تأثیر جریان سیال بر پاسخ دینامیکی وابسته به اندازه میکروتیرهای یکسر گیردار‌ با استفاده از تئوری‌‌‌ گرادیان کرنشی اصلاح شده و تئوری تیر تغییر شکل‌پذیر برشی هایپربولیک

نوع مقاله : گرایش دینامیک، ارتعاشات و کنترل

نویسندگان

1 دانشجوی دکتری، گروه مهندسی مکانیک، واحد لاهیجان، دانشگاه آزاد اسلامی، لاهیجان، ایران

2 نویسنده مسئول: استادیار، گروه مهندسی مکانیک، واحد لاهیجان، دانشگاه آزاد اسلامی، لاهیجان، ایران

3 استادیار، گروه مهندسی مکانیک، واحد لنگرود، دانشگاه آزاد اسلامی، لنگرود، ایران

4 استادیار، گروه مهندسی مکانیک، واحد لاهیجان، دانشگاه آزاد اسلامی، لاهیجان، ایران

چکیده

در این تحقیق، به مطالعه تحلیلی ارتعاشات القایی ناشی از جریان سیال در میکروتیرهای یکسرگیردار پرداخته شده است. معادلات حاکم بر حرکت بر اساس تئوری تیر هایپربولیک و در نظر گرفتن اندرکنش بین سازه و سیال استخراج شده است. به منظور در نظر گرفتن اثر اندازه‌های کوچک از تئوری گرادیان کرنش بهبود یافته استفاده شده است. هدف اصلی این مطالعه نشان دادن میزان تأثیر جریان سیال بر رفتار دینامیکی میکروتیرها می‌باشد. معادلات حرکت با استفاده از روش گالرکین گسسته‌سازی شده و سپس با روش حل عددی جواب معادلات به دست آمده است. با بی‌بعدسازی معادلات، پاسخ دینامیکی سیستم و منحنی‌های دامنه-سرعت جریان سیال به ازای مقادیر مختلف پارامتر اندازه‌های کوچک و سرعت جریان سیال استخراج و تأثیر این پارامترها بر رفتار دینامیکی سیستم مطالعه شده است. نتایج نشان می‌دهد که استفاده از تئوری تیر هایپربولیک نتایج دقیق‌تری نسبت به تئوری تیر‌های کلاسیک تیر اویلر-برنولی و تیموشنکو در اختیار می‌گذارد. مشاهده می‌شود که ناحیه قفل‌شدگی و حداکثر دامنه به وجود آمده در میکروتیر برای سه تئوری تحت بررسی متفاوت می‌باشد. همچنین، تئوری اویلر-برنولی فرکانس‌های طبیعی را بیشتر از دو تئوری دیگر پیش‌بینی می‌کند که علت آن صرف‌نظر کردن از اینرسی دورانی سطح مقطع تیر می‌باشد. تئوری تیر تیموشنکو فرکانس‌های نوسانات را بیشتر از تئوری تیر هایپربولیک پیش‌بینی می‌کند ولی به ازای مقادیر بزرگتر طول، فرکانس طبیعی دو تئوری تیر تیموشنکو و تیر هایپربولیک تقریباً برهم منطبق می‌شوند.

کلیدواژه‌ها


عنوان مقاله [English]

Fluid Flow Effects on Size-dependent Dynamic Response of Cantilever Microbeams using Modified Strain Gradient and Hyperbolic Shear Deformation Beam Theory

نویسندگان [English]

  • Babak Ramazani Darvazi 1
  • Javad Rezapour 2
  • Saeed Rouhi 3
  • Raheb Gholami 4
1 Ph.D. Student, Faculty of Mechanical Engineering, Lahijan Branch, Islamic Azad University, Lahijan, Iran
2 Corresponding author: Assistant Professor, Faculty of Mechanical Engineering, Lahijan Branch, Islamic Azad University, Lahijan, Iran
3 Assistant Professor, Faculty of Mechanical Engineering, Lahijan Branch, Islamic Azad University, Lahijan, Iran
4 Assistant Professor, Faculty of Mechanical Engineering, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
چکیده [English]

