Nonlinear size-dependent dynamic instability and local bifurcation of FG nanotubes transporting oscillatory fluids
doi: 10.1007/s10409-021-09075-x
-
摘要: 流体流动的振荡可能会引起纳米管的动态失稳, 这在纳米机电系统的设计中应得到重视. 文章研究了输流纳米管在传输谐波脉动流时的非线性动力失稳. 纳米管由两个功能梯度材料表面层和一个黏弹性夹层组成. 基于Gurtin-Murdoch的表面弹性理论和非局部应变梯度理论, 建立了考虑表面效应的非局部应变梯度模型. 此外, 纳米流体的尺寸依赖性由滑移流模型建立. 采用两步摄动-伽辽金截断-增量谐波平衡(IHB)方法得到了稳定边界, 并与采用Bolotin方法得到的线性解进行了比较. 此外, 采用龙格-库塔法绘制了稳定边界内外的幅频分岔曲线. 结果揭示了非局部应力、应变梯度、表面弹性和滑移流对响应的影响. 结果表明, 由IHB方法得到的稳定边界表示从高频到低频扫频时的两个分岔点. 不同的是, 当从低频向高频扫频时, 存在一个迟滞边界, 在该边界处会发生振幅突跳.Abstract: Oscillation of fluid flow may cause the dynamic instability of nanotubes, which should be valued in the design of nanoelectromechanical systems. Nonlinear dynamic instability of the fluid-conveying nanotube transporting the pulsating harmonic flow is studied. The nanotube is composed of two surface layers made of functionally graded materials and a viscoelastic interlayer. The nonlocal strain gradient model coupled with surface effect is established based on Gurtin-Murdoch’s surface elasticity theory and nonlocal strain gradient theory. Also, the size-dependence of the nanofluid is established by the slip flow model. The stability boundary is obtained by the two-step perturbation-Galerkin truncation-Incremental harmonic balance (IHB) method and compared with the linear solutions by using Bolotin’s method. Further, the Runge-Kutta method is utilized to plot the amplitude-frequency bifurcation curves inside/outside the region. Results reveal the influence of nonlocal stress, strain gradient, surface elasticity and slip flow on the response. Results also suggest that the stability boundary obtained by the IHB method represents two bifurcation points when sweeping from high frequency to low frequency. Differently, when sweeping to high frequency, there exists a hysteresis boundary where amplitude jump will occur.
-
Key words:
- Size-dependent effect /
- Slip flow /
- Fluid-conveying nanotube /
- Dynamic instability /
- Bifurcation
-
2. Comparison of the natural frequency under different steady flow velocities with Ref. [33].
4. Instability boundary, amplitude-frequency bifurcation diagram and phase diagrams in different parameter intervals.
5. Effects of slip flow on the instability boundary and amplitude-frequency bifurcation curve.
-
[1] H. M. Sedighi, Divergence and flutter instability of magneto-thermo-elastic C-BN hetero-nanotubes conveying fluid, Acta Mech. Sin. 36, 381 (2020). [2] M. R. Zarastvand, M. Ghassabi, and R. Talebitooti, Prediction of acoustic wave transmission features of the multilayered plate constructions: a review, J. Sandwich Struct. Mater. 24, 218 (2022). [3] H. Darvishgohari, M. R. Zarastvand, R. Talebitooti, and R. Shahbazi, Hybrid control technique for vibroacoustic performance analysis of a smart doubly curved sandwich structure considering sensor and actuator layers, J. Sandwich Struct. Mater. 