بررسی ارتعاشات غیرخطی میکرو لوله حامل سیّال تحت تحریک پارامتریک مغناطیسی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه آزاد اسلامی واحد سلماس

2 دانشگاه تبریز

چکیده

در این پژوهش، اثر پارامترهای مختلف سیستم روی پاسخ غیرخطی نوسانات جانبی میکرولوله تیرمانند حاوی سیّال با شرایط مرزی دو سر ساده نامتحرک تحت شرایط تشدید پارامتریک مغناطیسی محوری بررسی می­شود. از تئوری تغییر شکل‌های برشی مرتبۀ اوّل ردی و تئوری الاستیسیته غیرمحلی ارینگن برای استخراج معادلات غیرخطی حاکم بر حرکات جانبی میکرولوله با لحاظ کردن جملات غیرخطی هندسی ون‑کارمن استفاده می­شود. در سرعت‌های جریان بالاتر از سرعت بحرانی آستانه فلاتر (متناظر با کوپلینگ مو‌دهای اوّل و دوم)، رفتار سیستم غیرخطی دو درجۀ آزادی تحت شرایط تشدید پارامتریک مغناطیسی تحلیل می­شود. با استخراج منحنی‌های پاسخ غیرخطی، اثرات پارامتر‌های دامنۀ تحریک مغناطیسی، پارامتر فرکانس تحریک و پارامتر غیرمحلی تنش روی دامنۀ تشدید سیستم بررسی و مورد بحث قرار می­گیرد.

کلیدواژه‌ها


عنوان مقاله [English]

Nonlinear Vibration Analysis of Fluid Conveying Microtube under Parametric Magnetic Excitation

نویسندگان [English]

  • Akbar Allahverdizadeh 2
  • Behnam Dadashzadeh 2
  • Hamid Azimzadeh 1
1
2 University of Tabriz
چکیده [English]

In this research, effects of various system parameters on nonlinear response of transverse vibrations of beam-like fluid conveying microtube with fixed simply supported boundary conditions under axial magnetic parametric resonance condition is investigated. Reddy’s first order shear deformation theory and Eringen nonlocal elasticity theory are used to derive microtube nonlinear equations of transverse motion considering nonlinear geometric terms of von-Karman. For fluid flow velocities more than flutter critical velocity, behavior of 2 DoF nonlinear system is studied under parametric magnetic resonance condition. By deriving nonlinear response curves, effects of various parameters including magnetic excitation amplitude, parameter of excitation frequency and nonlocal stress parameter on resonance amplitude is investigated and discussed.

کلیدواژه‌ها [English]

