مدل سازی خیز بزرگ نانو تیرهای کرومی با استفاده از روش طراحی آزمایش ها

نوع مقاله : مقاله پژوهشی

نویسندگان

• وحید مدانلو
• یاسر تقی پور لاهیجانی
• احمد مشایخی
• بهنام آخوندی

دانشکده مهندسی مکانیک، دانشگاه صنعتی سیرجان، سیرجان، ایران

10.22067/jacsm.2023.83862.1198

چکیده

در این مقاله، خیز نانوتیرهای کرومی با استفاده از روش طراحی آزمایشها بررسی شده است. با استفاده از روش فاکتوریل کامل، تعداد 100 آزمایش طراحی شده که در آن طول و نیروی وارد بر نانوتیر به ترتیب در 25 و 4 سطح به‌عنوان متغیرهای ورودی و خیز نانوتیر به‌عنوان خروجی در نظر گرفته شد. در ابتدا، از هر 4 سطح نیرو (8، 5/9، 11 و 5/12 نانونیوتن)، برای تحلیل استفاده شده و معادلاتی بسته برای تخمین خیز نانوتیر حاصل شد. نتایج نشان داد که تأثیر طول نانوتیر بیشتر از نیروی وارد بر نانوتیر است به‌طوری که با افزایش طول، میزان خیز به‌صورت درجه سه تغییر می کند. مدل رگرسیون درجه سوم، با دقت بالایی خیز نانوتیر را پیش بینی کرده و میزان خطای آن نسبت به مدلهای رگرسیون درجه اول و دوم کمتر است. در ادامه، از دو سطح نیرو (8 و 11 نانونیوتن) برای تحلیل استفاده‌ شده و معادلات جدیدی برای تخمین خیز نانو تیر حاصل شد. از معادلات جدید برای درون‌یابی و برون‌یابی خیز نانوتیر به ترتیب در نیروهای 5/9 و 5/12 نانونیوتن استفاده شد. نتایج نشان داد که مدل رگرسیون با استفاده از دو سطح نیرو نیز با دقت زیادی میزان خیز نانوتیر را پیش بینی می کند. نتایج این تحقیق نشان داد که بدون نیاز به انجام آزمایشهای بیشتر و صرف هزینه، یا انجام محاسبات پیچیده و حل معادلات دیفرانسیل، می‌توان خیز نانوتیر را با فرمول‌هایی جبری و با دقت بالا تخمین زد.

کلیدواژه‌ها

• نانوتیر
• خیز بزرگ
• مدل رگرسیون
• طراحی آزمایش

موضوعات

• مکانیک جامد

---

عنوان مقاله [English]

Modeling of large deflection of the chromium nanobeams using design of experiments method

نویسندگان [English]

• Vahid Modanloo
• Yasser Taghipour Lahijani
• Ahmad Mashayekhi
• Behnam Akhoundi

Mechanical Engineering Department, Sirjan University of Technology, Sirjan, Iran

چکیده [English]

This paper investigates the deflection of chromium nanobeams using the design of experiments method. Using the full factorial method, a number of 100 experiments were designed in which the length and the force on the nanobeam were considered input variables at 25 and 4 levels, respectively and the deflection of the nanobeam was considered output. First, all 4 force levels (8, 9.5, 11, and 12.5 nN) were used for the analysis, and closed-form equations were obtained to estimate the deflection of the nanobeam. The results showed that the effect of the length is more than the force, by increasing the length so that the deflection changes with third degree. The third-order regression model predicts the deflection with high accuracy, and its error value is lower than the first and second-order regression models. Afterward, two levels of force (8 and 11 nN) were used for analysis, and new equations were obtained to estimate the deflection of the nanobeam. The new equations were used for interpolation and extrapolation of the nanobeam's deflection in forces of 9.5 and 12.5 nN, respectively. The results demonstrated that the regression model using two force levels accurately predicts the deflections of nanobeams as well. The results of this research demonstrated that it is possible to estimate the nanobeam's deflection without the need to perform more experiments and spend cost, perform complex calculations, and solve differential equations; the nanobeam's deflection can be accurately estimated with algebraic formulas.