An analytical study on fluid induced dynamics of cantilever microbeam is presented in this paper. Modified strain gradient theory has been used to consider the effect of small sizes. By considering the interaction between structure and fluid, the governing equations of motion are derived from hyperbolic beam theory. Governing equations of motion are discretized with the Galerkin method, and then the solution is found numerically. The dynamic response of the system and the amplitude-velocity curves of the fluid flow at different values of small size parameters and fluid flow velocity are determined and the effects of these parameters are examined. The results show that the hyperbolic beam theory provides more accurate results than classical Euler-Bernoulli and Timoshenko beam theories. Each of the three theories exhibits different lock-in regions and maximum amplitudes of the microbeam. It is also relevant to note that Euler-Bernoulli's theory predicts natural frequencies more than the other two theories, which ignores the rotational inertia of the beam's cross-section. Timoshenko beam theory predicts higher oscillation frequencies than hyperbolic beam theory, however, when the length is increased, the natural frequencies for the two theories are almost identical.

کلیدواژه‌ها [English]

  • Microbeam
  • Fluid-Induced Vibration
  • Hyperbolic Beam Theory
  • Natural Frequency

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[1] Borisenkov Y, Kholmyansky M, Krylov S, Liberzon A, Tsinober A. Multiarray micromachined probe for turbulence measurements assembled of suspended hot-film sensors. Journal of Microelectromechanical Systems. 2015;24(5):1503-9.##
[2] Tavakol B, Holmes DP. Voltage-induced buckling of dielectric films using fluid electrodes. Applied Physics Letters. 2016;108(11):112-31.##
[3] Gad-el-Hak M. Advances in fluid mechanics measurements: Springer Science & Business Media; 2013.##
[4] Gardner EL, Vincent TA, Jones RG, Gardner JW, Coull J, De Luca A, et al. MEMS thermal flow sensors—An accuracy investigation. IEEE Sensors Journal. 2019;19(8):2991-8.##
[5] Ejeian F, Azadi S, Razmjou A, Orooji Y, Kottapalli A, Warkiani ME, et al. Design and applications of MEMS flow sensors: A review. Sensors and Actuators A: Physical. 2019;295:483-502.##
[6] Tang Y, Li J, Xu L, Lee J-B, Xie H. Review of Electrothermal Micromirrors. Micromachines. 2022;13(3):429-42.##
[7] Pourreza T, Alijani A, Maleki VA, Kazemi A. Nonlinear vibration of nanosheets subjected to electromagnetic fields and electrical current. Advances in nano research. 2021;10(5):481-91.##
[8] Jahanghiry R, Yahyazadeh R, Sharafkhani N, Maleki VA. Stability analysis of FGM microgripper subjected to nonlinear electrostatic and temperature variation loadings. Science and Engineering of Composite Materials. 2016;23(2):199-207.##
[9] Mirtalebi H, Ebrahimi Mamaghani A. On the Vibrational Analysis of Cantilevered Fluid Conveying Micro-Beams Rested on Various Elastic Foundations. Amirkabir Journal of Mechanical Engineering. 2020;52(1):3-16.##
[10] Bakhsheshy A, Mahbadi H. The effect of accuracy of the length scale parameter on natural frequencies of porous rectangular microplate. Amirkabir Journal of Mechanical Engineering. 2021;53(Issue 2 (Special Issue)):1179-96.##
[11] Mousavi SMJ, Sharifi P, Mohammadi H. Analysis of Static Pull-in Instability and Nonlinear Vibrations of an Functionally Graded Micro-Resonator Beam. Amirkabir Journal of Mechanical Engineering. 2019;51(1):119-32.##
[12] Ajri M, Seyyed Fakhrabadi MM, Asemani H. Viscoelastic effects on nonlinear dynamics of microplates with fluid interaction based on consistent couple stress theory. Journal of Computational Applied Mechanics. 2021;52(3):394-407.##
