Analysis of Nonlinear Vibration of Functionally Graded Simply Supported Fluid-Conveying Microtubes Subjected to Transverse Excitation Loads
Abstract
:1. Introduction
2. Motion Equation
3. Equation Solving
4. Results and Discussions
4.1. Influence of Volume Fraction on Vibration Characteristics of the Microtubes
4.2. Influence of Dimensionless Microscale Parameters on Vibration Characteristics of the Microtubes
4.3. Influence of Excitation Loads on Vibration Characteristics of the Microtubes
5. Conclusions
- (1)
- Changes in the power-law index of the volume fraction of functionally graded materials affect the effective bending stiffness of the materials. By choosing an appropriate power-law index, the stability of the microtubes can be improved. The larger the dimensionless microscale parameters, the worse the stability of the microtubes and the more disordered the motion trajectory.
- (2)
- The amplitude of excitation loads has a significant influence on the dynamic behavior of the microtubes. When the microtubes are in a steady state, the greater the amplitude of excitation loads, the greater the vibration displacement of the microtubes. Once the microtubes are unstable, the effect of the amplitude of excitation loads on the vibration displacement of the microtubes is almost negligible.
- (3)
- The frequency of excitation loads leads to microtube resonance. When the microtubes are in a steady state, and the frequency of excitation loads is close to or equal to the natural frequency of the microtubes, the vibration displacement of the microtubes increases significantly. Once the frequency of excitation loads deviates from the microtube’s natural frequency, its effect on the microtubes will be significantly reduced. When the microtubes are in an unstable state, the frequency of excitation loads will cause the instability of the microtubes to increase, and the vibration displacement will increase significantly, resulting in chaos for the microtubes.
- (4)
- The influence of transverse excitation loads on the stability of fluid-conveying microtubes is very great, especially the frequency of excitation loads. Therefore, the application of microtubes should avoid the effect of excitation loads.
Author Contributions
Funding
Conflicts of Interest
References
- Roudbari, M.A.; Jorshari, T.D.; Lü, C.; Ansari, R.; Kouzani, A.Z.; Amabili, M. A review of size-dependent continuum mechanics models for micro- and nano-structures. Thin-Walled Struct. 2022, 170, 108562. [Google Scholar] [CrossRef]
- Lukiyanets, B.A.; Matulka, D.V. Size effects of a nanoobject in magnetic field. Condens. Matter Phys. 2020, 22, 23704. [Google Scholar] [CrossRef]
- Cardoso, R.; Ferry, B.; Montebello, C.; Meriaux, J.; Pommier, S.; Araújo, J. Study of size effects in fretting fatigue. Tribol. Int. 2019, 143, 106087. [Google Scholar] [CrossRef]
- Hao, R.B.; Lu, Z.Q.; Ding, H.; Chen, L.Q. A nonlinear vibration isolator supported on a flexible plate: Analysis and experiment. Nonlinear Dyn. 2022, 108, 941–958. [Google Scholar] [CrossRef]
- Babaei, H. On frequency response of FG-CNT reinforced composite pipes in thermally pre/post buckled configurations. Compos. Struct. 2021, 276, 114467. [Google Scholar] [CrossRef]
- Babaei, H. Large deflection analysis of FG-CNT reinforced composite pipes under thermal-mechanical coupling loading. Structures 2021, 34, 886–900. [Google Scholar] [CrossRef]
- Babaei, H.; Eslami, M.R. Nonlinear analysis of thermal-mechanical coupling bending of clamped FG porous curved micro-tubes. J. Therm. Stress. 2021, 44, 409–432. [Google Scholar] [CrossRef]
