On the Vibrational Analysis of Cantilevered Fluid Conveying Micro-Beams Rested on Various Elastic Foundations

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran

2 Mechanical Engineering department, Tarbiat Modares University, Tehran, Iran

Abstract

 In this research, using modified couple stress theory, dynamic stability of a cantilevered fluid conveying beam embedded in several types of surrounded elastic media has been studied. The governing equation for lateral vibrations of the micro-tube conveying fluid is derived using the extended Hamilton’s principle. The numerical results are obtained by employing the extended Galerkin’s method. For the sake of validation, the acquired results for simple cases are compared and outcomes indicate a very good agreement with those of previous studies available in the literature. The stability diagrams of different configurations with different flow velocities are studied and the effects of various factors such as material length scale, external diameter and different elastic properties on the stability of the system are considered. Results indicate that elastic surrounding media may enlarge the stability regions significantly at larger values of mass ratio parameter while decrease it for smaller values of mass ratio parameter. Furthermore, using elastic media mathematically defined by series functions provides the capability to simulate almost any real time operational environment the micro-tube embedded in and results in an optimal stability state of the micro-structure carrying fluid flow.

Keywords

Main Subjects


[1] H. Ashley, G. Haviland, Bending vibrations of a pipe line containing flowing fluid, Journal of Applied Mechanics-Transactions of the ASME, 17(3) (1950) 229-232.
[2] T.B. Benjamin, Dynamics of a system of articulated pipes conveying fluid-I. Theory, Proc. R. Soc. Lond. A, 261(1307) (1962) 457-486.
[3] M.P. Paidoussis, Fluid-structure interactions: slender structures and axial flow, Academic press, 1998.
[4] M. Paidoussis, Dynamics of tubular cantilevers conveying fluid, Journal of Mechanical Engineering Science, 12(2) (1970) 85-103.
[5] A.A. Bhirde, V. Patel, J. Gavard, G. Zhang, A.A. Sousa, A. Masedunskas, R.D. Leapman, R. Weigert, J.S. Gutkind, J.F. Rusling, Targeted killing of cancer cells in vivo and in vitro with EGF-directed carbon nanotube-based drug delivery, ACS nano, 3(2) (2009) 307-316.
[6] W. Xia, L. Wang, Microfluid-induced vibration and stability of structures modeled as microscale pipes conveying fluid based on non-classical Timoshenko beam theory, Microfluidics and Nanofluidics, 9(4-5) (2010) 955-962.
[7] L.-L. Ke, Y.-S. Wang, Flow-induced vibration and instability of embedded double-walled carbon nanotubes based on a modified couple stress theory, Physica E: Low-dimensional Systems and Nanostructures, 43(5) (2011) 1031-1039.
[8] T.-Z. Yang, S. Ji, X.-D. Yang, B. Fang, Microfluid-induced nonlinear free vibration of microtubes, International Journal of Engineering Science, 76 (2014) 47-55.
[9] M. Mohammadimehr, A. Mohammadi-Dehabadi, Z.K. Maraghi, The effect of non-local higher order stress to predict the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow, Physica B: Condensed Matter, 510 (2017) 48-59.
[10] A.W. McFarland, J.S. Colton, Role of material microstructure in plate stiffness with relevance to microcantilever sensors, Journal of Micromechanics and Microengineering, 15(5) (2005) 1060.
[11] R.D. Mindlin, Micro-structure in linear elasticity, Archive for Rational Mechanics and Analysis, 16(1) (1964) 51-78.
[12] F. Yang, A. Chong, D.C.C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39(10) (2002) 2731-2743.
[13] S. Park, X. Gao, Bernoulli–Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering, 16(11) (2006) 2355.
[14] L. Wang, Size-dependent vibration characteristics of fluid-conveying microtubes, Journal of Fluids and Structures, 26(4) (2010) 675-684.
[15] R. Bahaadini, A.R. Saidi, M. Hosseini, On dynamics of nanotubes conveying nanoflow, International Journal of Engineering Science, 123 (2018) 181-196.
[16] S. Ahangar, G. Rezazadeh, R. Shabani, G. Ahmadi, A. Toloei, On the stability of a microbeam conveying fluid considering modified couple stress theory, International Journal of Mechanics and Materials in Design, 7(4) (2011) 327.
[17] R. Ansari, R. Gholami, A. Norouzzadeh, S. Sahmani, Size-dependent vibration and instability of fluid-conveying functionally graded microshells based on the modified couple stress theory, Microfluidics and nanofluidics, 19(3) (2015) 509-522.
[18] H. Zeighampour, Y.T. Beni, Size-dependent vibration of fluid-conveying double-walled carbon nanotubes using couple stress shell theory, Physica E: Low-dimensional Systems and Nanostructures, 61 (2014) 28-39.
[19] A.G. Arani, M. Bagheri, R. Kolahchi, Z.K. Maraghi, Nonlinear vibration and instability of fluid-conveying DWBNNT embedded in a visco-Pasternak medium using modified couple stress theory, Journal of Mechanical Science and Technology, 27(9) (2013) 2645-2658.
[20] A.C. Eringen, D. Edelen, On nonlocal elasticity, International Journal of Engineering Science, 10(3) (1972) 233-248.
[21] R. Bahaadini, M. Hosseini, Nonlocal divergence and flutter instability analysis of embedded fluid-conveying carbon nanotube under magnetic field, Microfluidics and Nanofluidics, 20(7) (2016) 108.
[22] M. Hosseini, R. Bahaadini, Size dependent stability analysis of cantilever micro-pipes conveying fluid based on modified strain gradient theory, International Journal of Engineering Science, 101 (2016) 1-13.
[23] L. Yin, Q. Qian, L. Wang, Strain gradient beam model for dynamics of microscale pipes conveying fluid, Applied Mathematical Modelling, 35(6) (2011) 2864-2873.
[24] I. Lottati, A. Kornecki, The effect of an elastic foundation and of dissipative forces on the stability of fluid-conveying pipes, Journal of Sound Vibration, 109 (1986) 327-338.
[25] P. Djondjorov, V. Vassilev, V. Dzhupanov, Dynamic stability of fluid conveying cantilevered pipes on elastic foundations, in, Academic Press, 2001.
[26] J. Yoon, C. Ru, A. Mioduchowski, Flow-induced flutter instability of cantilever carbon nanotubes, International Journal of Solids and Structures, 43(11-12) (2006) 3337-3349.
[27] A.M. Dehrouyeh-Semnani, M. Nikkhah-Bahrami, M.R.H. Yazdi, On nonlinear vibrations of micropipes conveying fluid, International Journal of Engineering Science, 117 (2017) 20-33.
[28] A.E. Mamaghani, S. Khadem, S. Bab, Vibration control of a pipe conveying fluid under external periodic excitation using a nonlinear energy sink, Nonlinear Dynamics, 86(3) (2016) 1761-1795.
[29] A.E. Mamaghani, S.E. Khadem, S. Bab, S.M. Pourkiaee, Irreversible passive energy transfer of an immersed beam subjected to a sinusoidal flow via local nonlinear attachment, International Journal of Mechanical Sciences, 138 (2018) 427-447.
[30] R. Hosseini, M. Hamedi, A. Ebrahimi Mamaghani, H.C. Kim, J. Kim, J. Dayou, Parameter identification of partially covered piezoelectric cantilever power scavenger based on the coupled distributed parameter solution, International Journal of Smart and Nano Materials, 8(2-3) (2017) 110-124.
[31] M.A. Khorshidi, The material length scale parameter used in couple stress theories is not a material constant, International Journal of Engineering Science, 133 (2018) 15-25.