[13] Ajri M, Seyyed Fakhrabadi MM. Nonlinear free vibration of viscoelastic nanoplates based on modified couple stress theory. Journal of Computational Applied Mechanics. 2018;49(1):44-53.##
[14] Rouhi S, Xiros N, Aktosun E, Sultan C, VanZwieten J, Ioup J, et al., editors. A Small-Scale Experimental Ocean Current Turbine Apparatus for Power Measurement. ASME International Mechanical Engineering Congress and Exposition; 2021: American Society of Mechanical Engineers.##
[15] Mirtalebi SH, Ebrahimi-Mamaghani A, Ahmadian MT. Vibration control and manufacturing of intelligibly designed axially functionally graded cantilevered macro/micro-tubes. IFAC-PapersOnLine. 2019;52(10):382-7.##
[16] Ebrahimi-Mamaghani A, Sotudeh-Gharebagh R, Zarghami R, Mostoufi N. Thermo-mechanical stability of axially graded Rayleigh pipes. Mechanics Based Design of Structures and Machines. 2020:1-30.##
[17] Han SM, Benaroya H, Wei T. Dynamics of transversely vibrating beams using four engineering theories. Journal of Sound and vibration. 1999;225(5):935-88.##
[18] Younis MI, Nayfeh A. A study of the nonlinear response of a resonant microbeam to an electric actuation. Nonlinear Dynamics. 2003;31(1):91-117.##
[19] Brenes A, Juillard J, Dos Santos FV. Resonant pull-in of high-Q MEMS oscillators with arbitrary closed-loop phase shift. Procedia Engineering. 2016;168:941-5.##
[20] Andakhshideh A, Maleki S, Marashi SS. Investigation of nonlinear pull-in phenomena in functionally graded micro-beams under electrostatic excitation. Journal of Solid and Fluid Mechanics. 2018;8(3):137-51.##
[21] Gorthi S, Mohanty A, Chatterjee A. Cantilever beam electrostatic MEMS actuators beyond pull-in. Journal of Micromechanics and Microengineering. 2006;16(9):1800.##
[22] Batra RC, Porfiri M, Spinello D. Electromechanical model of electrically actuated narrow microbeams. Journal of Microelectromechanical systems. 2006;15(5):1175-89.##
[23] Nikpourian A, Ghazavi MR. Nonlinear Size-Dependent Analysis of an Initially Curved Microbeam. Modares Mechanical Engineering. 2019;19(2):247-58.##
[24] Najar F, Ghommem M, Abdelkefi A. A double-side electrically-actuated arch microbeam for pressure sensing applications. International Journal of Mechanical Sciences. 2020;178:105624.##
[25] Fallah M, Arab Maleki V. Renewable Energy Harvesting by Vortex-Induced Vibration of Bimorph Porous Beam with Piezoelectric Layer. Amirkabir Journal of Mechanical Engineering. 2021;53(8):9-24.##
[26] Ghommem M, Najar F, Arabi M, Abdel-Rahman E, Yavuz M. A unified model for electrostatic sensors in fluid media. Nonlinear Dynamics. 2020;101(1):271-91.##
[27] Li H, Ke L, Yang J, Kitipornchai S. Size-dependent free vibration of microbeams submerged in fluid. International Journal of Structural Stability and Dynamics. 2020;20(12):205-16.##
[28] Naik T, Longmire EK, Mantell SC. Dynamic response of a cantilever in liquid near a solid wall. Sensors and Actuators A: physical. 2003;102(3):240-54.##
[29] Chon JW, Mulvaney P, Sader JE. Experimental validation of theoretical models for the frequency response of atomic force microscope cantilever beams immersed in fluids. Journal of applied physics. 2000;87(8):3978-88.##
[30] Korayem MH, Sharahi HJ. Analysis of the effect of mechanical properties of liquid and geometrical parameters of cantilever on the frequency response function of AFM. The International Journal of Advanced Manufacturing Technology. 2011;57(5-8):477-89.##
[31] Golzar FG, Shabani R, Hatami H, Rezazadeh G. Dynamic response of an electrostatically actuated micro-beam in an incompressible viscous fluid cavity. Journal of Microelectromechanical Systems. 2013;23(3):555-62.##
[32] Jabbari G, Shabani R, Rezazadeh G. Nonlinear vibrations of an electrostatically actuated microresonator in an incompressible fluid cavity based on the modified couple stress theory. Journal of Computational and Nonlinear Dynamics. 2016;11(4):041029.##
