Nonlinear vibration analysis of pipeline considering the effects of soft nonlinear clamp

doi:10.1007/s10483-022-2903-7

Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (10): 1555-1568.doi: https://doi.org/10.1007/s10483-022-2903-7

Nonlinear vibration analysis of pipeline considering the effects of soft nonlinear clamp

Weijiao CHEN¹, Yiming CAO¹, Xumin GUO¹, Hui MA^1,2, Bangchun WEN¹, Bo WANG¹

1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China;
2. Key Laboratory of Vibration and Control of Aero-Propulsion Systems Ministry of Education of China, Northeastern University, Shenyang 110819, China

收稿日期:2022-01-11 修回日期:2022-08-10 发布日期:2022-10-25
通讯作者: Hui MA, E-mail: mahui 2007@163.com
基金资助:
the National Natural Science Foundation of China (No. 11972112), the Fundamental Research Funds for the Central Universities of China (Nos. N2103024 and N2003014), and the National Science and Technology Major Project of China (No. J2019-I-0008-0008)

Nonlinear vibration analysis of pipeline considering the effects of soft nonlinear clamp

Weijiao CHEN¹, Yiming CAO¹, Xumin GUO¹, Hui MA^1,2, Bangchun WEN¹, Bo WANG¹

1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China;
2. Key Laboratory of Vibration and Control of Aero-Propulsion Systems Ministry of Education of China, Northeastern University, Shenyang 110819, China

Received:2022-01-11 Revised:2022-08-10 Published:2022-10-25
Contact: Hui MA, E-mail: mahui 2007@163.com
Supported by:
the National Natural Science Foundation of China (No. 11972112), the Fundamental Research Funds for the Central Universities of China (Nos. N2103024 and N2003014), and the National Science and Technology Major Project of China (No. J2019-I-0008-0008)

摘要/Abstract

摘要： Soft nonlinear support is a major engineering project, but there are few relevant studies. In this paper, a dynamic pipeline model with soft nonlinear supports at both ends is established. By considering the influence of the Coriolis force and centrifugal force, the dynamical coupling equation of fluid-structure interaction is derived with extended Hamilton's principle. Then, the approximate analytical solutions are sought via the harmonic balance method. The amplitude-frequency response curves show that different effects can be determined by approximate analysis. It is demonstrated that the increase in the fluid velocity can increase the amplitude of the pipeline system. The frequency range of unstable response increases when the fluid pressure raises. The combination of the soft nonlinear clamp and the large geometrical deformation of the pipeline affects the nonlinear vibration characteristic of the system, and the external excitation force and damping have significant effects on the stability.

关键词: clamp soft nonlinear support, harmonic balance method, fluid-structure interaction, pipeline vibration analysis

Abstract: Soft nonlinear support is a major engineering project, but there are few relevant studies. In this paper, a dynamic pipeline model with soft nonlinear supports at both ends is established. By considering the influence of the Coriolis force and centrifugal force, the dynamical coupling equation of fluid-structure interaction is derived with extended Hamilton's principle. Then, the approximate analytical solutions are sought via the harmonic balance method. The amplitude-frequency response curves show that different effects can be determined by approximate analysis. It is demonstrated that the increase in the fluid velocity can increase the amplitude of the pipeline system. The frequency range of unstable response increases when the fluid pressure raises. The combination of the soft nonlinear clamp and the large geometrical deformation of the pipeline affects the nonlinear vibration characteristic of the system, and the external excitation force and damping have significant effects on the stability.

Key words: clamp soft nonlinear support, harmonic balance method, fluid-structure interaction, pipeline vibration analysis

中图分类号:

74H45

Weijiao CHEN, Yiming CAO, Xumin GUO, Hui MA, Bangchun WEN, Bo WANG. Nonlinear vibration analysis of pipeline considering the effects of soft nonlinear clamp[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(10): 1555-1568.

