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Meccanica

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18-01-2021

Steady-state responses of mechanical system attached to non-smooth vibration absorber with piecewise damping and stiffness

Authors: Min Sun, Wen-hua Hu, Jun Liu, Jian-en Chen

Published in: Meccanica | Issue 2/2021

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Abstract

The steady-state dynamic characteristics of non-smooth vibration absorbers are investigated. The complexification-averaging method is used to obtain the steady-state response equation of a harmonic excited primary system attached to the non-smooth absorbers, with the equation solved using a Matlab program based on the least square method. Research results indicate that the traditional purely nonlinear absorber loses its efficacy after the excitation amplitude reaches a certain value. The non-smooth absorber with piecewise linear damping, by contrast, can suppress vibration of the primary system within a larger range of excitation amplitude than the purely nonlinear absorber. Then, the cubic stiffness component is substituted by a piecewise stiffness component to further enhance the performance of the above non-smooth absorber and good results are obtained. The non-smooth absorber with both piecewise damping and stiffness shows the stronger vibration absorption performance. In addition, the differences of higher branches of response which induced by the three absorbers are analyzed and discussed.

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Hartog JPD (1947) Mechanical Vibrations. McGraw-Hill, New YorkMATH

Abe M, Fujino Y (1994) Dynamic characterization of multiple tuned mass dampers and some design formulas. Earthq Eng Struct D 23(8):813–835CrossRef

Roberson RE (1952) Synthesis of a nonlinear dynamic vibration absorber. J Franklin I 254(3):205–220MathSciNetCrossRef

Oueini SS, Chin CM, Nayfeh AH (1999) Dynamics of a cubic nonlinear vibration absorber. Nonlinear Dyn 20(3):283–295MATHCrossRef

Vakakis AF (2001) Inducing passive nonlinear energy sinks in vibrating systems. J Vib Acoust 123(3):324–332CrossRef

Lee YS, Vakakis AF, Bergman LA, McFarland DM, Kerschen G, Nucera F, Tsakirtzis S, Panagopoulos PN (2008) Passive non-linear targeted energy transfer and its applications to vibration absorption: a review. P I Mech Eng K-J Mul 222(2):77–134

Lu Z, Wang ZX, Zhou Y, Lu XL (2018) Nonlinear dissipative devices in structural vibration control: a review. J Sound Vib 423:18–49CrossRef

Ding H, Chen LQ (2020) Designs, analysis and applications of nonlinear energy sinks. Nonlinear Dyn 100(4):3061–3107CrossRef

Li T, Seguy S, Berlioz A (2017) On the dynamics around targeted energy transfer for vibro-impact nonlinear energy sink. Nonlinear Dyn 87(3):1453–1466CrossRef

10.

Gourc E, Seguy S, Michon G, Berlioz A, Man BP (2015) Quenching chatter instability in turning process with a vibro-impact nonlinear energy sink. J Sound Vib 355:392–406CrossRef

11.

M.A. AL-Shudeifat, A.S. Saeed, Comparison of a modified vibro-impact nonlinear energy sink with other kinds of NESs, Meccanica. DOI: https://doi.org/10.1007/s11012-020-01193-3, 2020.

12.

Sarlis AA, Pasala DTR, Constantinou MC, Reinhorn AM, Nagarajaiah S, Taylor DP (2013) Negative stiffness device for seismic protection of structures. J Struct Eng 139(7):1124–1133CrossRef

13.

Sun Y, Zhou JS, Gong D, Sun WJ (2018) Two dimensional dynamic vibration absorber of high speed electric multiple unit (EMU) train based on negative stiffness. J Tongji Univ 46(6):854–860

14.

Georgiades F, Vakakis AF, Mcfarland DM, Bergman LA (2005) Shock isolation through passive energy pumping caused by nonsmooth nonlinearities. Int J Bifurcat Chaos 15(6):1989–2001CrossRef

15.

Gendelman OV (2008) Targeted energy transfer in systems with non-polynomial nonlinearity. J Sound Vib 315(3):732–745CrossRef

16.

Lamarque CH, Gendelman OV, Savadkoohi AT, Etcheverria E (2011) Targeted energy transfer in mechanical systems by means of non-smooth nonlinear energy sink. Acta Mech 221(1–2):175–200MATHCrossRef

17.

