A time-varying boundary method for multimodal vibration suppression of beam

Abstract

As common components in huge underwater gliders, modal vibrations of flexible beams can affect the durability of structures and the precision of system. The current methods for suppressing the beam vibrations include the damping suppression, active control and absorbers, etc. The above control methods were gradually developed for the low frequencies and wide band. The accurate structures and excitation parameters should be obtained in the design processing. In this work, a time-varying boundary method is proposed based on the energy transfer phenomenon of time-varying boundary structure. The proposed method is effective for suppressing multi-order structure resonance simultaneously. A dynamic model of a time-varying boundary beam is established. The vibrations of time-varying boundary beam are obtained by a time-domain piecewise analytical method, which are compared with those from a finite element software. The vibrations of time-varying boundary beams and time-invariant beams are compared. The vibration suppression effect of time-varying boundary method is verified. The effects of the damping, time-varying range and time-varying speed on the vibration suppression characteristics are analyzed. The time-varying position optimization area is obtained. Note that the time-varying boundary method can simultaneously suppress the multimodal resonances of beam and reduce the resonance peaks with the highest energy.

Keywords

time-varying boundary method / multimodal vibration suppression / boundary control / frequency domain energy dispersion

References

[1] WeiL, SunY, ZengJ, et al. . Experimental and numerical investigation of fatigue failure for metro bogie cowcatchers due to modal vibration and stress induced by rail corrugation [J]. Engineering Failure Analysis, 2022, 142: 106810

[2] TangX, CaiX, PengH, et al. . Experimental and simulation investigation into the cause and treatment of rail corrugation for metro [J]. Journal of Central South University, 2022, 29(12): 3925-3938

[3] LiuS, JiangL, ZhouW, et al. . Influence of mortar gap on natural vibration frequencies of high-speed railway track-bridge system [J]. Journal of Central South University, 2022, 29(8): 2807-2819

[4] GaoG, ZhongW, MengY, et al. . Microvibration test and numerical simulation analysis of precision instrument workshop [J]. Journal of Engineering Geology, 2020, 28(5): 1076-1083

[5] HanY, LiuY, CaiC, et al. . Effects of sudden change in wind loads on running performance of trains on a highway-railway one-story bridge in crosswinds [J]. Journal of Central South University, 2022, 29(8): 2621-2638

[6] WangP, YangY, XuH, et al. . Effect of static and dynamic misalignment of rolling bearing on nonlinear vibration characteristics of rotor system [J]. Journal of Central South University, 2023, 30(3): 871-903

[7] LiuJ, NiH, ZhouR, et al. . A simulation analysis of ball bearing lubrication characteristics considering the cage clearance [J]. Journal of Tribology, 2023, 145(4): 044301

[8] LiuJ, LiX, XiaM. A dynamic model for the planetary bearings in a double planetary gear set [J]. Mechanical Systems and Signal Processing, 2023, 194110257

[9] MaoJ, XiaoY, YuZ, et al. . Probabilistic model and analysis of coupled train-ballasted track-subgrade system with uncertain structural parameters [J]. Journal of Central South University, 2021, 2872238-2256

[10] WuZ, ZhangN. Response of train-bridge system under intensive seismic excitation by random vibration method [J]. Journal of Central South University, 2022, 29(8): 2467-2484

[11] LianJ, DingX, ZhangL. Shaking table test on seismic response of an accumulation landslide reinforced by pile-plate retaining wall based on the time-frequency analysis method [J]. Journal of Central South University, 2023, 30(5): 1710-1721

[12] GuoW, ChenX, YeY, et al. . Coupling vibration analysis of high-speed maglev train-viaduct systems with control loop failure [J]. Journal of Central South University, 2022, 29(8): 2771-2790

[13] MoradA M, KamelM, KhalilM K. Vibration damping of aircraft propeller blades using shunted piezoelectric transducers [J]. IOP Conference Series: Materials Science and Engineering, 2021, 1172(1): 012007

[14] EISA A I A, LI Shu-sen, ZHANG Yan, et al. Transient analysis method of an axially magnetized novel passive eddy current damper for suppressing lateral vibrations [J]. Mathematical Problems in Engineering, 2022: 38008992. DOI: https://doi.org/10.1155/2022/3808992.