- Yinusa, A.A.; Sobamowo, M.G.; Adelaja, A.O. Nonlinear vibration analysis of an embedded branched nanofluid-conveying carbon nanotubes: Influence of downstream angle, temperature change and two dimensional external magnetic field. Nano. Mater Sci. 2020, 2, 323–332. [Google Scholar] [CrossRef]
- Dini, A.; Zandi-Baghche-Maryam, A.; Shariati, M. Effects of van der Waals forces on hygro-thermal vibration and stability of fluid-conveying curved double-walled carbon nanotubes subjected to external magnetic field. Phys. E Low-Dimens. Syst. Nanostruct. 2019, 106, 156–169. [Google Scholar] [CrossRef]
- Mahmoudpour, E.; Esmaeili, M. Nonlinear free and forced vibration of carbon nanotubes conveying magnetic nanoflow and subjected to a longitudinal magnetic field using stress-driven nonlocal integral model. Thin-Walled Struct. 2021, 166, 108134. [Google Scholar] [CrossRef]
- Ninh, D.G.; Tien, N.D.; Hoang, V.N.T.; Bich, D.H. Vibration of cylindrical shells made of three layers W-Cu composite containing heavy water using Flügge-Lur’e-Bryrne theory. Thin. Wall Struct. 2019, 146, 106414. [Google Scholar] [CrossRef]
- Sadeghi-Goughari, M.; Jeon, S.; Kwon, H.-J. Fluid structure interaction of cantilever micro and nanotubes conveying magnetic fluid with small size effects under a transverse magnetic field. J. Fluids Struct. 2020, 94, 102951. [Google Scholar] [CrossRef]
- Tong, G.; Liu, Y.; Cheng, Q.; Dai, J. Stability analysis of cantilever functionally graded material nanotube under thermo-magnetic coupling effect. Eur. J. Mech. A Solids 2020, 80, 103929. [Google Scholar] [CrossRef]
- Lyu, Z.; Yang, Y.; Liu, H. High-accuracy hull iteration method for uncertainty propagation in fluid-conveying carbon nanotube system under multi-physical fields. Appl. Math. Model. 2019, 79, 362–380. [Google Scholar] [CrossRef]
- Cheng, Q.; Liu, Y.; Wang, G.; Liu, H.; Jin, M.; Li, R. Free vibration of a fluid-conveying nanotube constructed by carbon nanotube and boron nitride nanotube. Phys. E Low-Dimens. Syst. Nanostruct. 2019, 109, 183–190. [Google Scholar] [CrossRef]
- Bahaadini, R.; Saidi, A.R.; Hosseini, M. On dynamics of nanotubes conveying nanoflow. Int. J. Eng. Sci. 2018, 123, 181–196. [Google Scholar] [CrossRef]
- Ninh, D.G.; Tien, N.D. Investigation for electro-thermo-mechanical vibration of nanocomposite cylindrical shells with an internal fluid flow. Aerosp. Sci. Technol. 2019, 92, 501–519. [Google Scholar] [CrossRef]
- Ghayesh, M.H.; Farajpour, A.; Farokhi, H. Viscoelastically coupled mechanics of fluid-conveying microtubes. Int. J. Eng. Sci. 2019, 145, 103139. [Google Scholar] [CrossRef]
- Dehrouyeh-Semnani, A.M.; Zafari-Koloukhi, H.; Dehdashti, E.; Nikkhah-Bahrami, M. A parametric study on nonlinear flow-induced dynamics of a fluid-conveying cantilevered pipe in post-flutter region from macro to micro scale. Int. J. Non-Linear Mech. 2016, 85, 207–225. [Google Scholar] [CrossRef]
- Hosseini, M.; Bahaadini, R. Size dependent stability analysis of cantilever micro-pipes conveying fluid based on modified strain gradient theory. Int. J. Eng. Sci. 2016, 101, 1–13. [Google Scholar] [CrossRef]
- Hu, K.; Wang, Y.; Dai, H.; Wang, L.; Qian, Q. Nonlinear and chaotic vibrations of cantilevered micropipes conveying fluid based on modified couple stress theory. Int. J. Eng. Sci. 2016, 105, 93–107. [Google Scholar] [CrossRef]
- Guo, Y.; Xie, J.; Wang, L. Three-dimensional vibration of cantilevered fluid-conveying micropipes—Types of periodic motions and small-scale effect. Int. J. Non-Linear Mech. 2018, 102, 112–135. [Google Scholar] [CrossRef]
- Setoodeh, A.; Afrahim, S. Nonlinear dynamic analysis of FG micro-pipes conveying fluid based on strain gradient theory. Compos. Struct. 2014, 116, 128–135. [Google Scholar] [CrossRef]