23, 1453 (2021). [4] R. Ansari, R. Gholami, A. Norouzzadeh, and M. A. Darabi, Surface stress effect on the vibration and instability of nanoscale pipes conveying fluid based on a size-dependent Timoshenko beam model, Acta Mech. Sin. 31, 708 (2015). [5] B. Hu, J. Liu, Y. Wang, B. Zhang, and H. Shen, Wave propagation in graphene reinforced piezoelectric sandwich nanoplates via high-order nonlocal strain gradient theory, Acta Mech. Sin. 37, 1446 (2021). [6] W. M. Zhang, and L. Zuo, Vibration energy harvesting: from micro to macro scale, Acta Mech. Sin. 36, 555 (2020). [7] M. H. Ghayesh, H. Farokhi, and A. Farajpour, Global dynamics of fluid conveying nanotubes, Int. J. Eng. Sci. 135, 37 (2019). [8] F. Liang, A. Gao, X. F. Li, and W. D. Zhu, Nonlinear parametric vibration of spinning pipes conveying fluid with varying spinning speed and flow velocity, Appl. Math. Model. 95, 320 (2021). [9] D. Zhao, J. Liu, and C. Q. Wu, Stability and local bifurcation of parameter-excited vibration of pipes conveying pulsating fluid under thermal loading, Appl. Math. Mech.-Engl. Ed. 36, 1017 (2015). [10] Y. F. Zhang, M. H. Yao, W. Zhang, and B. C. Wen, Dynamical modeling and multi-pulse chaotic dynamics of cantilevered pipe conveying pulsating fluid in parametric resonance, Aerospace Sci. Tech. 68, 441 (2017). [11] L. Wang, A further study on the non-linear dynamics of simply supported pipes conveying pulsating fluid, Int. J. Non-Linear Mech. 44, 115 (2009). [12] A. R. Askarian, H. Haddadpour, R. D. Firouz-Abadi, and H. Abtahi, Nonlinear dynamics of extensible viscoelastic cantilevered pipes conveying pulsatile flow with an end nozzle, Int. J. Non-Linear Mech. 91, 22 (2017). [13] X. Tan, and H. Ding, Parametric resonances of Timoshenko pipes conveying pulsating high-speed fluids, J. Sound Vib. 485, 115594 (2020). [14] Q. Li, W. Liu, K. Lu, and Z. Yue, Three-dimensional parametric resonance of fluid-conveying pipes in the pre-buckling and post-buckling states, Int. J. Pressure Vessels Piping 189, 104287 (2021). [15] T. Jiang, H. Dai, and L. Wang, Three-dimensional dynamics of fluid-conveying pipe simultaneously subjected to external axial flow, Ocean Eng. 217, 107970 (2020). [16] L. Wang, T. L. Jiang, and H. L. Dai, Three-dimensional dynamics of supported pipes conveying fluid, Acta Mech. Sin. 33, 1065 (2017). [17] Y. D. Li, and Y. R. Yang, Nonlinear vibration of slightly curved pipe with conveying pulsating fluid, Nonlinear Dyn 88, 2513 (2017). [18] Q. Ni, M. Tang, Y. Wang, and L. Wang, In-plane and out-of-plane dynamics of a curved pipe conveying pulsating fluid, Nonlinear Dyn 75, 603 (2014). [19] L. Lü, Y. Hu, X. Wang, L. Ling, and C. Li, Dynamical bifurcation and synchronization of two nonlinearly coupled fluid-conveying pipes, Nonlinear Dyn 79, 2715 (2015). [20] V. V. Bolotin, and H. L. Armstrong, The dynamic stability of elastic systems, Am. J. Phys. 33, 752 (1965). [21] C. Pierre, and E. H. Dowell, A study of dynamic instability of plates by an extended incremental harmonic balance method, J. Appl. Mech. 52, 693 (1985). [22] Y. Fu, J. Zhong, X. Shao, and C. Tao, Analysis of nonlinear dynamic stability for carbon nanotube-reinforced composite plates resting on elastic foundations, Mech. Adv. Mater. Struct. 23, 1284 (2016). [23] J. Yoon, C. Q. Ru, and A. Mioduchowski, Flow-induced flutter instability of cantilever carbon nanotubes, Int. J. Solids Struct. 