BibTex RIS Kaynak Göster

Yerel olmayan elastisite teorisine göre akışkan taşıyan nanokirişin serbest titreşimlerinin analizi

Yıl 2017, Cilt: 23 Sayı: 1, 6 - 11, 01.03.2017

Öz

Bu
çalışmada, basit-basit ve ankastre-ankastre sınır şartları altında akışkan
taşıyan nanokirişin doğrusal titreşimleri incelenmiştir. Eringen’in yerel
olmayan elastisite teorisi Euler-Bernoulli kiriş modeline uygulanmıştır. Yerel
olmayan elastisite teorisi MEMS ve NEMS yapıların mekaniksel analizinde gelişen
popüler bir tekniktir. Hareket denklemlerini ve sınır şartlarını elde etmek
için Hamilton prensibi kullanılmıştır. Denklemler boyutsuz formda elde
edilmiştir. Elde edilen hareket denklemi ve sınır şartları malzeme ve geometrik
yapıdan bağımsız hale getirilmiştir. Akışkan hızının, ortalama sabit bir hız
etrafında harmonik olarak değiştiği kabul edilmiştir. Perturbasyon
metotlarından biri olan çok zaman ölçekli metot kullanılarak yaklaşık çözümler
elde edilmiştir. Perturbasyon serisindeki ilk terim doğrusal problemi
oluşturmaktadır. Doğrusal problemin çözümü ile tabii frekanslar ve mod yapıları
farklı sınır şartları için hesaplanmıştır. Her iki mesnet durumu için yerel
olmayan parametre




















 ve akışkan hızı

 artığında tabii frekanslar azalmaktadır.
Sonuçlar grafiklerle sunulmuş ve yorumlanmıştır.