[33] Mentzoni F, Kristiansen T. Numerical modeling of perforated plates in oscillating flow. Applied Ocean Research. 2019;84:1-11.##
[34] Rezaee M, Sharafkhani N. Electrostatically frequency tunable micro-beam-based piezoelectric fluid flow energy harvester. Smart Materials and Structures. 2017;26(7):075008.##
[35] Najar F, Ghommem M, Abdel-Rahman E. Arch microbeam bifurcation gas sensors. Nonlinear Dynamics. 2021;104(2):923-40.##
[36] Nasrabadi M, Sevbitov AV, Maleki VA, Akbar N, Javanshir I. Passive fluid-induced vibration control of viscoelastic cylinder using nonlinear energy sink. Marine Structures. 2022;81:103116.##
[37] Rezaee M, Sharafkhani N. Out-of-plane vibration of an electrostatically actuated microbeam immersed in flowing fluid. Nonlinear Dynamics. 2020;102(1):1-17.##
[[38] Ansari R, Gholami R, Sahmani S. Size-dependent vibration of functionally graded curved microbeams based on the modified strain gradient elasticity theory. Archive of Applied Mechanics. 2013;83(10):1439-49.##
[39] Fleck N, Hutchinson J. Strain gradient plasticity (advances in applied mechanics), Vol. 33. Elsevier, New York; 1997.##
[40] Wang YQ, Zhao HL, Ye C, Zu JW. A porous microbeam model for bending and vibration analysis based on the sinusoidal beam theory and modified strain gradient theory. International Journal of Applied Mechanics. 2018;10(05):1850059.##
[41] Lam DC, Yang F, Chong A, Wang J, Tong P. Experiments and theory in strain gradient elasticity. Journal of the Mechanics and Physics of Solids. 2003;51(8):1477-508.##
[42] Akgöz B, Civalek Ö. Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams. Composites Part B: Engineering. 2017;129:77-87.##
[43] Mantari J, Soares CG. Analysis of isotropic and multilayered plates and shells by using a generalized higher-order shear deformation theory. Composite Structures. 2012;94(8):2640-56.##
[44] Mahi A, Tounsi A. A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates. Applied Mathematical Modelling. 2015;39(9):2489-508.##
[45] Nguyen TN, Thai CH, Nguyen-Xuan H. On the general framework of high order shear deformation theories for laminated composite plate structures: A novel unified approach. International Journal of Mechanical Sciences. 2016;110:242-55.##
[46] Facchinetti ML, De Langre E, Biolley F. Coupling of structure and wake oscillators in vortex-induced vibrations. Journal of Fluids and structures. 2004;19(2):123-40.##
[47] Ciappi E, De Rosa S, Franco F, Guyader J-L, Hambric SA. Flinovia-Flow Induced Noise and Vibration Issues and Aspects: Springer; 2015.##
[48] Kong S, Zhou S, Nie Z, Wang K. Static and dynamic analysis of micro beams based on strain gradient elasticity theory. International Journal of Engineering Science. 2009;47(4):487-98.##
[49] Osterberg PM. Electrostatically actuated microelectromechanical test structures for material property measurement: Massachusetts Institute of Technology; 1995.##
[50] Shu C, Du H. Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates. International Journal of Solids and Structures. 1997;34(7):819-35.##
[51] Singh SS, Nair DK, Rajagopal A, Pal P, Pandey AK. Dynamic analysis of microbeams based on modified strain gradient theory using differential quadrature method. European Journal of Computational Mechanics. 2018;27(3):187-203.##
[52] Li Z, He Y, Zhang B, Lei J, Guo S, Liu D. Experimental investigation and theoretical modelling on nonlinear dynamics of cantilevered microbeams. European Journal of Mechanics-A/Solids. 2019;78:103834.##
دوره 18، شماره 3 - شماره پیاپی 69
شماره پیاپی 69، فصلنامه پاییز
مهر 1401
صفحه 53-68
  • تاریخ دریافت: 08 اردیبهشت 1401
  • تاریخ بازنگری: 20 خرداد 1401
  • تاریخ پذیرش: 24 تیر 1401
  • تاریخ انتشار: 01 مهر 1401