally graded rotating Timoshenko
beams that undergoes flapwise bending vibration are analysed. Beam models with
different material distribution properties are considered. The energy
expressions are derived by introducing several explanotary figures and tables.
Applying the Hamilton’s Principle to the derived energy expressions, governing
differential equations of motion and the boundary conditions are obtained. Related
formulation is coded by using MATLAB and in the solution part, the equations of
motion, including the parameters for the rotary inertia, shear deformation,
power
law index parameter
and
slenderness ratio are solved using an efficient mathematical technique, called
the differential transform method (DTM).   Natural
frequencies of the modeled beams are obtained. Increasing effects of the
slenderness ratio and the rotational speed and the decreasing effect of the
power-law index on the natural frequencies are investigated. Moreover,
differences between the natural frequencies of the beam models with different
material distribution characteristics is noticed and examined.  Obtained results are distributed in several
tables.

Kaynakça

  • Akash, B. A., Mamlook, R., Mohsen, S. M., 1999, “Multi-criteria selection of electric power plants using analytical hierarchy process”, Electric Power Systems Research, Cilt 52, Sayı 1, ss. 29-35.
  • Alshorbagy AE, Eltaher MA, Mahmoud FF, 2011, Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling, 35, 412–425.
  • Bhimaraddi A, Chandrashekhara K., 1991, Some observation on the modeling of laminated composite beams with general lay-ups, Composite Structures, 19, 371–380.
  • Chakraborty A, Gopalakrishnan S, Reddy JN., 2003, A new beam finite element for the analysis of functionally graded materials, International Journal of Mechanical Sciences, 45, 519–539.
  • Dadfarnia M., 1997, Nonlinear forced vibration of laminated beam with arbitrary lamination, M.Sc. Thesis, Sharif University of Technology.
  • Deng HD and Wei C, 2016, Dynamic characteristics analysis of bi-directional functionally graded Timoshenko beams, Composite Structures, in press.
  • Eringen, AC., 1980, Mechanics of Continua, Robert E. Krieger Publishing Company, Huntington, New York.
  • Giunta G, Crisafulli D, Belouettar S, Carrera E., 2011, Hierarchical theories for the free vibration analysis of functionally graded beams, Composite Structures, 94, 68–74.
  • Hodges, D. H., Dowell, E. H., 1974, Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades, NASA Technical Report,NASA TN D-7818.
  • Huang Y, Li XF., 2010, A new approach for free vibration of axially functionally graded beams with non-uniform cross-section, Journal of Sound and Vibration, 329, 2291–2303.
  • Kapuria S, Bhattacharyya M, Kumar AN., 2008, Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation, Composite Structures, 82, 390–402.
  • Kaya, M.O., Ozdemir Ozgumus, O., 2007, Flexural–torsional-coupled vibration analysis of axially loaded closed-section composite Timoshenko beam by using DTM, Journal of Sound and Vibration, 306, 495–506.
  • Kaya, M.O., Ozdemir Ozgumus, O., 2010, Energy expressions and free vibration analysis of a rotating uniform timoshenko beam featuring bending–torsion coupling, Journal of Vibration and Control, 16(6), 915–934.
  • Kollar, LR., Springer, GS., 2003, Mechanics of Composite Structures. Cambridge University Press, United Kingdom.
  • Lai SK, Harrington J, Xiang Y, Chow KW., 2012, Accurate analytical perturbation approach for large amplitude vibration of functionally graded beams, International Journal of Non-Linear Mechanics, 47, 473–480.
  • Li XF., 2008, A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli Beams, Journal of Sound and Vibration, 318, 1210–1229.
  • Li XF, Kang YA, Wu JX, 2013, Exact frequency equation of free vibration of exponentially funtionally graded beams, Applied Acoustics, 74 (3), 413-420.
  • Loja MAR, Barbosa JI, Mota Soares CM., 2012, A study on the modelling of sandwich functionally graded particulate composite, Composite Structures, 94, 2209–2217.
  • Loy C.T., Lam K.Y., Reddy J.N., 1999, Vibration of functionally graded cylinderical shells, International Journal of Mechanical Science, 41, 309-324.
  • Lu CF, Chen WQ., 2005, Free vibration of orthotropic functionally graded beams with various end conditions, Structural Engineering and Mechanics, 20, 465–476.
  • Ozdemir O., 2016, Application of The Differential Transform Method to The Free Vibration Analysis of Functionally Graded Timoshenko Beams, Journal of Theoretical and Applied Mechanics 54, 4, 1205-1217.
  • Ozdemir Ozgumus, O., Kaya, M.O., 2013, Energy expressions and free vibration analysis of a rotating Timoshenko beam featuring bending–bending-torsion coupling, Archive of Applied Mechanics, 83, 97–108.
  • Sina S.A., Navazi H.M., Haddadpour H., 2009, An analytical method for free vibration analysis of functionally graded beams, Materials and Design, 30, 741–747.
  • Şimsek M., 2010, Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories, Nuclear Engineering and Design, 240, 697–705.
  • Tang AY, Wu JX, Li XF and Lee KY, 2014, Exact frequency equations of free vibration of exponentially non-uniform functionally graded Timoshenko beams, International Journal of Mechanical Sciences, 89, 1-11.
  • Thai HT, Vo TP., 2012, Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories, International Journal of Mechanical Sciences, 62, 57–66.
  • Wang Z., Wang X., Xu G., Cheng S. and Zeng T., 2016, Free vibration of two directional functionally graded beams, Composite Structures, 135, 191-198.
  • Wattanasakulpong N, Prusty BG, Kelly DW, Hoffman M., 2012, Free vibration analysis of layered functionally graded beams with experimental validation, Materials & Design, 36, 182–190.
  • Zhong Z, Yu T., 2007, Analytical solution of a cantilever functionally graded beam, Composites Science and Technology, 67, 481–488.

