ارتعاشات غیرخطی لوله‌های حامل سیال تقویت شده با گرافن

نوع مقاله : مقاله پژوهشی

نویسندگان

بخش مهندسی مکانیک، دانشکده فنی و مهندسی، دانشگاه شهید باهنر کرمان، کرمان، ایران

چکیده

در این مطالعه ارتعاشات غیرخطی لوله‌های حامل سیال از جنس مواد مرکب چند لایه تقویت شده با صفحات گرافن با تکیه‌گاه ساده در دو انتها و بر اساس مدل تیر اویلر-برنولی به صورت تحلیلی مورد تحقیق قرار گرفته است. لایه‌های تشکیل‌دهنده دیواره لوله به صورت ترکیبی از مواد پلیمری و صفحات گرافن در نظر گرفته شده‌ و میزان تقویت‌کنندگی صفحات گرافن به صورت لایه‌ای در جهت ضخامت دیواره لوله تغییر می‌کند. چهار الگوی مختلف توزیع صفحات تقویت‌کننده گرافن در راستای ضخامت لوله، تغییر شکل‌های بزرگ و میدان کرنش غیرخطی ون-کارمن در نظر گرفته ‌شده است. معادلات غیرخطی حاکم به کمک اصل هامیلتون استخراج، با روش گالرکین به معادله دیفرانسیل معمولی تبدیل شده و با روش تحلیلی آنالیز هوموتوپی حل می‌گردد. تغییرات اولین فرکانس طبیعی غیرخطی سیستم بر حسب تغییرات دامنه اولیه، سرعت سیال عبوری، چگالی سیال عبوری و طول لوله و همچنین پاسخ زمانی ارتعاشات غیرخطی سیستم برای الگوهای مختلف توزیع صفحات گرافن شامل V، X، O و U ارائه و مورد تحلیل قرار می‌گیرد. نتایج نشان می‌دهد اولین فرکانس طبیعی غیرخطی سیستم برای تمامی الگوهای توزیع صفحات گرافن با افزایش سرعت سیال، چگالی سیال و همچنین طول لوله، کاهش یافته اما با افزایش دامنه اولیه سیستم افزایش می‌یابد و همچنین الگوی توزیع V طی تغییر پارامترهای مورد بررسی بیشترین فرکانس‌ غیرخطی را نسبت به سه الگوی توزیع دیگر دارا می‌باشد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Nonlinear Vibrations of Graphene Reinforced Pipes Conveying Fluid

نویسندگان [English]

  • Rasoul Khodabakhsh
  • Ali Reza Saidi
  • Reza Bahaadini
Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
چکیده [English]

In this study, nonlinear vibrations of simply-supported pipes conveying fluid made of multilayer graphene reinforced composite materials have been investigated analytically and based on the Euler-Bernoulli beam theory. The constituent layers of the pipe wall thickness are considered to be made of polymer and graphene platelets and the reinforcing graphene platelets are varied by layers in the pipe wall thickness direction. Four different patterns for distribution of reinforcing graphene platelets, large deformations, and Von-Karman nonlinear strain field are considered. The nonlinear governing equations are derived by the Hamilton principle, they are converted to the ordinary differential equations by the Galerkin method and then are solved analytically using the homotopy analysis method. The variations of the first nonlinear natural frequency of the system with respect to the variation of initial amplitude, fluid velocity, fluid density, pipe length, and also time response of the nonlinear vibrations of the system are presented for different distribution patterns V, X, O and U of the graphene platelets. The results show that the first nonlinear natural frequency of the system for all distribution patterns of graphene platelets is decreased by an increase of pipe length, fluid velocity, and density but increasing the initial amplitude increases the first nonlinear natural frequency and also the distribution pattern V has the highest nonlinear frequency comparing with the other distribution patterns.