  • Nonlinear vibrations
  • Fluid Conveying Microtube
  • Parametric Magnetic Resonance
  • Nonlocal Elastisity Theory
1. Paidoussis, M.P., Price, S.J. and De Langre, E., "Fluid-structure interactions: cross-flow-induced instabilities", Cambridge University Press, (2010).
2. Paidoussis, M.P. and Li, G.X., "Pipes conveying fluid: a model dynamical problem", Journal of Fluids and Structures, 7(2), pp. 137-204, (1993).
3. Sinha, J.K., Singh, S. and Rao, A.R., "Finite element simulation of dynamic behaviour of open-ended cantilever pipe conveying fluid", Journal of Sound and Vibration, 1(240): pp. 189-194, (2001).
4. Ansari, R., Norouzzadeh, A., Gholami, R., Shojaei, M. Faghih and Darabi, M. A. "Geometrically nonlinear free vibration and instability of fluid-conveying nanoscale pipes including surface stress effects", Microfluidics and Nanofluidics, 20(1), pp. 28, (2016).
5. Ansari, R., Norouzzadeh, A., Gholami, R., Shojaei, M. Faghih and Hosseinzadeh, M., "Size-dependent nonlinear vibration and instability of embedded fluid-conveying SWBNNTs in thermal environment", Physica E: Low-dimensional Systems and Nanostructures, 61, pp. 148-157, (2014).
6. Ghazavi, M.R. and Molki, H., "Nonlinear analysis of the micro/nanotube conveying fluid based on second strain gradient theory", Applied Mathematical Modelling, 60: pp. 77-93, (2018).
7. Ghazavi, M.-R., Rezazadeh, G. and Azizi, S., "Pure parametric excitation of a micro cantilever beam actuated by piezoelectric layers", Applied Mathematical Modelling, 34(12): pp. 4196-4207, (2010).
8. Eringen, A.C. and Edelen, D.G.B., "On nonlocal elasticity", International Journal of Engineering Science, 10(3), pp. 233-248, (1972).
9. Eringen, A.C., "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", Journal of Applied Physics, 54(9), pp. 4703-4710, (1983).
10. Lei, Y., Adhikari, S. and Friswell, M.I., "Vibration of nonlocal Kelvin–Voigt viscoelastic damped Timoshenko beams", International Journal of Engineering Science, 66, pp. 1-13, (2013).
11. Kiani, K., "Nanofluidic flow-induced longitudinal and transverse vibrations of inclined stocky single-walled carbon nanotubes", Computer Methods in Applied Mechanics and Engineering, 276, pp. 691-723, (2014).
12. Arani, A.G., Haghparast, E., Maraghi, Z. Khoddami and Amir, S., "Nonlocal vibration and instability analysis of embedded DWCNT conveying fluid under magnetic field with slip conditions consideration", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 229(2), pp. 349-363, (2015).
13. Sadeghi-Goughari, M., Jeon, S. and Kwon, H.-J., "Flutter instability of cantilevered carbon nanotubes caused by magnetic fluid flow subjected to a longitudinal magnetic field", Physica E: Low-dimensional Systems and Nanostructures, 98, pp. 184-190, (2018).
14. Bahaadini, R. and Hosseini, M., "Effects of nonlocal elasticity and slip condition on vibration and stability analysis of viscoelastic cantilever carbon nanotubes conveying fluid", Computational Materials Science, 114, pp. 151-159, (2016).
15. Bahaadini, R., Hosseini, M. and Jamali, B., "Flutter and divergence instability of supported piezoelectric nanotubes conveying fluid", Physica B: Condensed Matter, 529: pp. 57-65, (2018).
16. Yang, T.-Z., Ji, Sh., Yang, X.-D. and Fang, B., "Microfluid-induced nonlinear free vibration of microtubes", International Journal of Engineering Science, 76, pp. 47-55, (2014).
17. Saadatnia, Z. and Esmailzadeh, E. "Nonlinear harmonic vibration analysis of fluid-conveying piezoelectric-layered nanotubes", Composites Part B: Engineering, 123, pp. 193-209, (2017).
18. Yang, X., Yang, T. and Jin, J., "Dynamic stability of a beam-model viscoelastic pipe for conveying pulsative fluid", Acta Mechanica Solida Sinica, 20(4): pp. 350-356, (2007).
19. Arani, A.G., Amir, S., Dashti, P. and Yousefi, M., "Flow-induced vibration of double bonded visco-CNTs under magnetic fields considering surface effect", Computational Materials Science, 86, pp. 144-154, (2014).
20. Zhang, W., Yang, J. and Hao, Y., "Chaotic vibrations of an orthotropic FGM rectangular plate based on third-order shear deformation theory", Nonlinear Dynamics, 59(4), pp. 619-660, (2010).
21. Amabili, M. and Farhadi, S., "Shear deformable versus classical theories for nonlinear vibrations of rectangular isotropic and laminated composite plates", Journal of Sound and Vibration, 320(3), pp. 649-667, (2009).
22. Fu, Y.-m. and Ruan, J.-l., "Nonlinear active control of damaged piezoelectric smart laminated plates and damage detection", Applied Mathematics and Mechanics, 29(4): pp. 421-436, (2008).
23. Ghorbanpour Arani, A., Amir, S. and Karamali Ravandia, A. "Nonlinear flow-induced flutter instability of double CNTs using Reddy beam theory", Journal of Computational Applied Mechanics, 46(1): pp. 1-12, (2015).
24. Wang, L., "A modified nonlocal beam model for vibration and stability of nanotubes conveying fluid", Physica E: Low-dimensional Systems and Nanostructures, 44(1), pp. 25-28, (2011).
25. Eslami, H., "Nonlinear flutter and forced oscillations of rectangular symmetric cross-ply and orthotropic panels using harmonic balance and perturbation methods", Old Dominion University, (1987).
26. Onawola, O.O. and Sinha, S.C., "A feedback linearization approach for panel flutter suppression with piezoelectric actuation", Journal of Computational and Nonlinear Dynamics, 6(3), pp. 031006, (2011).
27. Guo, X.Y., Zhang, W. and Yao, M., "Nonlinear dynamics of angle-ply composite laminated thin plate with third-order shear deformation", Science China Technological Sciences, 53(3), pp. 612-622, (2010).
CAPTCHA Image