کلیدواژه‌ها [English]

• Nanobeam
• Large Deflection
• Regression Model
• Design of Experiment

مراجع

 

[1]   Y. Jiang, L. Li, and Y. Hu, “ A nonlocal surface theory for surface–bulk interactions and its application to mechanics of nanobeams,”  International Journal of Engineering Science, vol. 172, p. 103624, 2022.

[2]   A. A. Nuhu and B. Safaei, “ State-of-the-art of vibration analysis of small-sized structures by using nonclassical continuum theories of elasticity,” Archives of Computational Methods in Engineering, vol. 29, no. 7, pp. 4959-5147, 2022.

[3]   S. Sahmani, A. M. Fattahi, and N. Ahmed, “ Analytical mathematical solution for vibrational response of postbuckled laminated FG-GPLRC nonlocal strain gradient micro-/nanobeams,”  Engineering with Computers, vol. 35, pp. 1173-1189, 2019.

[4]   S. Sahmani and M. Mohammadi Aghdam, “ Small scale effects on the large amplitude nonlinear vibrations of multilayer functionally graded composite nanobeams reinforced with graphene-nanoplatelets,”  International Journal of Nanoscience and Nanotechnology, vol. 14, no. 3, pp. 207-227, 2018.

[5]   D. Zeng and Q. Zheng, “ Large deflection theory of nanobeams,”  Acta Mechanica Solida Sinica, vol. 23, no. 5, pp. 394-399, 2010.

[6]   S. Cuenot, C. Frétigny, S. Demoustier-Champagne, and B. Nysten, “ Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy,”  Physical Review B, vol. 69, no. 16, p. 165410, 2004.

[7]   G. Jing et al., “ Surface effects on elastic properties of silver nanowires: contact atomic-force microscopy,”  Physical review B, vol. 73, no. 23, p. 235409, 2006.

[8]   E. W. Wong, P. E. Sheehan, and C. M. Lieber, “ Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes,” science, vol. 277, no. 5334, pp. 1971-1975, 1997.

[9]   S. Nilsson, E.-L. Sarwe, and L. Montelius, “ Fabrication and mechanical characterization of ultrashort nanocantilevers,” Applied Physics Letters, vol. 83, no. 5, pp. 990-992, 2003.

[10] S. G. Nilsson, X. Borrise, and L. Montelius, “ Size effect on Young’s modulus of thin chromium cantilevers,” Applied Physics Letters, vol. 85, no. 16, pp. 3555-3557, 2004.

[11] N. Søndergaard, S. Ghatnekar-Nilsson, T. Guhr, and L. Montelius, “ Understanding mechanical properties of nanostructures using Euler’s theory,” Nanotechnology, vol. 18, no. 25, p. 255502, 2007.

[12] Y. Sapsathiarn and R. Rajapakse,  “ A model for large deflections of nanobeams and experimental comparison,” IEEE Transactions on Nanotechnology, vol. 11, no. 2, pp. 247-254, 2011.

[13] Y. Taghipour and G. H. Baradaran, “ A finite element modeling for large deflection analysis of uniform and tapered nanowires with good interpretation of experimental results,”  International Journal of Mechanical Sciences, vol. 114, pp. 111-119, 2016.

[14] Y. Taghipour and S. Darfarin, “ A Method for Comparison of Large Deflection in Beams,” International Journal of Applied Mechanics and Engineering, vol. 27, no. 4, pp. 179-193, 2022, doi: doi:10.2478/ijame-2022-0058.

[15] A. Naderi, T. Quoc-Thai, X. Zhuang, and X. Jiang, “ Vibration Analysis of a Unimorph Nanobeam with a Dielectric Layer of Both Flexoelectricity and Piezoelectricity,”  Materials, vol. 16, no. 9, p. 3485, 2023.

