Investigation of linear vibration behavior of middle supported nanobeam

Year 2020, Volume: 7 Issue: 3, 1450 - 1459, 30.09.2020

Burak Yapanmış , Süleyman Murat Bağdatlı , Necla Toğun

https://doi.org/10.31202/ecjse.741269

Cited By: 2

Abstract

In this study, linear
vibration of middle supported nanobeam, which is commonly used in nano electro-mechanical
systems, is analyzed. Eringen’s nonlocal elasticity theory is used to capture
nanoscale effect. Equation of motion of nanobeam is derived with the Hamilton
principle. Multiple scale methods, which is one of the perturbation techniques,
is performed for solving the equation of motion. Support position and nonlocal
effect are focused on the research. The results are presented with graphs and
table. In conclusion, when the nonlocal parameter is getting a raise, more
nanoscale structure is obtained. Highest rigidity and linear natural frequency
are received with mid-position of the support.

Keywords

Nanobeam, linear vibration, nonlocal elasticity, perturbation methods

Ortadan destekli nano kirişin doğrusal titreşim davranışının incelenmesi

Abstract

Bu
çalışmada, nano elektromekanik sistemlerde yaygın olarak kullanılan ortadan
destekli nano kirişin doğrusal titreşimi analiz edilmiştir. Nano ölçeği
yakalayabilmek için Eringen’in yerel olmayan elastisite teorisi kullanılmıştır.
Nano kirişin hareket denklemi Hamilton prensibi ile elde edilir. Hareket
denklemini çözmek için pertürbasyon tekniklerinden biri olan çok ölçekli metot
uygulanmıştır. Orta mesnet pozisyonu ve yerel olmayan etki araştırmada odak
nokta olmuştur. Sonuçlar grafikler ve tablo ile sunulmuştur. Sonuç olarak,
yerel olmayan parametre artmasıyla daha fazla nano ölçekli yapı elde
edilmektedir. İkinci desteğin orta konuma yerleştirilmesiyle en yüksek rijitlik
ve doğrusal doğal frekans değerleri elde edilir.

Keywords

Nanokiriş, doğrusal titreşim, yerel olmayan elastisite, pertürbasyon metodu

References

• [1]. Kouh, T., Hanay, M. S., Ekinci, K. L. (2017), "Nanomechanical motion transducers for miniaturized mechanical systems", Micromachines, 8(4), 108, 1-27. doi: 10.3390/mi8040108. [2]. Leijssen, R., La Gala, G. R., Freisem, L., Muhonen, J. T., Verhagen, E., "Nonlinear cavity optomechanics with nanomechanical thermal fluctuations" Nature Communications, 2017, 8(16024); 1–10. [3]. Frank, I. W., Deotare, P. B., McCutcheon, M. W., Loncar, M., "Programmable photonic crystal nanobeam cavities", Optics Express, 2010, 18(8); 8705–8712. [4]. Briscoe, J., Dunn, S., "Piezoelectric nanogenerators–a review of nanostructured piezoelectric energy harvesters", Nano Energy, 2015, 14; 15–29. [5]. Sharma R., Akshath U.S., Bhatt P., Raghavarao K.S.M.S., "Interferometric detection of chloramphenicol via its immunochemicalrecognition at polymer-coated nano-corrugated surfaces", Sensors & Actuators: B. Chemical.,2019, 290; 110–117. [6]. Ogia, H., Iwagamib, S., Nagakuboa, A., Taniguchic, T., Onod, T., "Nano-plate biosensor array using ultrafast heat transport through proteins" Sensors & Actuators: B. Chemical., 2019, 278; 15–20. [7]. Murmu, T., Pradhan, S., "Thermal effects on the stability of embedded carbon nanotubes", Computational Materials Science, 2010, 47; 721–726. [8]. Shahali, H., Hasan, J., Wang, H., Tesfamichael, T., Yan, C., Yarlagadda P. K., "Evaluation of particle beam lithography for fabrication of metallic nanostructures", Procedia Manufacturing, 2019, 30, 261–267. [9]. Koçak, A., Karasu, B., Nanotaneciklerin Genel Değerlendirilmesi, El-Cezeri Journal of Science and Engineering, 2018, 5(1), 191-236. [10]. Li C., Chou T.W., "Elastic wave velocities in single-walled carbon nanotubes", Phys. Rev. B, 2006,73(24); 245407. [11]. Liew K.M., Wong C. H., Tan M. J., "Twisting effects of carbon nanotube bundles subjected to axial compression and tension", Journal of Applied Physics, 2006, 99; 114312. [12]. Sanchez-Portal, D., Artacho, E., Soler, J.M., Rubio, A. and Ordejon, P., "Ab initio structural elastic and vibrational properties of carbon nanotubes", Phys Rev B, 1999, 59; 12678–12688. [13]. Liu Y., Reddy J., "A nonlocal curved beam model based on a modified couple stress theory", Int. J. Struct. Stabil. Dynam.,2011, 11(3); 495-512. [14]. Faraji-Oskouie M., Norouzzadeh A., Ansari R., Rouhi H., "Bending of small-scale Timoshenko beams based on the integral/ differential nonlocal-micropolar elasticity theory: a finite element approach", Appl. Math. Mechanics,2019, 40(6); 767-782. [15]. Nix, W. D., Gao, H., "Indentation size effects in crystalline materials: A law for strain gradient plasticity", Journal of the Mechanics and Physics of Solids,1998, 46; 411–425. [16]. Lu L., Guo X., Zhao J., "On the mechanics of Kirchhoff and Mindlin plates incorporating surface energy", Int. J. Eng. Sci.,2018, 124(3); 24-40. [17]. Eringen, A.C., "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 1983, 54; 4703–4707. [18]. Peddieson, J., Buchanan, G.R., Mcnıtt, R.P., "Application of Nonlocal Continuum Models to Nanotechnology", Int. J. Eng. Sci.,2003, 41(3-5); 305–312. [19]. Reddy, J.N. , "Nonlocal theories of bending, buckling and vibration of beams", Int. J. Eng. Sci., 2007, 45 (2-8); 288–307. [19] Nix, W. D., Gao, H., "Indentation size effects in crystalline materials: A law for strain gradient plasticity", Journal of the Mechanics and Physics [20]. Nix, W. D., Gao, H., Indentation size effects in crystalline materials: A law for strain gradient plasticity, Journal of the Mechanics and Physics, 1998, 45 (3), 411-425. [21]. Reddy, J.N., Pang, S.D., "Nonlocal continuum theories of beams for the analysis of carbon nanotubes", J. Appl. Phys., 2008, 103 (2); 1-15. [22]. Aydogdu, M. A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration. Physica. 2009, E 41, 1651–1655. [23]. Bağdatlı, S. M., "Non-linear vibration of nanobeams with various boundary condition based on nonlocal elasticity theory", Composites Part B, 2015, 80; 43-52. [24]. Ghayesh, M. H., Farajpour, A., "Nonlinear mechanics of nanoscale tubes via nonlocal strain gradient theory. International Journal of Engineering Science, 2018 129; 84-95. [25]. Romano, G., Barretta, R., Diaco, M., "On Nonlocal integral models for elastic nano-beams", International Journal of Mechanical Sciences, 2017, 131(132); 490–499. [26]. Arani, A.G., Dashti, P., Amir, S., Yousefi, M., "Nonlinear vibration of coupled nano and microstructures conveying fluid based on Timoshenko beam model under two-dimensional magnetic field", Acta Mech., 2015, 226; 2729–2760. [27]. Nayfeh A. H., "Introduction to Perturbation Techniques", Wiley, New York, ABD,2011.