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Thermoelastic vibration analysis of micro-scale functionally graded material fluid-conveying pipes in elastic medium

弹性介质中的微尺度功能梯度材料管热弹性振动分析

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Abstract

Micro-scale functionally graded material (FGM) pipes conveying fluid have many significant applications in engineering fields. In this work, the thermoelastic vibration of FGM fluid-conveying tubes in elastic medium is studied. Based on modified couple stress theory and Hamilton’s principle, the governing equation and boundary conditions are obtained. The differential quadrature method (DQM) is applied to investigating the thermoelastic vibration of the FGM pipes. The effect of temperature variation, scale effect of the microtubule, micro-fluid effect, material properties, elastic coefficient of elastic medium and outer radius on thermoelastic vibration of the FGM pipes conveying fluid are studied. The results show that in the condition of considering the scale effect and micro-fluid of the microtubule, the critical dimensionless velocity of the system is higher than that of the system which calculated using classical macroscopic model. The results also show that the variations of temperature, material properties, elastic coefficient and outer radius have significant influences on the first-order dimensionless natural frequency.

摘要

微尺度功能梯度材料输流微管在许多工程领域有着十分重要的应用价值。本文采用修正的偶应 力理论和哈密顿原理建立了振动方程,并通过微分求积法求解研究嵌入弹性介质的微尺度功能梯度材 料输流管的热弹性振动问题。综合考虑温度变化、微尺寸效应、微流体效应、材料属性变化、弹性基 体的弹性系数变化和管道外径变化对微尺度功能梯度材料输流管的热弹性振动影响。研究结果表明: 在考虑微尺度和微流体效应的情况下,系统的无量纲临界流速高于经典模型下的系统无量纲临界流 速;温度、材料属性、弹性基体的弹性系数、管道外径等因素的变化对系统的一阶固有频率都有显著 的影响。

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References

  1. PAIDOUSSIS M P, LI G X. Pipes conveying fluid: A model dynamical problem [J]. Journal of Fluids and Structures, 1993, 7(2): 137–204.

    Article  Google Scholar 

  2. CAGGIONI M, TRAINI D, YOUNG P M, SPICER P T. Microfluidic production of endoskeleton droplets with controlled size and shape [J]. Powder Technology, 2018, 329: 129–136.

    Article  Google Scholar 

  3. VALENCIA P M, FAROKHZAD O C, KARNIK R, LANGER R. Microfluidic technologies for accelerating the clinical translation of nanoparticles [J]. Nature Nanotechnology, 2012, 7(10): 623–629.

    Article  Google Scholar 

  4. ELVIRA K S, CASADEVALL X C I, WOOTTON R C R, DEMELLO A J. The past, present and potential for microfluidic reactor technology in chemical synthesis [J]. Nature Chemistry, 2013, 5(11): 905–915.

    Article  Google Scholar 

  5. YANG Hai-lin, LI Jing, FANG Hua-chan, ZHOU Zhong-cheng, TONG Xiao-yang, RUAN Jian-ming. Synthesis, characterization and biological activity in vitro of FeCrAl(f)/HA asymmetrical biological functionally gradient materials [J]. Journal of Central South University, 2014, 21(2): 447–453.

    Article  Google Scholar 

  6. MA Q, CLARKE D R. Size dependent hardness of silver single crystals [J]. Journal of Materials Research, 1995, 10(4): 853–863.

    Article  Google Scholar 

  7. CHONG A C M, LAM D C C. Strain gradient plasticity effect in indentation hardness of polymers [J]. Journal of Materials Research, 1999, 14(10): 4103–4110.

    Article  Google Scholar 

  8. LAM D C C, YANG F, CHONG A C M, WANG J, TONG P. Experiments and theory in strain gradient elasticity [J]. Journal of the Mechanics and Physics of Solids, 2003, 51(8): 1477–1508.

    Article  MATH  Google Scholar 

  9. MCFARLAND A W, COLTON J S. Role of material micro-structure in plate stiffness with relevance to microcantilever sensors [J]. Journal of Micromechanics and Microengineering, 2005, 15(5): 1060–1067.

    Article  Google Scholar 

  10. DENG J, LIU Y, LIU W. Size dependent vibration analysis of multi span functionally graded material micropipes conveying fluid using a hybrid method [J]. Microfluidics and Nanofluidics, 2017, 21(8): 1–15.

