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Ortadan mesnetli mikro kirişin doğrusal titreşim hareketleri

Year 2021, Volume: 36 Issue: 2, 1089 - 1104, 05.03.2021
https://doi.org/10.17341/gazimmfd.734809

Abstract

İmalat teknolojisindeki gelişmeler neticesinde ortaya çıkan mikro ve nano elektromekanik sistemler (MEMS ve NEMS); biyosensörler, aktüatörler ve atomik kuvvet mikroskopları (AKM) gibi mikro ve nano yapıya sahip sistemlerde çok yaygın olarak kullanılmaktadır. NEMS ve MEMS’ de kiriş veya benzeri elemanlar ve yapılar bulunmaktadır. Bu elemanlar sabit kesitli olduğu gibi değişken kesitlere de sahip olabilmektedirler. Söz konusu sistemler içindeki kiriş elemanların statik ve dinamik davranış karakterlerinin bilinmesi çok önemlidir. Çünkü sistemin sorunsuz çalışması için ihtiyaç duyulan çalışma frekansının, tasarlanan sistemin doğal frekansı ile aynı olmaması gerekmektedir. Bu nedenden dolayı mikro ve nano elemanların serbest titreşim analizlerinin yapılması sorunsuz bir tasarım için hayati önem taşımaktadır. Bu kapsamda, ortadan mesnetli mikro kirişin titreşim analizleri yapılmıştır. Mikro kiriş seramik özellikte olup elektrik alan içerisine yerleştirilmiş ve mesnetlerin pozisyonları değiştirilerek titreşim karakterleri incelenmiştir. Hareket denklemleri modifiye gerilme çifti teorisi kullanılarak Hamilton metoduna göre elde edilmiştir. Hareket denklemi, pertürbasyon metotlarından biri olan çok zaman ölçekli metot ile çözümü elde edilmiştir. Doğal frekanslar ve mod şekilleri, boyutsuz parametreler mesnet konumu, gerilme katsayısı ve mikrokirişlik katsayısına bağlı olarak elde edilmiştir.

References

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  • [3] Ahangar, S., Rezazadeh,G., Shabani, R., Ahmadi, G., Toloei, A. On the Stability of Microbeam Conveying Fluid Considering Modified Couple Stress Theory. International Journal of Mechanics and Materials in Design, 7(4), 327-342; 2011.
  • [4] Akgöz, B., Civalek, Ö. Buckling Analysis of Functionally Graded Microbeams Based on Strain Gradient Theory. Acta Mechanica, 224(9), 2185-2201; 2013.
  • [5] Şimşek, M., Aydın, M., Yurtcu, H. H., Reddy, J. N. Size-Dependent Vibration of a Microplate Under The Action of a Moving Load Based on The Modified Couple Stress Theory. Acta Mechanica, 226(11), 3807-3822; 2015.
  • [6] Ghasabi, S. A., Shahgholi, M., Arbabtafti, M. Dynamic bifurcations analysis of a micro rotating shaft considering non-classical theory and internal damping. Meccanica, 53(15), 3795-3805; 2018.
  • [7] Ghayesh, M.H., Amabili, M., Farokhi, H. Nonlinear Forced Vibrations of a Microbeam Based on The Starin Gradient Elasticity Theory. International Journal of Engineering Science, 63, 52-60; 2012.
  • [8] Noori, J., Fariborz, S.J., Vafa, J.P. A Higher-Order Micro-Beam Model with Application Free Vibration. Mechanics of Advanced Materials & Structures, 23(4) 443-450; 2016.
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  • [10] El-Sayed, T.A., El-Mongy, H.H. Free Vibration and Stability Analysis of a Multi-Span Pipe Conveying Fluid Using Exact and Variational İteration Methods Combined with Transfer matrix Method. Applied Mathematical Modelling, 71, 173-193; 2019.
  • [11] Allahkarami, F., Saryazdi, M. G., Nikkhah-Bahrami, M. Nonlinear Forced Vibration of Curved Microbeam Resting on Nonlinear Foundation Using The Modified Strain Gradient Theory. International Applied Mechanics, 54(6), 718-738; 2018.
  • [12] Atcı, D., Bağdatlı, S.M. Vibrations of Fluid Conveying Microbeams Under Non-ideal Boundary Conditions. Microsystem Technologies: Micro- and Nanosystems Information Storage and Processing Systems, 23(10); 2017.
  • [13] Kural, S., Özkaya, E. Size-Dependent Vibrations Of A Micro Beam Conveying Fluid And Resting On An Elastic Foundation. Journal of Vibration and Control, 23(7), 1106-1114; 2015.
  • [14] Kural, S. Investigation of 3:1 And 2:1 Internal Resonances In Fluid Conveying Microbeam. Technical Journal / Tehnički Glasnik, 12 (1/2), 18-26; 2018.
  • [15] Togun, N., Bağdatli, S. M. The vibration of nanobeam resting on elastic foundation using modified couple stress theory. Technical Journal / Tehnički Glasnik, 12(4), 221-225; 2018.
  • [16] Demir, Ç , Akgöz, B , Erdinç, M , Mercan, K , Civalek, Ö . Elastik bir malzeme ile temas halinde olan grafen tabakanın titreşim hesabı, Journal of The Faculty of Engineering and Architecture of Gazi University. 32(2); 2017.
  • [17] Togun, N., Bağdatli, S. M. Size dependent nonlinear vibration of the tensioned nanobeam based on the modified couple stress theory. Composites Part B: Engineering, 97, 255-262; 2016.
  • [18] Togun, N., Bağdatlı, S. M. Investigation of the Size Effect in Euler-Bernoulli Nanobeam Using the Modified Couple Stress Theory. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, 13(4), 893-899; 2017.
  • [19] Xie, W.C., Lee, H.P., Lim, S.P. Nonlinear Dynamic Analysis of MEMS Switches by Nonlinear Modal Analysis. Nonlinear Dynamics, 31, 243–256; 2003.
  • [20] Zhang, G. Y. , Gao, X. L., Ding, S. R. Band gaps for wave propagation in 2-D periodic composite structures incorporating microstructure effects. Acta Mechanica, 229, 4199–4214; 2018.
  • [21] Bağdatlı, S.M., Öz, H.R.,Özkaya, E. Non-Linear Transverse Vibrations and 3:1 Internal Resonances of A Tensioned Beam On Multiple Supports. Mathematical and Computational Applications, 16(1), 203-215; 2011.
  • [22] Wang,L. Size-depent vibration characteristics of fluid-conveying microtubes. Journal of Fluids and Structures, 26,675-684; 2010.
Year 2021, Volume: 36 Issue: 2, 1089 - 1104, 05.03.2021
https://doi.org/10.17341/gazimmfd.734809