کلیدواژه‌ها [English]

  • Pipes conveying fluid
  • Nonlinear vibrations
  • Homotopy analysis method
  • Functionally graded materials
  • Graphene platelets

مراجع

[1] R. Ibrahim, Overview of mechanics of pipes conveying fluids—Part I: Fundamental studies, Journal of Pressure Vessel Technology, 132(3) (2010) 034001.
[2] R. Bahaadini, A.R. Saidi, M. Hosseini, On dynamics of nanotubes conveying nanoflow, International Journal of Engineering Science, 123 (2018) 181-196.
[3] R. Bahaadini, A.R. Saidi, Stability analysis of thin-walled spinning reinforced pipes conveying fluid in thermal environment, European Journal of Mechanics-A/Solids, 72 (2018) 298-309.
[4] T. El-Sayed, H. El-Mongy, Free vibration and stability analysis of a multi-span pipe conveying fluid using exact and variational iteration methods combined with transfer matrix method, Applied Mathematical Modelling, 71 (2019) 173-193.
[5] T. Jiang, Z. Liu, H. Dai, L. Wang, F. He, Nonplanar multi-modal vibrations of fluid-conveying risers under shear cross flows, Applied Ocean Research, 88 (2019) 187-209.
[6] R. Bahaadini, A.R. Saidi, M. Hosseini, Flow-induced vibration and stability analysis of carbon nanotubes based on the nonlocal strain gradient Timoshenko beam theory, Journal of Vibration and Control, 25(1) (2019) 203-218.
[7] S. Sazesh, S. Shams, Vibration analysis of cantilever pipe conveying fluid under distributed random excitation, Journal of Fluids and Structures, 87 (2019) 84-101.
[8] M. Ghane, A.R. Saidi, R. Bahaadini, Vibration of Fluid-Conveying Nanotubes Subjected to Magnetic Field Based on the Thin-Walled Timoshenko Beam Theory, Applied Mathematical Modelling,  (2019).
[9] M. Paıdoussis, C. Semler, Nonlinear dynamics of a fluid-conveying cantilevered pipe with an intermediate spring support, Journal of Fluids and Structures, 7(3) (1993) 269-298.
[10] T. Monprapussorn, S. Chucheepsakul, T. Huang, The coupled radial–axial deformations analysis of flexible pipes conveying fluid, International journal for numerical methods in engineering, 59(11) (2004) 1399-1452.
[11] W. Lin, N. Qiao, Nonlinear dynamics of a fluid-conveying curved pipe subjected to motion-limiting constraints and a harmonic excitation, Journal of Fluids and Structures, 24(1) (2008) 96-110.
[12] Y. Modarres-Sadeghi, M. Païdoussis, Nonlinear dynamics of extensible fluid-conveying pipes, supported at both ends, Journal of Fluids and Structures, 25(3) (2009) 535-543.
[13] X.-Y. Mao, H. Ding, L.-Q. Chen, Steady-state response of a fluid-conveying pipe with 3: 1 internal resonance in supercritical regime, Nonlinear Dynamics, 86(2) (2016) 795-809.
[14] G. Peng, Y. Xiong, Y. Gao, L. Liu, M. Wang, Z. Zhang, Non-linear dynamics of a simply supported fluid-conveying pipe subjected to motion-limiting constraints: Two-dimensional analysis, Journal of Sound and Vibration, 435 (2018) 192-204.
[15] X. Tan, H. Ding, L.-Q. Chen, Nonlinear frequencies and forced responses of pipes conveying fluid via a coupled Timoshenko model, Journal of Sound and Vibration, 455 (2019) 241-255.
[16] A. Abdelbaki, M. Païdoussis, A. Misra, A nonlinear model for a hanging cantilevered pipe discharging fluid with a partially-confined external flow, International Journal of Non-Linear Mechanics, 118 (2020) 103290.
[17] M. Kheiri, Nonlinear dynamics of imperfectly-supported pipes conveying fluid, Journal of Fluids and Structures, 93 (2020) 102850.
[18] P. Shahali, H. Haddadpour, S.A.H. Kordkheili, Nonlinear dynamics of viscoelastic pipes conveying fluid placed within a uniform external cross flow, Applied Ocean Research, 94 (2020) 101970.
[19] Y. Tang, T. Yang, Post-buckling behavior and nonlinear vibration analysis of a fluid-conveying pipe composed of functionally graded material, Composite Structures, 185 (2018) 393-400.