参考文献

[1] KHUDAYAROV, B. A., KOMILOVA, K. M., and TURAEV, F. Z. Numerical study of the effect of viscoelastic properties of the material and bases on vibration fatigue of pipelines conveying pulsating fluid flow. Engineering Failure Analysis, 115, 104635(2020)
[2] KHUDAYAROV, B. A. and TURAEV, F. Z. Mathematical simulation of nonlinear oscillations of viscoelastic pipelines conveying fluid. Applied Mathematical Modelling, 66, 662-679(2019)
[3] ZHOU, X. Q., YU, D. Y., SHAO, X. Y., ZHANG, C. Y., and WANG, S. Dynamics characteristic of steady fluid conveying in the periodical partially viscoelastic composite pipeline. Composites Part B:Engineering, 111, 387-408(2017)
[4] WANG, Y. H. and CHEN, Y. M. Dynamic analysis of the viscoelastic pipeline conveying fluid with an improved variable fractional order model based on shifted Legendre polynomials. Fractal and Fractional, 3(4), 52(2019)
[5] GUO, X. M., MA, H., ZHANG, X. F., YE, Z., FU, Q., LIU, Z. H., and HAN, Q. K. Uncertain frequency responses of clamp-pipeline systems using an interval-based method. IEEE Access, 8, 29370-29384(2020)
[6] LIN, J. Z., ZHAO, Y. L., ZHU, Q. Y., HAN, S., MA, H., and HAN, Q. K. Nonlinear characteristic of clamp loosing in aero-engine pipeline system. IEEE Access, 9, 64076-64084(2021)
[7] JIANG, F., DING, Z. Y., WU, Y. W., BAI, H. B., SHAO, Y. C., and ZI, B. Energy dissipation characteristics and parameter identification of symmetrically coated damping structure of pipelines under different temperature environment. Symmetry, 12(8), 1283(2020)
[8] LIU, G. M., LI, S. J., LI, Y. H., and CHEN, H. Vibration analysis of pipelines with arbitrary branches by absorbing transfer matrix method. Journal of Sound and Vibration, 332(24), 6519-6536(2013)
[9] QUAN, L. X., CHE, S. C., GUO, C. H., GAO, H. H., and GUO, M. Axial vibration characteristics of fluid-structure interaction of an aircraft hydraulic pipe based on modified friction coupling model. Applied Sciences, 10(10), 3548(2020)
[10] GUO, X. M., CAO, Y. M., MA, H., XIAO, C. L., and WEN, B. C. Dynamic analysis of an Lshaped liquid-filled pipe with interval uncertainty. International Journal of Mechanical Sciences, 217, 107040(2022)
[11] ZHU, H. Z., WANG, W. B., YIN, X. W., and GAO, C. F. Spectral element method for vibration analysis of three-dimensional pipes conveying fluid. International Journal of Mechanics and Materials in Design, 15(2), 345-360(2019)
[12] ZHANG, Y. L., GAO, P. X., LIU, X. F., YU, T., and HUANG, Z. H. Fluid-induced vibration of a hydraulic pipeline with piezoelectric active constrained layer-damping materials. Coatings, 11(7), 757(2021)
[13] LIU, X. D., SUN, W., and GAO, Z. H. Optimization of hoop layouts for reducing vibration amplitude of pipeline system using the semi-analytical model and genetic algorithm. IEEE Access, 8, 224394-224408(2020)
[14] KAVIANIPOUR, O. Effects of the passive electromagnetic damper on the behavior of a fluidconveying pipeline. Proceedings of the Institution of Mechanical Engineers Part C:Journal of Mechanical Engineering Science, 233(7), 2329-2339(2019)
[15] MAO, X. Y., DING, H., and CHEN, L. Q. Steady-state response of a fluid-conveying pipe with 3:1 internal resonance in supercritical regime. Nonlinear Dynamics, 86(2), 795-809(2016)
[16] ZANG, J. and CHEN, L. Q. Complex dynamics of a harmonically excited structure coupled with a nonlinear energy sink. Acta Mechanica Sinica, 33(4), 801-822(2017)
[17] DING, H., TAN, X., and DOWELL, E. H. Natural frequencies of a super-critical transporting Timoshenko beam. European Journal of Mechanics-A/Solids, 66, 79-93(2017)
[18] ZHANG, Y. W., HOU, S., ZHANG, Z., ZANG, J., NI, Z. Y., and TENG, Y. Y. Nonlinear vibration absorption of laminated composite beams in complex environment. Nonlinear Dynamics, 99(4), 2605-2622(2020)
[19] WANG, H., RONGONG, J. A., and TOMLINSON, G. R. Nonlinear static and dynamic properties of metal rubber dampers. Energy, 10(1), 1301-1315(2010)
[20] XU, J. D., GUO, B. T., ZHU, Z. G., and LI, Q. H. Vibration characteristics of metal rubber materials (in Chinese). Journal of Aerospace Power, 19(5), 4(2004)
[21] ALKHARABSHEH, S. A. and YOUNIS, M. I. Dynamics of MEMS arches of flexible supports. Journal of Microelectromechanical Systems, 22(1), 216-224(2012)