Fonksiyonel Derecelendirilmiş Dönen Timoshenko Kirişlerin Titreşim Analizi

Yıl 2019, Cilt: 7 Sayı: 2, 272 - 286, 01.06.2019
https://doi.org/10.15317/Scitech.2019.198

Öz

Bu
çalışma kapsamında, düzlem dışı eğilme (flaplama hareketi) deplasmanı altında fonksiyonel
derecelendirilmiş, dönen Timoshenko kirişlerin titreşim analizi yapılmıştır. Farklı
malzeme dağılımlarına sahip kiriş modelleri incelenmiş ve enerji ifadeleri,
çeşitli şekil ve tablolar kullanılarak çıkarılmış ve bu enerji denklemlerine
Hamilton Prensibi uygulanarak hareket denklemleri ve sınır şartları elde
edilmiştir ve ilgili denklemler, MATLAB programında kodlanmıştır. Çözüm
aşamasında; dönme ataleti, kayma etkisi, malzeme dağılımı üstel fonksiyonu, kiriş
narinlik oranı gibi çok çeşitli parametrelerin katıldığı hareket denklemleri ve
sınır şartlarına, etkin ve hızlı bir matematiksel yöntem olan Diferansiyel
Dönüşüm Yöntemi (Differential Transform Method) uygulanmıştır. Modellenen kirişlere
ait doğal frekanslar hesaplanmıştır. Narinlik oranı ve dönme hızının frekanslar
üzerindeki yükseltici etkileri ve malzeme dağılımı ile ilgili olarak güç
indeksinin, frekanslar üzerindeki azaltıcı etkisi incelenmiştir. Ayrıca, farklı
malzeme dağılım karakterlerine sahip kirişlere air frekans değerleri arasındaki
farklar fark edilmiş ve incelenmiştir. Elde edilen sonuçlar, çeşitli tablolarda
sunulmuştur.

