Semi-Analytical Study of Fluid-Induced Nonlinear Vibrations in Viscoelastic Beams with Standard Linear Solid Model Using Multiple Time Scales Method

Document Type : Research Article

Authors

1 Assistant Professor, Department of Mechanical engineering, Guilan University, Rasht, Iran,

2 PhD candidate, Department of Mechanical engineering, Guilan University, Rasht, Iran

Abstract

In this research, the behavior of nonlinear vibrations of the viscoelastic Euler-Bernoulli beam under the influence of external fluid flow has been studied. The governing equations of motion are obtained by assuming Von-Karman nonlinear strain-displacement relations and considering the interaction between structure and fluid. To consider more realistic hypotheses, contrary to previous researches, the effect of viscoelastic behavior has been evaluated using a more complete and practical model called the Standard linear solid model. After non-dimensionalizing the motion equations, the governing nonlinear differential equations are discretized using the Galerkin method. Then, the system's analytical response is acquired through the method of multiple time scales. After verifying the results and confirming the semi-analytical method's accuracy with the numerical solution results, different parameters' effect on the system's dynamic behavior has been analyzed. The results indicate that the viscoelastic behavior and the nonlinear model significantly affect the lock-in area and the maximum amplitude of the viscoelastic beam vibrations. In most studies on viscoelastic beams' vibrations, the damping effect in nonlinear terms has been neglected. However, this study demonstrates that the effect of damping on terms related to the nonlinearity of strain fields is substantial.