Starosvetsky Y, Gendelman OV (2009) Vibration absorption in systems with a nonlinear energy sink: Nonlinear damping. J Sound Vib 324(3–5):916–939CrossRef

18.

Lamarque CH, Savadkoohi AT, Dimitrijevic Z (2014) Dynamics of a linear system with time-dependent mass and a coupled light mass with non-smooth potential. Meccanica 49(1):135–145MathSciNetMATHCrossRef

19.

Lamarque CH, Savadkoohi AT, Charlemagne S, Abdoulhadi P (2017) Nonlinear vibratory interactions between a linear and a non-smooth forced oscillator in the gravitational field. Mech Syst and Signal Pr 89:131–148CrossRef

20.

Shui X, Wang SM (2018) Investigation on a mechanical vibration absorber with tunable piecewise-linear stiffness. Mech Syst and Signal Pr 100:330–343CrossRef

21.

Gendelman OV, Sigalov G, Manevitch LI, Mane M, Vakakis AF, Bergman LA (2012) Dynamics of an eccentric rotational nonlinear energy sink. J Appl Mech 79(1):011012CrossRef

22.

M.A. AL-Shudeifat, Highly efficient nonlinear energy sink, Nonlinear Dyn. 76(4): 1905–1920, 2014.

23.

M.A. AL-Shudeifat, Asymmetric Magnet-Based Nonlinear Energy Sink, J Comput Nonlin Dyn. 10(1): 014502, 2015.

24.

M.A. AL-Shudeifat, N.E. Wierschem, L.A. Bergman, A.F. Vakakis, Numerical and experimental investigations of a rotating nonlinear energy sink, Meccanica. 52(4–5): 763–779, 2017.

25.

Benarous N, Gendelman OV (2016) Nonlinear energy sink with combined nonlinearities: Enhanced mitigation of vibrations and amplitude locking phenomenon. P I Mech Eng C-J Mec 230(1):21–33CrossRef

26.

Fang X, Wen JH, Yin JF, Yu DL (2017) Highly efficient continuous bistable nonlinear energy sink composed of a cantilever beam with partial constrained layer damping. Nonlinear Dyn 87(4):2677–2695CrossRef

27.

Farid M, Gendelman OV (2017) Tuned pendulum as nonlinear energy sink for broad energy range. J Vib Control 23(3):373–388MathSciNetCrossRef

28.

Tsiatas GC, Charalampakis AE (2018) A new hysteretic nonlinear energy sink (HNES). Commun Nonlinear Sci 60:1–11MATHCrossRef

29.

Habib G, Romeo F (2017) The tuned bistable nonlinear energy sink. Nonlinear Dyn 89(1):179–196CrossRef

30.

Mattei PO, Poncot R, Pachebat M, Cote R (2016) Nonlinear targeted energy transfer of two coupled cantilever beams coupled to a bistable light attachment. J Sound Vib 373:29–51CrossRef

31.

Wang JJ, Wierschem N, Spencer BF, Lu XL (2015) Experimental study of track nonlinear energy sinks for dynamic response reduction. Eng Struct. 94:9–15CrossRef

32.

Zang J, Yuan TC, Lu ZQ, Zhang YW, Ding H, Chen LQ (2018) A lever-type nonlinear energy sink. J Sound Vib. 437:119–134CrossRef

33.

Gourc E, Seguy S, Michon G, Berlioz A (2013) Chatter control in turning process with a nonlinear energy sink. Adv Mater R 698:89–98

34.

Bab S, Khadem SE, Shahgholi M, Abbasi A (2017) Vibration attenuation of a continuous rotor-blisk-journal bearing system employing smooth nonlinear energy sinks. Mech Syst Signal PR 84:128–157CrossRef

35.

Lee YS, Vakakis AF, Bergman LA, Mcfarland DM, Kerschen G (2007) Suppression aeroelastic instability using broadband passive targeted energy transfers, part 1: Theory. AIAA J 45(3):693–711CrossRef

36.

Zhang WF, Liu Y, Cao SL, Chen JH, Zhang ZX, Zhang JZ (2017) Targeted energy transfer between 2-D wing and nonlinear energy sinks and their dynamic behaviors. Nonlinear Dyn 90(3):1841–1850CrossRef

37.