43, 3337 (2006). [24] F. Zheng, Y. Lu, and A. Ebrahimi-Mamaghani, Dynamical stability of embedded spinning axially graded micro and nanotubes conveying fluid, Waves Random Complex Media 1 (2020). [25] H. A. Esmaeili, M. Khaki, an M. Abbasi, Dynamic instability response in nanocomposite pipes conveying pulsating ferrofluid flow considering structural damping effects, Struct. Eng. Mech. 68 , 359 (2018)[26] M. H. Ghayesh, A. Farajpour, and H. Farokhi, Effect of flow pulsations on chaos in nanotubes using nonlocal strain gradient theory, Commun. Nonlinear Sci. Numer. Simul. 83, 105090 (2020). [27] F. Liang, and Y. Su, Stability analysis of a single-walled carbon nanotube conveying pulsating and viscous fluid with nonlocal effect, Appl. Math. Model. 37, 6821 (2013). [28] R. Bahaadini, M. Hosseini, and M. Amiri, Dynamic stability of viscoelastic nanotubes conveying pulsating magnetic nanoflow under magnetic field, Eng. Comput. 37, 2877 (2021). [29] R. Bahaadini, A. R. Saidi, and M. Hosseini, Dynamic stability of fluid-conveying thin-walled rotating pipes reinforced with functionally graded carbon nanotubes, Acta Mech. 229, 5013 (2018). [30] M. R. Zarastvand, M. Ghassabi, and R. Talebitooti, A review approach for sound propagation prediction of plate constructions, Arch. Computat. Methods Eng. 28, 2817 (2021). [31] M. R. Zarastvand, M. Ghassabi, and R. Talebitooti, Acoustic insulation characteristics of shell structures: a review, Arch. Computat. Methods Eng. 28, 505 (2021). [32] M. H. Jalaei, A. G. Arani, and H. Nguyen-Xuan, Investigation of thermal and magnetic field effects on the dynamic instability of FG Timoshenko nanobeam employing nonlocal strain gradient theory, Int. J. Mech. Sci. 161-162, 105043 (2019). [33] Q. Jin, Y. Ren, H. Jiang, and L. Li, A higher-order size-dependent beam model for nonlinear mechanics of fluid-conveying FG nanotubes incorporating surface energy, Compos. Struct. 269, 114022 (2021). [34] P. Zhang, and Y. Fu, A higher-order beam model for tubes, Eur. J. Mech.-A Solids 38, 12 (2013). [35] C. W. Lim, G. Zhang, and J. N. Reddy, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, J. Mech. Phys. Solids 78, 298 (2015). [36] M. E. Gurtin, and A. Ian Murdoch, A continuum theory of elastic material surfaces, Arch. Rational Mech. Anal. 57, 291 (1975). [37] L. Lu, X. Guo, and J. Zhao, On the mechanics of Kirchhoff and Mindlin plates incorporating surface energy, Int. J. Eng. Sci. 124, 24 (2018). [38] J. Dai, Y. Liu, and G. Tong, Stability analysis of a periodic fluid-conveying heterogeneous nanotube system, Acta Mech. Solid Sin. 33, 756 (2020). [39] A. Amiri, R. Talebitooti, and L. Li, Wave propagation in viscous-fluid-conveying piezoelectric nanotubes considering surface stress effects and Knudsen number based on nonlocal strain gradient theory, Eur. Phys. J. Plus 133, 1 (2018). [40] M. Sadeghi-Goughari, and M. Hosseini, The effects of non-uniform flow velocity on vibrations of single-walled carbon nanotube conveying fluid, J. Mech. Sci. Technol. 29, 723 (2015). [41] A. Farajpour, H. Farokhi, M. H. Ghayesh, and S. Hussain, Nonlinear mechanics of nanotubes conveying fluid, Int. J. Eng. Sci. 133, 132 (2018). [42] Y. Ren, L. Li, Q. Jin, L. Nie, and F. Peng, Vibration and snap-through of fluid-conveying graphene reinforced composite pipes under low-velocity impact, AIAA J 59, 5091 (2021). -
下载:
点击查看大图
图(8) / 表(1)
计量
- 文章访问数: 45
- HTML全文浏览量: 43
- PDF下载量: 0
- 被引次数: 0
京公网安备 11010502036328号 京ICP备17033152号