- She, G.-L.; Yuan, F.-G.; Ren, Y.-R.; Liu, H.-B.; Xiao, W.-S. Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory. Compos. Struct. 2018, 203, 614–623. [Google Scholar] [CrossRef]
- Ma, T.; Mu, A. Study on the Stability of Functionally Graded Simply Supported Fluid-Conveying Microtube under Multi-Physical Fields. Micromachines 2022, 13, 895. [Google Scholar] [CrossRef]
- Guo, Y. Fluid-Induced Nonlinear Vibration of a Cantilevered Microtube with Symmetric Motion Constraints. Shock Vib. 2020, 2020, 8852357. [Google Scholar] [CrossRef]
- Sabahi, M.A.; Saidi, A.R.; Khodabakhsh, R. An analytical solution for nonlinear vibration of functionally graded porous micropipes conveying fluid in damping medium. Ocean Eng. 2022, 245, 110482. [Google Scholar] [CrossRef]
- Yuan, Y.; Zhao, X.; Zhao, Y.; Sahmani, S.; Safaei, B. Dynamic stability of nonlocal strain gradient FGM truncated conical microshells integrated with magnetostrictive facesheets resting on a nonlinear viscoelastic foundation. Thin-Walled Struct. 2020, 159, 107249. [Google Scholar] [CrossRef]
- Amiri, A.; Masoumi, A.; Talebitooti, R. Flutter and bifurcation instability analysis of fluid-conveying micro-pipes sandwiched by magnetostrictive smart layers under thermal and magnetic field. Int. J. Mech. Mater. Des. 2020, 16, 569–588. [Google Scholar] [CrossRef]
- Ghane, M.; Saidi, A.R.; Bahaadini, R. Vibration of fluid-conveying nanotubes subjected to magnetic field based on the thin-walled Timoshenko beam theory. Appl. Math. Model. 2020, 80, 65–83. [Google Scholar] [CrossRef]
- Zhu, B.; Chen, X.; Dong, Y.; Li, Y. Stability analysis of cantilever carbon nanotubes subjected to partially distributed tangential force and viscoelastic foundation. Appl. Math. Model. 2019, 73, 190–209. [Google Scholar] [CrossRef]
- Hołubowski, R.; Glabisz, W.; Jarczewska, K. Transverse vibration analysis of a single-walled carbon nanotube under a random load action. Phys. E Low-Dimens. Syst. Nanostruct. 2019, 109, 242–247. [Google Scholar] [CrossRef]
- Bahaadini, R.; Hosseini, M. Flow-induced and mechanical stability of cantilever carbon nanotubes subjected to an axial compressive load. Appl. Math. Model. 2018, 59, 597–613. [Google Scholar] [CrossRef]
- Bahaadini, R.; Hosseini, M.; Jamalpoor, A. Nonlocal and surface effects on the flutter instability of cantilevered nanotubes conveying fluid subjected to follower forces. Phys. B Condens. Matter 2017, 509, 55–61. [Google Scholar] [CrossRef]
- Zhu, B.; Xu, Q.; Li, M.; Li, Y. Nonlinear free and forced vibrations of porous functionally graded pipes conveying fluid and resting on nonlinear elastic foundation. Compos. Struct. 2020, 252, 112672. [Google Scholar] [CrossRef]
- Dehrouyeh-Semnani, A.M.; Nikkhah-Bahrami, M.; Yazdi, M.R.H. On nonlinear vibrations of micropipes conveying fluid. Int. J. Eng. Sci. 2017, 117, 20–33. [Google Scholar] [CrossRef]
- Selmi, A.; Hassis, H. Vibration analysis of post-buckled fluid-conveying functionally graded pipe. Compos. Part C Open Access 2021, 4, 100117. [Google Scholar] [CrossRef]
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Ma, T.; Mu, A. Analysis of Nonlinear Vibration of Functionally Graded Simply Supported Fluid-Conveying Microtubes Subjected to Transverse Excitation Loads. Micromachines 2022, 13, 2114. https://doi.org/10.3390/mi13122114
Ma T, Mu A. Analysis of Nonlinear Vibration of Functionally Graded Simply Supported Fluid-Conveying Microtubes Subjected to Transverse Excitation Loads. Micromachines. 2022; 13(12):2114. https://doi.org/10.3390/mi13122114
Chicago/Turabian StyleMa, Tao, and Anle Mu. 2022. "Analysis of Nonlinear Vibration of Functionally Graded Simply Supported Fluid-Conveying Microtubes Subjected to Transverse Excitation Loads" Micromachines 13, no. 12: 2114. https://doi.org/10.3390/mi13122114