[20] A.M. Dehrouyeh-Semnani, E. Dehdashti, M.R.H. Yazdi, M. Nikkhah-Bahrami, Nonlinear thermo-resonant behavior of fluid-conveying FG pipes, International Journal of Engineering Science, 144 (2019) 103141.
[21] R.S. Reddy, S. Panda, A. Gupta, Nonlinear dynamics of an inclined FG pipe conveying pulsatile hot fluid, International Journal of Non-Linear Mechanics, 118 (2020) 103276.
[22] R. Khodabakhsh, A.R. Saidi, R. Bahaadini, An analytical solution for nonlinear vibration and post-buckling of functionally graded pipes conveying fluid considering the rotary inertia and shear deformation effects, Applied Ocean Research, 101 (2020) 102277.
[23] S. Stankovich, D.A. Dikin, G.H. Dommett, K.M. Kohlhaas, E.J. Zimney, E.A. Stach, R.D. Piner, S.T. Nguyen, R.S. Ruoff, Graphene-based composite materials, nature, 442(7100) (2006) 282-286.
[24] S. Villar-Rodil, J.I. Paredes, A. Martínez-Alonso, J.M. Tascón, Preparation of graphene dispersions and graphene-polymer composites in organic media, Journal of Materials Chemistry, 19(22) (2009) 3591-3593.
[25] J. Yang, H. Wu, S. Kitipornchai, Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams, Composite Structures, 161 (2017) 111-118.
[26] H. Mojiri, S.J. Salami, Free vibration and dynamic transient response of functionally graded composite beams reinforced with graphene nanoplatelets (GPLs) resting on elastic foundation in thermal environment, Mechanics Based Design of Structures and Machines,  (2020) 1-21.
[27] M. Song, Y. Gong, J. Yang, W. Zhu, S. Kitipornchai, Nonlinear free vibration of cracked functionally graded graphene platelet-reinforced nanocomposite beams in thermal environments, Journal of Sound and Vibration, 468 (2020) 115115.
[28] R. Bahaadini, A.R. Saidi, Aeroelastic analysis of functionally graded rotating blades reinforced with graphene nanoplatelets in supersonic flow, Aerospace Science and Technology, 80 (2018) 381-391.
[29] A.R. Saidi, R. Bahaadini, K. Majidi-Mozafari, On vibration and stability analysis of porous plates reinforced by graphene platelets under aerodynamical loading, Composites Part B: Engineering, 164 (2019) 778-799.
[30] C. Li, Q. Han, Z. Wang, X. Wu, Analysis of wave propagation in functionally graded piezoelectric composite plates reinforced with graphene platelets, Applied Mathematical Modelling, 81 (2020) 487-505.
[31] A. Shariati, S. Qaderi, F. Ebrahimi, A. Toghroli, On buckling characteristics of polymer composite plates reinforced with graphene platelets, Engineering with Computers,  (2020) 1-12.
[32] Y. Wang, C. Feng, Z. Zhao, F. Lu, J. Yang, Torsional buckling of graphene platelets (GPLs) reinforced functionally graded cylindrical shell with cutout, Composite Structures, 197 (2018) 72-79.
[33] V.N. Viet Hoang, N.D. Tien, D.G. Ninh, V.T. Thang, D.V. Truong, Nonlinear dynamics of functionally graded graphene nanoplatelet reinforced polymer doubly-curved shallow shells resting on elastic foundation using a micromechanical model, Journal of Sandwich Structures & Materials,  (2020) 1099636220926650.
[34] J. Wang, F. Song, Y. Ding, M. Shao, The incorporation of graphene to enhance mechanical properties of polypropylene self-reinforced polymer composites, Materials & Design, 195 (2020) 109073.
[35] L. Ainsworth, Fibre-reinforced plastic pipes and applications, Composites, 12(3) (1981) 185-190.
[36] H. Derek, An introduction to composite materials, Cambridge University Press, 1981.
[37] B. Harris, Engineering composite materials,  (1999).
[38] J.H. Affdl, J. Kardos, The Halpin‐Tsai equations: a review, Polymer Engineering & Science, 16(5) (1976) 344-352.
[39] S.-J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, Ph. D. Thesis, Shanghai Jiao Tong University Shanghai, 1992.
[40] S. Liao, Beyond perturbation: introduction to the homotopy analysis method, Chapman and Hall/CRC, 2003.
نشریه مهندسی مکانیک امیرکبیر
دوره 53، شماره 8
آبان 1400
صفحه 4483-4500

فایل ها

هم رسانی

ارجاع به این مقاله

آمار