    Article  Google Scholar 

  11. XIA W, WANG L. Microfluid-induced vibration and stability of structures modelled as microscale pipes conveying fluid based on non-classical Timoshenko beam theory [J]. Microfluidics and Nanofluidics, 2010, 9(4, 5): 955–962.

    Article  Google Scholar 

  12. LIANG F, BAO R. Thermoelastic vibration of fluid-conveying microtubes embedded in elastic mediume [J]. Mechanics in Engineering, 2014, 36(6): 728–732.

    Google Scholar 

  13. NOROUZZADEH A, ANSARI R. Isogeometric vibration analysis of functionally graded nanoplates with the consideration of nonlocal and surface effects [J]. Thin-Walled Structures, 2018, 127: 354–372.

    Article  Google Scholar 

  14. ANSARI R, NOROUZZADEH A. Nonlocal and surface effects on the buckling behavior of functionally graded nanoplates: An isogeometric analysis [J]. Physica E: Low-dimensional Systems and Nanostructures, 2016, 84: 84–97.

    Article  Google Scholar 

  15. CHEN A, JIAN S. Dynamic behavior of axially functionally graded pipes conveying fluid [J]. Mathematical Problems in Engineering, 2017, 2017(1): 1–11.

    MathSciNet  Google Scholar 

  16. SHENG G G, WANG X. Dynamic characteristics of fluid-conveying functionally graded cylindrical shells under mechanical and thermal loads [J]. Composite Structures, 2011, 93(1): 162–170

    Article  Google Scholar 

  17. SOFIYEV A H, HUI D, HUI V C, ERDEM H, YUAN G Q, SCHNACK E, GULDAL V. The nonlinear vibration of orthotropic functionally graded cylindrical shells surrounded by an elastic foundation within first order shear deformation theory [J]. Composites Part B: Engineering, 2017, 116: 170–185.

    Article  Google Scholar 

  18. ZHANG Z, LIU Y, HAN T. Two parameters affecting the dynamics characteristics of a uniform conical assembled pipe conveying fluid [J]. Journal of Vibration and Control, 2017, 23(3): 361–372.

    Article  MathSciNet  Google Scholar 

  19. LI B, GAO H, LIU Y, YUE Z. Transient response analysis of multi span pipe conveying fluid [J]. Journal of Vibration and Control, 2013, 19(14): 2164–2176.

    Article  MathSciNet  Google Scholar 

  20. ANSARI R, GHOLAMI R, NOROUZZADEH A. Size-dependent thermo-mechanical vibration and instability of conveying fluid functionally graded nanoshells based on Mindlin’s strain gradient theory [J]. Thin-Walled Structures, 2016, 105: 172–184.

    Article  Google Scholar 

  21. ANSARI R, NOROUZZADEH A, GHOLAMI R, FAGHIHSHOJAEI M, HOSSEINZADEH M. Size-dependent nonlinear vibration and instability of embedded fluid-conveying SWBNNTs in thermal environment [J]. Physica E: Low-dimensional Systems and Nanostructures, 2014, 61: 148–157.

    Article  Google Scholar 

  22. ZHANG Y W, ZHOU L, FANG B, YANG T Z. Quantum effects on thermal vibration of single-walled carbon nanotubes conveying fluid [J]. Acta Mechanica Solida Sinica, 2017, 30(5): 550–556.

    Article  Google Scholar 

  23. ZHEN Y, FANG B. Thermal mechanical and nonlocal elastic vibration of single walled carbon nanotubes conveying fluid [J]. Computational Materials Science, 2010, 49(2): 276–282.

    Article  Google Scholar 

  24. ZHANG Z, LIU Y, ZHAO H, LIU W. Acoustic nanowave absorption through clustered carbon nanotubes conveying fluid [J]. Acta Mechanica Solida Sinica, 2016, 29(3): 257–270.

    Article  Google Scholar 

  25. ZHANG Z, LIU Y, ZHAO H, LIU W. Topology optimized vibration control of a fluid-conveying carbon nanotube with non-uniform magnetic field [J]. International Journal of Applied Mechanics, 2015, 7(6): 1550092.

