On stability of a slightly curved Maxwell viscoelastic pipe conveying fluid resting on linear viscoelastic foundation

References

• Amabili, M., and M. P. Païdoussis. 2003. “Review of Studies on Geometrically Nonlinear Vibrations and Dynamics of Circular Cylindrical Shells and Panels, with and without Fluid-structure Interaction.” Applied Mechanics Reviews 56. doi:10.1115/1.1565084.
   Google Scholar
• Chandra, P. K., and P. J. a. Sobral. 2000. “Calculation of Viscoelastic Properties of Edible Films: Application of Three Models.” Ciênciae Tecnologia de Alimentos 20: 250–256. doi:10.1590/s0101-20612000000200021.
   Google Scholar
• Chen, L. Q., and X. D. Yang. 2005. “Steady-state Response of Axially Moving Viscoelastic Beams with Pulsating Speed: Comparison of Two Nonlinear Models.” International Journal of Solids and Structures 42: 37–50. doi:10.1016/j.ijsolstr.2004.07.003.
   Web of Science ®Google Scholar
• Choi, J., O. Song, and S. K. Kim. 2013. “Nonlinear Stability Characteristics of Carbon Nanotubes Conveying Fluids.” Acta Mechanica 224: 1383–1396. doi:10.1007/s00707-013-0809-2.
   Web of Science ®Google Scholar
• Deng, J., Y. Liu, Z. Zhang, and W. Liu. 2017. “Stability Analysis of Multi-span Viscoelastic Functionally Graded Material Pipes Conveying Fluid Using a Hybrid Method.” European Journal of Mechanics A/Solids. 65: 257–270. doi:10.1016/j.euromechsol.2017.04.003.
   Web of Science ®Google Scholar
• Dodds, H. L., and H. L. Runyan. 1965. “Effect of High-Velocity Fluid Flow on the Bending Vibrations and Static Divergence of a Simply Supported Pipe.”
   Google Scholar
• Farokhi, H., M. H. Ghayesh, a. Gholipour, and M. Tavallaeinejad. 2017. “Nonlinear Oscillations of Viscoelastic Microplates.” International Journal of Engineering Science 118: 56–69. doi:10.1016/j.ijengsci.2017.05.006.
   Web of Science ®Google Scholar
• Farshbaf, R., Z. Mousa, and R. Saeed. 2019. “Nonlinear Vibration and Stability Analysis of Viscoelastic Rayleigh Beams Axially Moving on a Flexible Intermediate Support.” Iranian Journal of Sciience and Technolology Transaction of Mechanical Engineering doi:10.1007/s40997-019-00305-z.
   Web of Science ®Google Scholar
• Ghayesh, M. H., and H. Farokhi. 2018. “On the Viscoelastic Dynamics of Fluid-conveying Microtubes.” International Journal of Engineering Science 127: 186–200. doi:10.1016/j.ijengsci.2018.02.010.
   Web of Science ®Google Scholar
• Holmes, P. J. 1977. “Bifurcations to Divergence and Flutter in Flow-induced Oscillations: A Finite Dimensional Analysis.” Journal of Sound and Vibration 53: 471–503. doi:10.1016/0022-460X(77)90521-1.
   Web of Science ®Google Scholar
• Housner, G. W. 1952. “Bending Vibrations of a Pipe Line Containing Flowing Fluid.” ASME Journal of Applied Mechanics 19: 205–208.
   Web of Science ®Google Scholar
• Li, L., and Y. Hu. 2016. “Wave Propagation in Fluid-conveying Viscoelastic Carbon Nanotubes Based on Nonlocal Strain Gradient Theory.” Computational Material Science 112: 282–288. doi:10.1016/j.commatsci.2015.10.044.
   Web of Science ®Google Scholar
• Nematollahi, M. S., H. Mohammadi, and S. Taghvaei. 2019. “Fluttering and Divergence Instability of Functionally Graded Viscoelastic Nanotubes Conveying Fluid Based on Nonlocal Strain Gradient Theory.” Chaos 29: 1–11. doi:10.1063/1.5057738.