[22] GAO, P. X., ZHAI, J. Y., QU, F. Z., and HAN, Q. K. Vibration and damping analysis of aerospace pipeline conveying fluid with constrained layer damping treatment. Proceedings of the Institution of Mechanical Engineers, Part G:Journal of Aerospace Engineering, 232(8), 1529-1541(2017)
[23] CHEN, L. Q., ZHANG, Y. L., ZHANG, G. C., and DING, H. Evolution of the double-jumping in pipes conveying fluid flowing at the supercritical speed. International Journal of Non-Linear Mechanics, 58, 11-21(2014)
[24] TAN, X., MAO, X. Y., DING, H., and CHEN, L. Q. Vibration around non-trivial equilibrium of a supercritical Timoshenko pipe conveying fluid. Journal of Sound and Vibration, 428, 104-118(2018)
[25] LU, Z, Q., ZHANG, K. K., DING, H., and CHEN, L. Q. Internal resonance and stress distribution of pipes conveying fluid in supercritical regime. International Journal of Mechanical Sciences, 186, 105900(2020)
[26] HE, J. H. Hamilton's principle for dynamical elasticity. Applied Mathematics Letters, 72, 65-69(2017)
[27] ZHANG, Y. W., CHEN, W. J., NI, Z. Y., ZANG, J., and HOU, S. Supersonic aerodynamic piezoelectric energy harvesting performance of functionally graded beams. Composite Structures, 233, 111537(2020)
[28] AZARIPOUR, S. and BAGHANI, M. Vibration analysis of FG annular sector in moderately thick plates with two piezoelectric layers. Applied Mathematics and Mechanics (English Edition), 40(6), 783-804(2019) https://doi.org/10.1007/s10483-019-2468-8
[29] YAS, M. H. and RAHIMI, S. Thermal vibration of functionally graded porous nanocomposite beams reinforced by graphene platelets. Applied Mathematics and Mechanics (English Edition), 41(8), 1209-1226(2020) https://doi.org/10.1007/s10483-020-2634-6
[30] GHAYESH, M. H. Nonlinear vibration analysis of axially functionally graded shear-deformable tapered beams. Applied Mathematical Modelling, 59, 583-596(2018)
[31] YANG, T. Z., LIU, T., TANG, Y., HOU, S., and LYU, X. F. Enhanced targeted energy transfer for adaptive vibration suppression of pipes conveying fluid. Nonlinear Dynamics, 97(3), 1937-1944(2019)
[32] YE, S. Q., MAO, X. Y., DING, H., JI, J. C., and CHEN, L. Q. Nonlinear vibrations of a slightly curved beam with nonlinear boundary conditions. International Journal of Mechanical Sciences, 168, 105294(2019)
[33] GAO, K., HUANG, Q., KITIPORNCHAI, S., and YANK, J. Nonlinear dynamic buckling of functionally graded porous beams. Mechanics of Advanced Materials and Structures, 28(4), 418-429(2021)
[34] LI, Q. Y., WU, D., CHEN, X. J., LIU, L., YU, Y. G., and GAO, W. Nonlinear vibration and dynamic buckling analyses of sandwich functionally graded porous plate with graphene platelet reinforcement resting on Winkler-Pasternak elastic foundation. International Journal of Mechanical Sciences, 148, 596-610(2018)
[35] ABBASZADEH, M. and DEHGHAN, M. Investigation of the Oldroyd model as a generalized incompressible Navier-Stokes equation via the interpolating stabilized element free Galerkin technique. Applied Numerical Mathematics, 150, 274-294(2020)
[36] LU, Z. Q., WU, D., DING, H., and CHEN, L. Q. Vibration isolation and energy harvesting integrated in a Stewart platform with high static and low dynamic stiffness. Applied Mathematical Modelling, 89, 249-267(2021)
[37] FAROKHI, H. and GHAYESH, M. H. Supercritical nonlinear parametric dynamics of Timoshenko microbeams. Communications in Nonlinear Science and Numerical Simulation, 59, 592-605(2018)
[38] LIU, Y. F., QIN, Z. Y., and CHU, F. L. Nonlinear dynamic responses of sandwich functionally graded porous cylindrical shells embedded in elastic media under 1:1 internal resonance. Applied Mathematics and Mechanics (English Edition), 42(6), 805-818(2021) https://doi.org/10.1007/s10483-021-2740-7
[39] DING, H., ZHU, M. H., and CHEN, L. Q. Nonlinear vibration isolation of a viscoelastic beam. Nonlinear Dynamics, 92(2), 325-349(2018)

Nonlinear vibration analysis of pipeline considering the effects of soft nonlinear clamp

Nonlinear vibration analysis of pipeline considering the effects of soft nonlinear clamp

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