Kaynakça

  • Akash, B. A., Mamlook, R., Mohsen, S. M., 1999, “Multi-criteria selection of electric power plants using analytical hierarchy process”, Electric Power Systems Research, Cilt 52, Sayı 1, ss. 29-35.
  • Alshorbagy AE, Eltaher MA, Mahmoud FF, 2011, Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling, 35, 412–425.
  • Bhimaraddi A, Chandrashekhara K., 1991, Some observation on the modeling of laminated composite beams with general lay-ups, Composite Structures, 19, 371–380.
  • Chakraborty A, Gopalakrishnan S, Reddy JN., 2003, A new beam finite element for the analysis of functionally graded materials, International Journal of Mechanical Sciences, 45, 519–539.
  • Dadfarnia M., 1997, Nonlinear forced vibration of laminated beam with arbitrary lamination, M.Sc. Thesis, Sharif University of Technology.
  • Deng HD and Wei C, 2016, Dynamic characteristics analysis of bi-directional functionally graded Timoshenko beams, Composite Structures, in press.
  • Eringen, AC., 1980, Mechanics of Continua, Robert E. Krieger Publishing Company, Huntington, New York.
  • Giunta G, Crisafulli D, Belouettar S, Carrera E., 2011, Hierarchical theories for the free vibration analysis of functionally graded beams, Composite Structures, 94, 68–74.
  • Hodges, D. H., Dowell, E. H., 1974, Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades, NASA Technical Report,NASA TN D-7818.
  • Huang Y, Li XF., 2010, A new approach for free vibration of axially functionally graded beams with non-uniform cross-section, Journal of Sound and Vibration, 329, 2291–2303.
  • Kapuria S, Bhattacharyya M, Kumar AN., 2008, Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation, Composite Structures, 82, 390–402.
  • Kaya, M.O., Ozdemir Ozgumus, O., 2007, Flexural–torsional-coupled vibration analysis of axially loaded closed-section composite Timoshenko beam by using DTM, Journal of Sound and Vibration, 306, 495–506.
  • Kaya, M.O., Ozdemir Ozgumus, O., 2010, Energy expressions and free vibration analysis of a rotating uniform timoshenko beam featuring bending–torsion coupling, Journal of Vibration and Control, 16(6), 915–934.
  • Kollar, LR., Springer, GS., 2003, Mechanics of Composite Structures. Cambridge University Press, United Kingdom.
  • Lai SK, Harrington J, Xiang Y, Chow KW., 2012, Accurate analytical perturbation approach for large amplitude vibration of functionally graded beams, International Journal of Non-Linear Mechanics, 47, 473–480.
  • Li XF., 2008, A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli Beams, Journal of Sound and Vibration, 318, 1210–1229.
  • Li XF, Kang YA, Wu JX, 2013, Exact frequency equation of free vibration of exponentially funtionally graded beams, Applied Acoustics, 74 (3), 413-420.
  • Loja MAR, Barbosa JI, Mota Soares CM., 2012, A study on the modelling of sandwich functionally graded particulate composite, Composite Structures, 94, 2209–2217.
  • Loy C.T., Lam K.Y., Reddy J.N., 1999, Vibration of functionally graded cylinderical shells, International Journal of Mechanical Science, 41, 309-324.
  • Lu CF, Chen WQ., 2005, Free vibration of orthotropic functionally graded beams with various end conditions, Structural Engineering and Mechanics, 20, 465–476.
  • Ozdemir O., 2016, Application of The Differential Transform Method to The Free Vibration Analysis of Functionally Graded Timoshenko Beams, Journal of Theoretical and Applied Mechanics 54, 4, 1205-1217.
  • Ozdemir Ozgumus, O., Kaya, M.O., 2013, Energy expressions and free vibration analysis of a rotating Timoshenko beam featuring bending–bending-torsion coupling, Archive of Applied Mechanics, 83, 97–108.
  • Sina S.A., Navazi H.M., Haddadpour H., 2009, An analytical method for free vibration analysis of functionally graded beams, Materials and Design, 30, 741–747.
  • Şimsek M., 2010, Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories, Nuclear Engineering and Design, 240, 697–705.
  • Tang AY, Wu JX, Li XF and Lee KY, 2014, Exact frequency equations of free vibration of exponentially non-uniform functionally graded Timoshenko beams, International Journal of Mechanical Sciences, 89, 1-11.
  • Thai HT, Vo TP., 2012, Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories, International Journal of Mechanical Sciences, 62, 57–66.
  • Wang Z., Wang X., Xu G., Cheng S. and Zeng T., 2016, Free vibration of two directional functionally graded beams, Composite Structures, 135, 191-198.
  • Wattanasakulpong N, Prusty BG, Kelly DW, Hoffman M., 2012, Free vibration analysis of layered functionally graded beams with experimental validation, Materials & Design, 36, 182–190.
  • Zhong Z, Yu T., 2007, Analytical solution of a cantilever functionally graded beam, Composites Science and Technology, 67, 481–488.
Toplam 29 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Özge Özdemir