   Web of Science ®Google Scholar
• Orolu, K. O., T. a. Fashanu, and a. a. Oyediran. 2019. “Cusp Bifurcation of Slightly Curved Tensioned Pipe Conveying Hot Pressurized Fluid.” JVC/Journal Vibration and Control 25: 1109–1121. doi:10.1177/1077546318813401.
   Web of Science ®Google Scholar
• Owoseni, O. D., K. O. Orolu, and a. a. Oyediran. 2017. “Dynamics of Slightly Curved Pipe Conveying Hot Pressurized Fluid Resting on Linear and Nonlinear Viscoelastic Foundations.” Journal of Vibration and Acoustics 140: 021005. doi:10.1115/1.4037703.
   Web of Science ®Google Scholar
• Science, N., C. Phenomena, S. Zhou, G. Song, Z. Ren, and B. Wen. 2016. “Chaos, Solitons and Fractals Nonlinear Analysis of a Parametrically Excited Beam with Intermediate Support by Using Multi-dimensional Incremental Harmonic Balance Method.” Chaos, Solitons and Fractals 93: 207–222. doi:10.1016/j.chaos.2016.10.022.
   Web of Science ®Google Scholar
• Shepherd, T. N., J. Zhang, T. C. Ovaert, R. K. Roeder, and G. L. Niebur. 2011. “Direct Comparison of Nanoindentation and Macroscopic Measurements of Bone Viscoelasticity.” Journal of Mechanical Behavavior of Biomedical Material 4: 2055–2062. doi:10.1016/j.jmbbm.2011.07.004.
   PubMed Web of Science ®Google Scholar
• Sun, L. X., Y. J. Jian, L. Chang, H. Y. Zhang, and Q. S. Liu. 2013. “Alternating Current Electro-osmotic Flow of the Maxwell Fluids through a Circular Micro-Pipe.” Journal of Mechanics 29: 233–240. doi:10.1017/jmech.2012.138.
   Web of Science ®Google Scholar
• Tang, Y., Y. Zhen, and B. Fang. 2018. “Nonlinear Vibration Analysis of a Fractional Dynamic Model for the Viscoelastic Pipe Conveying Fluid.” Applied Mathematical Modelling. 56: 123–136. doi:10.1016/j.apm.2017.11.022.
   Web of Science ®Google Scholar
• Wang, Z., Z. Zhang, and F. Zhao. 2005. “Stability Analysis of Viscoelastic Curved Pipes Conveying Fluid.” Applied Mathematical Mechanics 26: 807-813.
   Google Scholar
• Wang, Z., F. Zhao, Z. Feng, and H. Liu. 2002. “Dynamic Behaviors of Non-conservative Viscoelastic Pipe Conveying Fluid.” Jixie Gongcheng Xuebao/Chinese Journal of Mechanical Engineering. doi:10.3901/jme.2002.04.017.
   Google Scholar
• Yang, B. F. T. Z. 2012. “Stability in Parametric Resonance of an Axially Moving Beam Constituted by a Fractional Differentiation Law.” Archieve of Applied Mechanics 82: 1763–1770. doi:10.1007/s00419-012-0624-6.
   Web of Science ®Google Scholar
• Yang, B. F. T. Z. 2013. “Asymptotic Analysis of an Axially Viscoelastic String Constituted by a Fractional Differentiation Law.” International Journal of Non-Linear Mechanics 49: 170–174. doi:10.1016/j.ijnonlinmec.2012.10.001.
   Web of Science ®Google Scholar
• Zhao, F. Q., Z. M. Wang, Z. Y. Feng, and H. Z. Liu. 2001. “Stability Analysis of Maxwell Viscoelastic Pipes Conveying Fluid with Both Ends Simply Supported.” Applied Mathematics and Mechanics (English Ed.) 22: 1436–1445. doi:10.1023/a:1022843012114.
   Google Scholar