Kaynakça

  • Eringen AC. “On differential-equations of nonlocal elasticity and solutions of screw dislocation and surface waves”. Journal of Applied Physics, 54(9), 4703-4710, 1983.
  • Yoon J, Ru CQ, Mioduchowski A. “Vibration and instability of carbon nanotubes conveying fluid”. Composites Science and Technology, 65(9), 1326-1336, 2005.
  • Reddy CD, Lu C, Rajendran S, and Liew KM. “Free vibration analysis of fluid-conveying single-walled carbon nanotubes”. Applied Physics Letters, 90, 133122, 2007.
  • Lin W, Qiao N. “On vibration and instability of carbon nanotubes conveying fluid”. Computational Materials Science, 43(2), 399-402, 2008.
  • Khosravian N, Tabar HR. “Computational modelling of a non-viscous fluid flow in a multi-walled carbon nanotube modelled as a Timoshenko beam”. Nanotechnology, 19(27), 275703, 2008.
  • Chang WJ, Lee HL. “Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model”. Physics Letters: A, 373(10), 982-985, 2009.
  • Peddieson J, Buchanan GR, McNitt RP. “Application of nonlocal continuum models to nanotechnology”. International Journal of Engineering Science, 41(3-5), 305-312, 2003.
  • Lee HL, Chang WJ. “Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory”. Journal of Applied Physics, 103 (024302), 1-4, 2008.
  • Deng Q, Yang Z. “Vibration of fluid-filled multi-walled carbon nanotubes seen via nonlocal elasticity theory”. Acta Mechanica Solida Sinica, 27(6), 568-578, 2014.
  • Wang L. “Vibration and instability analysis of tubular nano and micro-beams conveying fluid using nonlocal elasticity theory”. Physica E: Low-dimensional Systems and Nanostructures, 41(10), 1835-1840, 2009.
  • Wang L. “Dynamical behaviors of double-walled carbon nanotubes conveying fluid accounting for the role of small scale effect”. Computational Materials Science, 45(2), 584-588, 2009.
  • Wang L. “Vibration analysis of fluid-conveying nanotubes with consideration of surface effects”. Physica E: Lowdimensional Systems and Nanostructures, 43(1), 437-439, 2010.
  • Wang L. “A modified nonlocal beam model for vibration and stability of nanotubes conveying fluid”. Physica E: Lowdimensional Systems and Nanostructures, 44(1),25-28, 2011.
  • Xia W, Wang L. “Vibration characteristics of fluid-conveying carbon nanotubes with curved longitudinal shape”. Computational Materials Science, 49(1), 99-103, 2010.
  • Kiani, K. “Vibration behavior of simply supported inclined single-walled carbon nanotubes conveying viscous fluids flow using nonlocal Rayleigh beam model”. Applied Mathematical Modelling, 37(4), 1836-1850, 2013.
  • Zhen Y, Fang B. “Thermal-mechanical and nonlocal elastic vibration of single-walled carbon nanotubes conveying fluid”. Computational Materials Science, 49(2), 276-282, 2010.
  • Afkhami Z, Farid M. “Thermal-mechanical vibration and instability of carbon nanocones conveying fluid using nonlocal Timoshenko beam model”. Journal of Vibration and Control, 20, 1-15, 2014.
  • Atabakhshian V, Shooshtari A, Karimi M. “Electro-thermal vibration of a smart coupled nanobeam system with an internal flow based on nonlocal elasticity theory”. Physica B: Condensed Matter, 456, 375-382, 2015.
  • Ghavanloo E, Fazelzadeh SA. “Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid”. Physica E: low-dimensional Systems and Nanostructures, 44(1), 17-24, 2011.
  • Bağdatlı SM. “Nonlinear vibration of nanobeams with various boundary condition based on nonlocal elasticity theory”. Composites Part B: Engineering, 80, 43-52, 2015.
  • Bağdatlı SM. “Non-linear transverse vibrations of tensioned nanobeams using nonlocal beam theory”. Structural Engineering Mechanics, 55(2), 281-298, 2015.
  • Togun N, Bağdatlı SM. “Size dependent nonlinear vibration of the tensioned nanobeam based on the modified couple stress theory”. Composites Part B: Engineering, 97, 255-262, 2016.
  • Togun N. “Nonlocal beam theory for nonlinear vibrations of a nanobeam resting on elastic foundation”. Boundary Value Problems, 57, 1-14, 2016.
  • Togun N, Bagdatli SM. “Nonlinear vibration of a nanobeam on a Pasternak elastic foundation based on nonlocal Euler-Bernoulli beam theory”. Mathematical and Computational Applications, 21(3), 1-19, 2016.
  • Togun N. “Linear vibration analysis of nanobeam carrying nanoparticle based on nonlocal elasticity theory”. 2. International Conference on Advances in Mechanical and Robotics Engineering, Zürich, Switzerland, 25-26 October, 2014.
  • Eringen AC. Nonlocal Continuum Field Theories. Newyork, USA, Springer-Verlag, 2002.
  • Nayfeh AH, Mook DT. Nonlinear Oscillations, New York, USA, John Wiley, 1979.
  • Nayfeh AH. Introduction to Perturbation Techniques. New York, USA, John Wiley, 1981.

Free vibrations analysis of fluid conveying nanobeam based on nonlocal elasticity theory

Yıl 2017, Cilt: 23 Sayı: 1, 6 - 11, 01.03.2017

Öz

In
this study, linear vibration analysis of a nanobeam conveying fluid is
investigated under simple-simple and clamped-clamped boundary conditions.
Eringen’s nonlocal elasticity theory is applied to Euler-Bernoulli beam model.
Nonlocal elasticity theory is a popular growing technique for the mechanical
analyses of MEMS and NEMS structures. The Hamilton’s principle is employed to
derive the governing equations and boundary conditions. Non-dimensional form of
equations is obtained. The obtained equations of motion and boundary conditions
are independent from material and geometric structure. It is assumed that fluid
velocity is harmonically changed about a constant average speed. Approximate
solutions were obtained using the Method of Multiple Scales, a perturbation
method. The first term in perturbation series composes linear problem. Natural
frequencies and mode shapes are calculated by solving the linear problem for
different boundary conditions. For both boundary conditions, the natural
frequencies are decreased by increasing the nonlocal parameter




















 and the fluid velocity

. The
results are presented and interpreted by graphics.