[16] Y. Taghipour and M. Zeinali, “ Functionally graded nanobeams subjected to large deflection by considering surface effects,”  Scientia Iranica, 2023. doi: 10.24200/sci.2023.60997.7113

[17] H. Darban, R. Luciano, and R. Darban, “Buckling of cracked micro-and nanocantilevers,” Acta Mechanica, vol. 234, no. 2, pp. 693-704, 2023.

[18] M. E. Khater, “ A Generalized Model for Curved Nanobeams Incorporating Surface Energy,” Micromachines, vol. 14, no. 3, p. 663, 2023. [Online]. Available: https://www.mdpi.com/2072-666X/14/3/663

[19] E. Raeisi Estabragh and G. H. Baradaran, “Numerical study of large deflection of nanobeam according to the MCST and SE,” Mechanics of Advanced Materials and Structures, pp. 1-11, 2023. https://doi.org/10.1080/15376494.2023.2180120

[20] S. A. Faghidian, K. K. Żur, and I. Elishakoff, “ Nonlinear flexure mechanics of mixture unified gradient nanobeams,” Communications in Nonlinear Science and Numerical Simulation, vol. 117, p. 106928, 2023/02/01/ 2023, doi: https://doi.org/10.1016/j.cnsns.2022.106928. 

[21] X. Wang, S. Wu, J. Yin, Z. Moradi, M. Safa, and M. Amine Khadimallah, “ On the electromechanical energy absorption of the reinforced composites piezoelectric MEMS via Adaptive neuro-fuzzy inference system and MCS theory,” Composite Structures, vol. 303, p. 116246, 2023/01/01/ 2023.

 doi: https://doi.org/10.1016/j.compstruct.2022.116246.

[22] A. Naderi, S. Behdad, and M. Fakher, “ Size dependent effects of two phase viscoelastic medium on damping vibrations of smart nanobeams: an efficient implementation of GDQM,” Smart Materials and Structures, vol. 31, no. 4, p. 045007, 2022/02/24 2022.

[23] V. S. Chandel and M. Talha, “ Stochastic thermo-elastic vibration characteristics of functionally graded porous nano-beams using first-order perturbation-based nonlocal finite element model,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 236, no. 15, pp. 8563-8581, 2022, doi: 10.1177/09544062221086242.

[24] Hamada, H.M. Al-Attar, A.A. Tayeh, B. Bin Mat Yahaya, F. Abu Aisheh, Y.I. “Optimising concrete containing palm oil clinker and palm oil fuel ash using response surface method,” Ain Shams Engineering Journal, vol. 14 no.10, pp. 102150, 2023. https://doi.org/10.1016/j.asej.2023.102150

[25] Ba, E.C.T. Martins, P.S. dos Santos, C.E. Maia, L.H.A. Barbosa, J.W. Dumont, M.R. “Study of the behavior of skewness (Rsk) and kurtosis (Rku) parameters in the dry drilling process of Al-Mg-Si alloy 6351 T6 using a Diamond-Like Carbon coated high-speed steel tool,” Tribology International, vol. 191, pp. 109149, 2024,

doi: https://doi.org/10.1016/j.triboint.2023.109149.

[26] J. Shao, Z. Fan, Y. Huang, Y. Zhan, and Q. Cai, “ Multi-objective optimization of double-walled steel cofferdams based on response surface methodology and particle swarm optimization algorithm,” in Structures, Elsevier, vol. 49:pp. 256-266. 2023.

[27] V. Alimirzaloo and V. Modanloo, “Investigation of the forming force in torsion extrusion process of aluminum alloy 1050,” International Journal of Engineering, vol. 30, no. 6, pp. 920-925, 2017.

[28] D. C. Montgomery, Design and analysis of experiments. John wiley & sons, 2017.

[29] M. Moradian, A. Doniavi, V. Modanloo, and V. Alimirzaloo, “ Process parameters optimization in gas blow forming of pin-type metal bipolar plates using Taguchi and finite element methods,” vol. 10, no. 2. Pp.101-108 2017.