Keywords

Main Subjects


[1] M. Minaei, M. Rezaee, V. Arab Maleki, Vibration Analysis of Viscoelastic Carbon Nanotube under Electromagnetic Fields based on the Nonlocal Timoshenko Beam Theory, Iranian Journal of Mechanical Engineering, 22(3) (2020) 54-76.
[2] E. Carrera, M. Filippi, P. Mahato, A. Pagani, Free-vibration tailoring of single-and multi-bay laminated box structures by refined beam theories, Thin-Walled Structures, 109 (2016) 40-49.
[3] H. Asadi, M. Aghdam, Large amplitude vibration and post-buckling analysis of variable cross-section composite beams on nonlinear elastic foundation, International Journal of Mechanical Sciences, 79 (2014) 47-55.
[4] S.H. Mirafzal, A.M. Khorasani, A.H. Ghasemi, Optimizing time delay feedback for active vibration control of a cantilever beam using a genetic algorithm, Journal of Vibration and Control, 22(19) (2016) 4047-4061.
[5] E. Özkaya, M. Pakdemirli, Non-linear vibrations of a beam–mass system with both ends clamped, Journal of Sound and Vibration, 221(3) (1999) 491-503.
[6] M. Salehi, F. Ansari, Viscoelastic buckling of Euler-Bernoulli and Timoshenko beams under time variant general loading conditions, Iranian Polymer Journal, 15(3) (2006) 183-193.
[7] M.H. Ghayesh, F. Alijani, M.A. Darabi, An analytical solution for nonlinear dynamics of a viscoelastic beam-heavy mass system, Journal of Mechanical Science and Technology, 25(8) (2011) 1915-1923.
[8] L.-Y. Xiong, G.-C. Zhang, H. Ding, L.-Q. Chen, Nonlinear forced vibration of a viscoelastic buckled beam with 2: 1 internal resonance, Mathematical Problems in Engineering, 2014 (2014).
[9] E. Naudascher, D. Rockwell, Flow-induced vibrations: an engineering guide, Courier Corporation, 2012.
[10] M. Rezaee, V. Arab maleki, Passive Vibration Control of Fluid Conveying Pipes using Dynamic Vibration Absorber, Amirkabir Journal of Mechanical Engineering, 51(3) (2019) 111-120.
[11] M. Rezaee, V. Arab Maleki, A new analytical method to investigate the vibrational behavior of fluid embedded pipe, Iranian Journal of Mechanical Engineering 15(1) (2013) 6-20.
[12] T. Sarpkaya, A critical review of the intrinsic nature of vortex-induced vibrations, Journal of Fluids and Structures, 19(4) (2004) 389-447.
[13] J.-s. Wang, D. Fan, K. Lin, A review on flow-induced vibration of offshore circular cylinders, Journal of Hydrodynamics, 32(3) (2020) 415-440.
[14] K.-S. Hong, U.H. Shah, Vortex-induced vibrations and control of marine risers: A review, Ocean Engineering, 152 (2018) 300-315.
[15] A. Khan, Numerical simulation of vortex induced vibration and related parameters in cross flow shell and tubes heat exchanger: a review, Tech J Univ Eng Technol Taxila, 34 (2014) 45-67.
[16] C. Williamson, R. Govardhan, Vortex-induced vibrations, Annu. Rev. Fluid Mech., 36 (2004) 413-455.
[17] M. Horowitz, C. Williamson, Vortex-induced vibration of a rising and falling cylinder, Journal of Fluid Mechanics, 662 (2010) 35-46.
[18] P. Bearman, Circular cylinder wakes and vortex-induced vibrations, Journal of Fluids and Structures, 27(5) (2011) 648-658.
[19] R. Bourguet, G.E. Karniadakis, M.S. Triantafyllou, Phasing mechanisms between the in-line and cross-flow vortex-induced vibrations of a long tensioned beam in shear flow, Computers & Structures, 122 (2013) 155-163.
[20] X. Wu, F. Ge, Y. Hong, A review of recent studies on vortex-induced vibrations of long slender cylinders, Journal of Fluids and Structures, 28 (2012) 292-308.
[21] A.M. Marra, C. Mannini, G. Bartoli, Measurements and improved model of vortex-induced vibration for an elongated rectangular cylinder, Journal of Wind Engineering and Industrial Aerodynamics, 147 (2015) 358-367.
[22] X. Han, W. Lin, Y. Tang, C. Zhao, K. Sammut, Effects of natural frequency ratio on vortex-induced vibration of a cylindrical structure, Computers & Fluids, 110 (2015) 62-76.
[23] S.J. Daniels, I.P. Castro, Z.-T. Xie, Numerical analysis of freestream turbulence effects on the vortex-induced vibrations of a rectangular cylinder, Journal of Wind Engineering and Industrial Aerodynamics, 153 (2016) 13-25.
[24] X. Jiang, Y. Andreopoulos, T. Lee, Z. Wang, Numerical investigations on the vortex-induced vibration of moving square cylinder by using incompressible lattice Boltzmann method, Computers & Fluids, 124 (2016) 270-277.
[25] W. Wang, B. Song, Z. Mao, W. Tian, T. Zhang, P. Han, Numerical investigation on vortex-induced vibration of bluff bodies with different rear edges, Ocean Engineering, 197 (2020) 23-45.
[26] P.K. Sahoo, S. Chatterjee, Nonlinear dynamics of vortex-induced vibration of a nonlinear beam under high-frequency excitation, International Journal of Non-Linear Mechanics, 129 (2021) 123-143.
[27] R.S. Lakes, Viscoelastic materials, Cambridge University Press, 2009.
[28] N. Heymans, J.-C. Bauwens, Fractal rheological models and fractional differential equations for viscoelastic behavior, Rheologica Acta, 33(3) (1994) 210-219.
[29] M.L. Facchinetti, E. De Langre, F. Biolley, Coupling of structure and wake oscillators in vortex-induced vibrations, Journal of Fluids and structures, 19(2) (2004) 123-140.
[30] M. Keber, M. Wiercigroch, Dynamics of a vertical riser with weak structural nonlinearity excited by wakes, Journal of Sound and Vibration, 315(3) (2008) 685-699.
[31] E. Ciappi, S. De Rosa, F. Franco, J.-L. Guyader, S.A. Hambric, Flinovia-Flow Induced Noise and Vibration Issues and Aspects, Springer, 2015.
[32] H. Dai, L. Wang, Q. Qian, Q. Ni, Vortex-induced vibrations of pipes conveying fluid in the subcritical and supercritical regimes, Journal of Fluids and Structures, 39 (2013) 322-334.