Abstract

References

  • [1] Fu, Y.M., Zhang, J. Nonlinear Static and Dynamic Responses of an Electrically Actuated Viscoelastic Microbeam. Acta Mechanica Sinica, 25(2), 211-218; 2009.
  • [2] Xu, L., Yang, Q. Multi-Field Coupled Dynamics for a Micro Beam. Mechanics Based Design of Structures & Machines, 43 (1), 57-73; 2015.
  • [3] Ahangar, S., Rezazadeh,G., Shabani, R., Ahmadi, G., Toloei, A. On the Stability of Microbeam Conveying Fluid Considering Modified Couple Stress Theory. International Journal of Mechanics and Materials in Design, 7(4), 327-342; 2011.
  • [4] Akgöz, B., Civalek, Ö. Buckling Analysis of Functionally Graded Microbeams Based on Strain Gradient Theory. Acta Mechanica, 224(9), 2185-2201; 2013.
  • [5] Şimşek, M., Aydın, M., Yurtcu, H. H., Reddy, J. N. Size-Dependent Vibration of a Microplate Under The Action of a Moving Load Based on The Modified Couple Stress Theory. Acta Mechanica, 226(11), 3807-3822; 2015.
  • [6] Ghasabi, S. A., Shahgholi, M., Arbabtafti, M. Dynamic bifurcations analysis of a micro rotating shaft considering non-classical theory and internal damping. Meccanica, 53(15), 3795-3805; 2018.
  • [7] Ghayesh, M.H., Amabili, M., Farokhi, H. Nonlinear Forced Vibrations of a Microbeam Based on The Starin Gradient Elasticity Theory. International Journal of Engineering Science, 63, 52-60; 2012.
  • [8] Noori, J., Fariborz, S.J., Vafa, J.P. A Higher-Order Micro-Beam Model with Application Free Vibration. Mechanics of Advanced Materials & Structures, 23(4) 443-450; 2016.
  • [9] Rahmani, O., Hosseini, S.A.H., Ghoytasi, I., Golmohammadi, H. Buckling and Free Vibration of Shallow Curved Micro/Nano-Beam Based on Starin Gradient Theory Under Thermal Loading with Temperature-Dependent Properties. Applied Physics A, 123(1); 2016.
  • [10] El-Sayed, T.A., El-Mongy, H.H. Free Vibration and Stability Analysis of a Multi-Span Pipe Conveying Fluid Using Exact and Variational İteration Methods Combined with Transfer matrix Method. Applied Mathematical Modelling, 71, 173-193; 2019.
  • [11] Allahkarami, F., Saryazdi, M. G., Nikkhah-Bahrami, M. Nonlinear Forced Vibration of Curved Microbeam Resting on Nonlinear Foundation Using The Modified Strain Gradient Theory. International Applied Mechanics, 54(6), 718-738; 2018.
  • [12] Atcı, D., Bağdatlı, S.M. Vibrations of Fluid Conveying Microbeams Under Non-ideal Boundary Conditions. Microsystem Technologies: Micro- and Nanosystems Information Storage and Processing Systems, 23(10); 2017.
  • [13] Kural, S., Özkaya, E. Size-Dependent Vibrations Of A Micro Beam Conveying Fluid And Resting On An Elastic Foundation. Journal of Vibration and Control, 23(7), 1106-1114; 2015.
  • [14] Kural, S. Investigation of 3:1 And 2:1 Internal Resonances In Fluid Conveying Microbeam. Technical Journal / Tehnički Glasnik, 12 (1/2), 18-26; 2018.
  • [15] Togun, N., Bağdatli, S. M. The vibration of nanobeam resting on elastic foundation using modified couple stress theory. Technical Journal / Tehnički Glasnik, 12(4), 221-225; 2018.
  • [16] Demir, Ç , Akgöz, B , Erdinç, M , Mercan, K , Civalek, Ö . Elastik bir malzeme ile temas halinde olan grafen tabakanın titreşim hesabı, Journal of The Faculty of Engineering and Architecture of Gazi University. 32(2); 2017.
  • [17] Togun, N., Bağdatli, S. M. Size dependent nonlinear vibration of the tensioned nanobeam based on the modified couple stress theory. Composites Part B: Engineering, 97, 255-262; 2016.
  • [18] Togun, N., Bağdatlı, S. M. Investigation of the Size Effect in Euler-Bernoulli Nanobeam Using the Modified Couple Stress Theory. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, 13(4), 893-899; 2017.
  • [19] Xie, W.C., Lee, H.P., Lim, S.P. Nonlinear Dynamic Analysis of MEMS Switches by Nonlinear Modal Analysis. Nonlinear Dynamics, 31, 243–256; 2003.
  • [20] Zhang, G. Y. , Gao, X. L., Ding, S. R. Band gaps for wave propagation in 2-D periodic composite structures incorporating microstructure effects. Acta Mechanica, 229, 4199–4214; 2018.
  • [21] Bağdatlı, S.M., Öz, H.R.,Özkaya, E. Non-Linear Transverse Vibrations and 3:1 Internal Resonances of A Tensioned Beam On Multiple Supports. Mathematical and Computational Applications, 16(1), 203-215; 2011.
  • [22] Wang,L. Size-depent vibration characteristics of fluid-conveying microtubes. Journal of Fluids and Structures, 26,675-684; 2010.
There are 22 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Makaleler
Authors

