Nonlinear size-dependent dynamic instability and local bifurcation of FG nanotubes transporting oscillatory fluids
doi: 10.1007/s10409-021-09075-x
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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.
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Key words:
- Size-dependent effect /
- Slip flow /
- Fluid-conveying nanotube /
- Dynamic instability /
- Bifurcation
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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.
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