[15] ChenY, ZhuQ, ZhaiJ. Experimental investigation on fatigue of blade specimen subjected to resonance and effect of a damping hard coating treatment [J]. Journal of Central South University, 2021, 282445-453

[16] JuB, GuoZ, LiuY, et al. . Self-sensing vibration suppression of piezoelectric cantilever beam based on improved mirror circuit [J]. IEEE Access, 2019, 7148381-148392

[17] WenG, HeJ, LiuJ, et al. . Design, analysis and semi-active control of a quasi-zero stiffness vibration isolation system with six oblique springs [J]. Nonlinear Dynamics, 2021, 106(1): 309-321

[18] ZhangY, HouS, ZhangZ, et al. . Nonlinear vibration absorption of laminated composite beams in complex environment [J]. Nonlinear Dynamics, 2020, 99(4): 2605-2622

[19] QianF, ZuoL. Tuned nonlinear spring-inerterdamper vibration absorber for beam vibration reduction based on the exact nonlinear dynamics model [J]. Journal of Sound and Vibration, 2021, 509: 116246

[20] BukhariM, BarryO. Exact nonlinear dynamic analysis of a beam with a nonlinear vibration absorber and with various boundary conditions [J]. Journal of Computational and Nonlinear Dynamics, 2020, 15(1): 011003

[21] WangX, WuH, YangB. Nonlinear multimodal energy harvester and vibration absorber using magnetic softening spring [J]. Journal of Sound and Vibration, 2020, 476115332

[22] LiW, WierschemN E, LiX, et al. . Numerical study of a symmetric single-sided vibro-impact nonlinear energy sink for rapid response reduction of a cantilever beam [J]. Nonlinear Dynamics, 2020, 1002951-971

[23] FangB, TheurichT, KrackM, et al. . Vibration suppression and modal energy transfers in a linear beam with attached vibro-impact nonlinear energy sinks [J]. Communications in Nonlinear Science and Numerical Simulation, 2020, 91105415

[24] WeiB, WangP, YangT, et al. . Effects of friction variability on isolation performance of rolling-spring systems [J]. Journal of Central South University, 2016, 23(1): 233-239

[25] TalebitootiM, FadaeeM. Effects of carbon nanotube reinforcements on vibration suppression of magnetorheological fluid sandwich beam [J]. Journal of Intelligent Material Systems and Structures, 2019, 30(7): 1053-1069

[26] ZenkourA M, El-ShahranyH D. Vibration suppression analysis for laminated composite beams embedded actuating magnetostrictive layers [J]. Applied and Computational Mechanics, 2019, 50(1): 69-75

[27] ZenkourA M, El-ShahranyH D. Vibration suppression of advanced plates embedded magnetostrictive layers via various theories [J]. Journal of Materials Research and Technology, 2020, 9(3): 4727-4748

[28] ReddyR S, PandaS, GuptaA. Nonlinear dynamics and active control of smart beams using shear/extensional mode piezoelectric actuators [J]. International Journal of Mechanical Sciences, 2021, 204106495

[29] HosseiniS M, KalhoriH, Al-JumailyA. Active vibration control in human forearm model using paired piezoelectric sensor and actuator [J]. Journal of Vibration and Control, 2021, 27(19–20): 2231-2242

[30] LiJ, DengH, JiangW. Dynamic response and vibration suppression of a cantilevered pipe conveying fluid under periodic excitation [J]. Journal of Vibration and Control, 2019, 25(11): 1695-1705

[31] DattaP. Active vibration control of axially functionally graded cantilever beams by finite element method [J]. Materials Today: Proceedings, 2021, 442543-2550

[32] El-BorgiS, FernandesR, RajendranP, et al. . Multiple bandgap formation in a locally resonant linear metamaterial beam: Theory and experiments [J]. Journal of Sound and Vibration, 2020, 488: 115647

[33] JinY, ShiY, YuG, et al. . A multifunctional honeycomb metastructure for vibration suppression [J]. International Journal of Mechanical Sciences, 2020, 188105964

[34] JinY, LiuK, XiongL, et al. . A non-traditional variant nonlinear energy sink for vibration suppression and energy harvesting [J]. Mechanical Systems and Signal Processing, 2022, 181109479

[35] ZhangW, ChangZ, ChenJ. Vibration reduction for an asymmetric elastically supported beam coupled to an inertial nonlinear energy sink [J]. Journal of Vibration Engineering & Technologies, 2023, 11(4): 1711-1723

[36] ZhangZ, DingH, ZhangY, et al. . Vibration suppression of an elastic beam with boundary inerter-enhanced nonlinear energy sinks [J]. Acta Mechanica Sinica, 2021, 37(3): 387-401

[37] MaC, ZhangX, XieS, et al. . Active linear quadratic Gaussian control of the vibration of a flexible beam with a time-varying mass [J]. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 2015, 229(6): 475-484

[38] LeiX, ShenL, ChenZ, et al. . Experimental analysis of additional aerodynamic effects caused by wind-driven rain on bridge main girder [J]. Journal of Central South University, 2022, 29(8): 2743-2756

[39] KeS, GeY, ZhaoL, et al. . Wind-induced responses of super-large cooling towers [J]. Journal of Central South University, 2013, 20(11): 3216-3228

[40] WangF, XiaoW, YaoY, et al. . An analytical procedure to predict transverse vibration response of jack-up riser under the random wave load [J]. Shock and Vibration, 2020, 20201-9

[41] TangY, MaZ. Nonlinear vibration of axially moving beams with internal resonance, speed-dependent tension, and tension-dependent speed [J]. Nonlinear Dynamics, 2019, 98(4): 2475-2490