Kaynakça

  • Eringen AC. “On differential-equations of nonlocal elasticity and solutions of screw dislocation and surface waves”. Journal of Applied Physics, 54(9), 4703-4710, 1983.
  • Yoon J, Ru CQ, Mioduchowski A. “Vibration and instability of carbon nanotubes conveying fluid”. Composites Science and Technology, 65(9), 1326-1336, 2005.
  • Reddy CD, Lu C, Rajendran S, and Liew KM. “Free vibration analysis of fluid-conveying single-walled carbon nanotubes”. Applied Physics Letters, 90, 133122, 2007.
  • Lin W, Qiao N. “On vibration and instability of carbon nanotubes conveying fluid”. Computational Materials Science, 43(2), 399-402, 2008.
  • Khosravian N, Tabar HR. “Computational modelling of a non-viscous fluid flow in a multi-walled carbon nanotube modelled as a Timoshenko beam”. Nanotechnology, 19(27), 275703, 2008.
  • Chang WJ, Lee HL. “Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model”. Physics Letters: A, 373(10), 982-985, 2009.
  • Peddieson J, Buchanan GR, McNitt RP. “Application of nonlocal continuum models to nanotechnology”. International Journal of Engineering Science, 41(3-5), 305-312, 2003.
  • Lee HL, Chang WJ. “Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory”. Journal of Applied Physics, 103 (024302), 1-4, 2008.
  • Deng Q, Yang Z. “Vibration of fluid-filled multi-walled carbon nanotubes seen via nonlocal elasticity theory”. Acta Mechanica Solida Sinica, 27(6), 568-578, 2014.
  • Wang L. “Vibration and instability analysis of tubular nano and micro-beams conveying fluid using nonlocal elasticity theory”. Physica E: Low-dimensional Systems and Nanostructures, 41(10), 1835-1840, 2009.
  • Wang L. “Dynamical behaviors of double-walled carbon nanotubes conveying fluid accounting for the role of small scale effect”. Computational Materials Science, 45(2), 584-588, 2009.
  • Wang L. “Vibration analysis of fluid-conveying nanotubes with consideration of surface effects”. Physica E: Lowdimensional Systems and Nanostructures, 43(1), 437-439, 2010.
  • Wang L. “A modified nonlocal beam model for vibration and stability of nanotubes conveying fluid”. Physica E: Lowdimensional Systems and Nanostructures, 44(1),25-28, 2011.
  • Xia W, Wang L. “Vibration characteristics of fluid-conveying carbon nanotubes with curved longitudinal shape”. Computational Materials Science, 49(1), 99-103, 2010.
  • Kiani, K. “Vibration behavior of simply supported inclined single-walled carbon nanotubes conveying viscous fluids flow using nonlocal Rayleigh beam model”. Applied Mathematical Modelling, 37(4), 1836-1850, 2013.
  • Zhen Y, Fang B. “Thermal-mechanical and nonlocal elastic vibration of single-walled carbon nanotubes conveying fluid”. Computational Materials Science, 49(2), 276-282, 2010.
  • Afkhami Z, Farid M. “Thermal-mechanical vibration and instability of carbon nanocones conveying fluid using nonlocal Timoshenko beam model”. Journal of Vibration and Control, 20, 1-15, 2014.
  • Atabakhshian V, Shooshtari A, Karimi M. “Electro-thermal vibration of a smart coupled nanobeam system with an internal flow based on nonlocal elasticity theory”. Physica B: Condensed Matter, 456, 375-382, 2015.
  • Ghavanloo E, Fazelzadeh SA. “Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid”. Physica E: low-dimensional Systems and Nanostructures, 44(1), 17-24, 2011.
  • Bağdatlı SM. “Nonlinear vibration of nanobeams with various boundary condition based on nonlocal elasticity theory”. Composites Part B: Engineering, 80, 43-52, 2015.
  • Bağdatlı SM. “Non-linear transverse vibrations of tensioned nanobeams using nonlocal beam theory”. Structural Engineering Mechanics, 55(2), 281-298, 2015.
  • Togun N, Bağdatlı SM. “Size dependent nonlinear vibration of the tensioned nanobeam based on the modified couple stress theory”. Composites Part B: Engineering, 97, 255-262, 2016.
  • Togun N. “Nonlocal beam theory for nonlinear vibrations of a nanobeam resting on elastic foundation”. Boundary Value Problems, 57, 1-14, 2016.
  • Togun N, Bagdatli SM. “Nonlinear vibration of a nanobeam on a Pasternak elastic foundation based on nonlocal Euler-Bernoulli beam theory”. Mathematical and Computational Applications, 21(3), 1-19, 2016.
  • Togun N. “Linear vibration analysis of nanobeam carrying nanoparticle based on nonlocal elasticity theory”. 2. International Conference on Advances in Mechanical and Robotics Engineering, Zürich, Switzerland, 25-26 October, 2014.
  • Eringen AC. Nonlocal Continuum Field Theories. Newyork, USA, Springer-Verlag, 2002.
  • Nayfeh AH, Mook DT. Nonlinear Oscillations, New York, USA, John Wiley, 1979.
  • Nayfeh AH. Introduction to Perturbation Techniques. New York, USA, John Wiley, 1981.
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Makale
Yazarlar