Şevki Akkoca 0000-0002-5689-6307

Süleyman Murat Bağdatlı 0000-0002-5152-9604

Necla Toğun 0000-0001-7921-6290

Publication Date March 5, 2021
Submission Date May 18, 2020
Acceptance Date December 19, 2020
Published in Issue Year 2021 Volume: 36 Issue: 2

Cite

APA Akkoca, Ş., Bağdatlı, S. M., & Toğun, N. (2021). Ortadan mesnetli mikro kirişin doğrusal titreşim hareketleri. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 36(2), 1089-1104. https://doi.org/10.17341/gazimmfd.734809
AMA Akkoca Ş, Bağdatlı SM, Toğun N. Ortadan mesnetli mikro kirişin doğrusal titreşim hareketleri. GUMMFD. March 2021;36(2):1089-1104. doi:10.17341/gazimmfd.734809
Chicago Akkoca, Şevki, Süleyman Murat Bağdatlı, and Necla Toğun. “Ortadan Mesnetli Mikro kirişin doğrusal titreşim Hareketleri”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 36, no. 2 (March 2021): 1089-1104. https://doi.org/10.17341/gazimmfd.734809.
EndNote Akkoca Ş, Bağdatlı SM, Toğun N (March 1, 2021) Ortadan mesnetli mikro kirişin doğrusal titreşim hareketleri. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 36 2 1089–1104.
IEEE Ş. Akkoca, S. M. Bağdatlı, and N. Toğun, “Ortadan mesnetli mikro kirişin doğrusal titreşim hareketleri”, GUMMFD, vol. 36, no. 2, pp. 1089–1104, 2021, doi: 10.17341/gazimmfd.734809.
ISNAD Akkoca, Şevki et al. “Ortadan Mesnetli Mikro kirişin doğrusal titreşim Hareketleri”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 36/2 (March 2021), 1089-1104. https://doi.org/10.17341/gazimmfd.734809.
JAMA Akkoca Ş, Bağdatlı SM, Toğun N. Ortadan mesnetli mikro kirişin doğrusal titreşim hareketleri. GUMMFD. 2021;36:1089–1104.
MLA Akkoca, Şevki et al. “Ortadan Mesnetli Mikro kirişin doğrusal titreşim Hareketleri”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, vol. 36, no. 2, 2021, pp. 1089-04, doi:10.17341/gazimmfd.734809.
Vancouver Akkoca Ş, Bağdatlı SM, Toğun N. Ortadan mesnetli mikro kirişin doğrusal titreşim hareketleri. GUMMFD. 2021;36(2):1089-104.