    Article  Google Scholar 

  26. ANSARI R, GHOLAMI R, NOROUZZADEH A, SAHMANI S. Size-dependent vibration and instability of fluid-conveying functionally graded microshells based on the modified couple stress theory [J]. Microfluidics and Nanofluidics, 2015, 19(3): 509–522.

    Article  Google Scholar 

  27. SETOODEH A R, AFRAHIM S. Nonlinear dynamic analysis of FG micro-pipes conveying fluid based on strain gradient theory [J]. Composite Structures, 2014, 116(1): 128–135.

    Article  Google Scholar 

  28. YANG F, CHONG A C M, LAM D C C, TONG P. Couple stress based strain gradient theory for elasticity [J]. International Journal of Solids and Structures, 2002, 39(10): 2731–2743.

    Article  MATH  Google Scholar 

  29. REDDY J N. Microstructure-dependent couple stress theories of functionally graded beams [J]. Journal of the Mechanics and Physics of Solids, 2011, 59(11): 2382–2399.

    Article  MathSciNet  MATH  Google Scholar 

  30. ASGHARI M, AHMADIAN M T, KAHROBAIYAN M H, RAHAEIFARD M. On the size-dependent behavior of functionally graded microbeams [J]. Materials and Design, 2010, 31(5): 2324–2329.

    Article  Google Scholar 

  31. NATEGHI A, SALAMAT-TALAB M. Thermal effect on size dependent behavior of functionally graded microbeams based on modified couple stress theory [J]. Composite Structures, 2013, 96: 97–110.

    Article  Google Scholar 

  32. PAIDOUSSIS M P. Fluid-structure interaction: Slender structures and axial flow [M]. New York: Academic Press, 2014.

    Google Scholar 

  33. WANG L, LIU H T, NI Q, WU Y. Flexural vibrations of microscale pipes conveying fluid by considering the size effects of micro-flow and micro-structure [J]. International Journal of Engineering Science, 2013, 71(71): 92–101.

    Article  MathSciNet  MATH  Google Scholar 

  34. GUO C Q, ZHANG C H, PAIDOUSSIS M P. Modification of equation of motion of fluid-conveying pipe for laminar and turbulent flow profiles [J]. Journal of Fluids and Structures, 2010, 26(5): 793–803.

    Article  Google Scholar 

  35. KUTIN J, BAJSIC I. Fluid-dynamic loading of pipes conveying fluid with a laminar mean-flow velocity profile [J]. Journal of Fluids and Structures, 2014, 50: 171–183.

    Article  Google Scholar 

  36. WANG Yong-liang. Differential quadrature method and differential quadrature element method—Theory and application [D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2001. (in Chinese)

    Google Scholar 

  37. ZHEN Ya-xin. Investigation on the dynamical behavior of carbon nanotubes conveying fluid [D]. Harbin: Harbin Institute of Technology, 2012. (in Chinese)

    Google Scholar 

  38. FUNG T C. Imposition of boundary conditions by modifying the weighting coefficient matrices in the differential quadrature method [J]. International Journal of Numerical Mathematic Engineering, 2003, 56(3): 405–432.

    Article  MathSciNet  MATH  Google Scholar 

  39. XU Yang-jian, ZHANG Jing-jun, TU Dai-hui. Transient thermal stress analysis of functionally gradient material plate with temperature-dependent material properties under convective heat transfer boundary [J]. Chinese Journal of Mechanical Engineering, 2005, 41(7): 198–204. (in Chinese)

    Article  Google Scholar 

  40. WANG L. Size-dependent vibration characteristics of fluid-conveying microtubes [J]. Journal of Fluids and Structures, 2010, 26(4): 675–684.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, 710129, China

    Guo-jun Tong  (仝国军), Yong-shou Liu  (刘永寿), Hui-chao Liu  (刘会超) & Jia-yin Dai  (戴嘉茵)

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  1. Guo-jun Tong  (仝国军)
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  2. Yong-shou Liu  (刘永寿)
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  3. Hui-chao Liu  (刘会超)
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  4. Jia-yin Dai  (戴嘉茵)
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Correspondence to Yong-shou Liu  (刘永寿).

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Tong, Gj., Liu, Ys., Liu, Hc. et al. Thermoelastic vibration analysis of micro-scale functionally graded material fluid-conveying pipes in elastic medium. J. Cent. South Univ. 26, 2785–2796 (2019). https://doi.org/10.1007/s11771-019-4213-5

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