Süleyman Murat Bağdatlı

Necla Toğun

Yayımlanma Tarihi 1 Mart 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 23 Sayı: 1

Kaynak Göster

APA Bağdatlı, S. M., & Toğun, N. (2017). Yerel olmayan elastisite teorisine göre akışkan taşıyan nanokirişin serbest titreşimlerinin analizi. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 23(1), 6-11.
AMA Bağdatlı SM, Toğun N. Yerel olmayan elastisite teorisine göre akışkan taşıyan nanokirişin serbest titreşimlerinin analizi. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. Mart 2017;23(1):6-11.
Chicago Bağdatlı, Süleyman Murat, ve Necla Toğun. “Yerel Olmayan Elastisite Teorisine göre akışkan taşıyan nanokirişin Serbest titreşimlerinin Analizi”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 23, sy. 1 (Mart 2017): 6-11.
EndNote Bağdatlı SM, Toğun N (01 Mart 2017) Yerel olmayan elastisite teorisine göre akışkan taşıyan nanokirişin serbest titreşimlerinin analizi. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 23 1 6–11.
IEEE S. M. Bağdatlı ve N. Toğun, “Yerel olmayan elastisite teorisine göre akışkan taşıyan nanokirişin serbest titreşimlerinin analizi”, Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, c. 23, sy. 1, ss. 6–11, 2017.
ISNAD Bağdatlı, Süleyman Murat - Toğun, Necla. “Yerel Olmayan Elastisite Teorisine göre akışkan taşıyan nanokirişin Serbest titreşimlerinin Analizi”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 23/1 (Mart 2017), 6-11.
JAMA Bağdatlı SM, Toğun N. Yerel olmayan elastisite teorisine göre akışkan taşıyan nanokirişin serbest titreşimlerinin analizi. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. 2017;23:6–11.
MLA Bağdatlı, Süleyman Murat ve Necla Toğun. “Yerel Olmayan Elastisite Teorisine göre akışkan taşıyan nanokirişin Serbest titreşimlerinin Analizi”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, c. 23, sy. 1, 2017, ss. 6-11.
Vancouver Bağdatlı SM, Toğun N. Yerel olmayan elastisite teorisine göre akışkan taşıyan nanokirişin serbest titreşimlerinin analizi. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. 2017;23(1):6-11.





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