Tian W, Li YM, Li P, Yang ZC, Zhao T (2019) Passive control of nonlinear aeroelasticity in hypersonic 3-D wing with a nonlinear energy sink. J Sound Vib 462:114942CrossRef

38.

Yang K, Zhang YW, Ding H, Yang TZ, Li Y, Chen LQ (2017) Nonlinear energy sink for whole-spacecraft vibration reduction. J Vib Acoust 139(2):021011CrossRef

39.

Chen HY, Mao XY, Ding H, Chen LQ (2020) Elimination of multimode resonances of composite plate by inertial nonlinear energy sinks. Mech Syst Signal PR 135:106383CrossRef

40.

Tumkur RKR, Domany E, Gendelman OV, Masud A, Bergman LA, Vakakis AF (2013) Reduced-order model for laminar vortex-induced vibration of a rigid circular cylinder with an internal nonlinear absorber. Commun Nonlinear Sci 18(7):1916–1930MathSciNetMATHCrossRef

41.

Dai HL, Abdelkefi A, Wang L (2017) Vortex-induced vibrations mitigation through a nonlinear energy sink. Commun Nonlinear Sci 42:22–36MATHCrossRef

42.

Huang DM, Li RH, Yang GD (2019) On the dynamic response regimes of a viscoelastic isolation system integrated with a nonlinear energy sink. Commun Nonlinear Sci 79:104916MathSciNetMATHCrossRef

43.

Zhang W, Niu Y, Behdinan K (2020) Vibration characteristics of rotating pretwisted composite tapered blade with graphene coating layers. Aerosp Sci Technol 98:105644CrossRef

44.

Bai B, Li H, Zhang W, Cui YC (2020) Application of extremum response surface method-based improved substructure component modal synthesis in mistuned turbine bladed disk. J Sound Vib 472:115210CrossRef

45.

Guo XY, Jiang P, Cao DX, Wang CM (2020) Nonlinear vibrations of graphene piezoelectric microsheet under coupled excitations. Int J Nonlin Mech 124:103498CrossRef

46.

Ahmadabadi ZN, Khadem SE (2014) Nonlinear vibration control and energy harvesting of a beam using a nonlinear energy sink and a piezoelectric device. J Sound Vib 333(19):4444–4457CrossRef

47.

Li X, Zhang YW, Ding H, Chen LQ (2019) Dynamics and evaluation of a nonlinear energy sink integrated by a piezoelectric energy harvester under a harmonic excitation. J Vib Control 25(4):851–867MathSciNetCrossRef

48.

Zhang Y, Tang LH, Liu KF (2017) Piezoelectric energy harvesting with a nonlinear energy sink. J Intel Mat Syst Str 28(3):307–322CrossRef

49.

Fang ZW, Zhang YW, Li X, Ding H, Chen LQ (2017) Integration of a nonlinear energy sink and a giant magnetostrictive energy harvester. J Sound Vib 391:35–49CrossRef

50.

Gendelman OV (2011) Targeted energy transfer in systems with external and self-excitation. P I MECH ENG C-J MEC 225(C9):2007–2043CrossRef

51.

Chen JE, He W, Zhang W, Yao MH, Liu J, Sun M (2018) Vibration suppression and higher branch responses of beam with parallel nonlinear energy sinks. Nonlinear Dyn 91(2):885–904CrossRef

52.

Gourc E, Michon G, Seguy S, Berlioz A (2014) Experimental investigation and design optimization of targeted energy transfer under periodic forcing. J Vib Acoust 136(2):021021CrossRef

53.

M.A. AL-Shudeifat, Piecewise nonlinear energy sink, IDETC/CIE 2015. 57181: V008T13A038, 2015.

54.

M.A. AL-Shudeifat, Nonlinear energy sinks with piecewise-linear nonlinearities, J Comput Nonlin Dyn. 14(12): 124501, 2019.

Title: Steady-state responses of mechanical system attached to non-smooth vibration absorber with piecewise damping and stiffness
Authors: Min Sun
Wen-hua Hu
Jun Liu
Jian-en Chen
Publication date: 18-01-2021
Publisher: Springer Netherlands
Published in: Meccanica / Issue 2/2021
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI: https://doi.org/10.1007/s11012-020-01288-x

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