Yayımlanma Tarihi 1 Haziran 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 7 Sayı: 2

Kaynak Göster

APA Özdemir, Ö. (2019). VIBRATION ANALYSIS OF ROTATING TIMOSHENKO BEAMS WITH DIFFERENT MATERIAL DISTRIBUTION PROPERTIES. Selçuk Üniversitesi Mühendislik, Bilim Ve Teknoloji Dergisi, 7(2), 272-286. https://doi.org/10.15317/Scitech.2019.198
AMA Özdemir Ö. VIBRATION ANALYSIS OF ROTATING TIMOSHENKO BEAMS WITH DIFFERENT MATERIAL DISTRIBUTION PROPERTIES. sujest. Haziran 2019;7(2):272-286. doi:10.15317/Scitech.2019.198
Chicago Özdemir, Özge. “VIBRATION ANALYSIS OF ROTATING TIMOSHENKO BEAMS WITH DIFFERENT MATERIAL DISTRIBUTION PROPERTIES”. Selçuk Üniversitesi Mühendislik, Bilim Ve Teknoloji Dergisi 7, sy. 2 (Haziran 2019): 272-86. https://doi.org/10.15317/Scitech.2019.198.
EndNote Özdemir Ö (01 Haziran 2019) VIBRATION ANALYSIS OF ROTATING TIMOSHENKO BEAMS WITH DIFFERENT MATERIAL DISTRIBUTION PROPERTIES. Selçuk Üniversitesi Mühendislik, Bilim Ve Teknoloji Dergisi 7 2 272–286.
IEEE Ö. Özdemir, “VIBRATION ANALYSIS OF ROTATING TIMOSHENKO BEAMS WITH DIFFERENT MATERIAL DISTRIBUTION PROPERTIES”, sujest, c. 7, sy. 2, ss. 272–286, 2019, doi: 10.15317/Scitech.2019.198.
ISNAD Özdemir, Özge. “VIBRATION ANALYSIS OF ROTATING TIMOSHENKO BEAMS WITH DIFFERENT MATERIAL DISTRIBUTION PROPERTIES”. Selçuk Üniversitesi Mühendislik, Bilim Ve Teknoloji Dergisi 7/2 (Haziran 2019), 272-286. https://doi.org/10.15317/Scitech.2019.198.
JAMA Özdemir Ö. VIBRATION ANALYSIS OF ROTATING TIMOSHENKO BEAMS WITH DIFFERENT MATERIAL DISTRIBUTION PROPERTIES. sujest. 2019;7:272–286.
MLA Özdemir, Özge. “VIBRATION ANALYSIS OF ROTATING TIMOSHENKO BEAMS WITH DIFFERENT MATERIAL DISTRIBUTION PROPERTIES”. Selçuk Üniversitesi Mühendislik, Bilim Ve Teknoloji Dergisi, c. 7, sy. 2, 2019, ss. 272-86, doi:10.15317/Scitech.2019.198.
Vancouver Özdemir Ö. VIBRATION ANALYSIS OF ROTATING TIMOSHENKO BEAMS WITH DIFFERENT MATERIAL DISTRIBUTION PROPERTIES. sujest. 2019;7(2):272-86.

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