nach oben

Acta Mechanica

Erschienen in:

13.09.2022 | Original Paper

Analytical and numerical investigations on inerter-based NES absorber system with nonlinear damping

verfasst von: Rony Philip, B. Santhosh, Bipin Balaram

Erschienen in: Acta Mechanica | Ausgabe 11/2022

Einloggen, um Zugang zu erhalten

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

Two major concerns with the nonlinear energy sink (NES) when used as a passive vibration absorber are the mass of the NES and the threshold of external excitation to initiate the targeted energy transfer (TET). This work proposes an inertial NES with nonlinear damping to address the aforementioned concerns. An inerter replaces the conventional NES’s mass to reduce the absorber system’s effective mass. The addition of nonlinear damping created instability and therefore initiated the strongly modulated response (SMR) even for lower excitation amplitude which is the most favorable condition for TET. A base excited linear primary system appended with the proposed NES is used to demonstrate the claims. Multi-harmonic balance method (MHBM) combined with arc-length continuation and Floquet theory generates the frequency response plots and identifies the stable and unstable periodic solution branches. Numerical studies at the unstable periodic solution obtained by MHBM revealed the existence of SMR. The slow flow dynamics and the slow invariant manifold (SIM) associated with the SMR are derived using the complexification averaging (CX-A) method combined with the singular perturbation theory. The SIM topology is investigated for variations in the strength of nonlinearity, nonlinear damping factor, and mass ratio. The performance of the proposed inertial NES with nonlinear damping is compared with that of a conventional NES with viscous damping, and the merits are highlighted. It is observed that with the addition of nonlinear damping in the inertial NES, the SMR is initiated even at low excitation amplitude, and efficient energy transfer takes place from the linear oscillator to NES. The combined approach using MHBM and CX-A provided better insight into the analysis of NES-based vibration absorber systems.

Vorheriger Artikel Adaptive convexification of microsphere-based incremental damage for stress and strain softening at finite strains

Nächster Artikel 3D layerwise impact investigation of sandwich plates with multi-directional phase transformation SMA face sheets and nearly incompressible compliant hyperelastic cores

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

Geng, X.F., Ding, H., Mao, X.Y., Chen, L.Q.: Nonlinear energy sink with limited vibration amplitude. Mech. Syst. Signal Process. 156, 107625 (2021)

Lamarque, C.H., Gendelman, O.V., Ture, Savadkoohi A., Etcheverria, E.: Targeted energy transfer in mechanical systems by means of non-smooth nonlinear energy sink. Acta Mech. 221(1), 175–200 (2011)MATH

Vakakis, A.F., Manevitch, L.I., Gendelman, O., Bergman, L.: Dynamics of linear discrete systems connected to local, essentially non-linear attachments. J. Sound Vib. 264(3), 559–577 (2003)

Kerschen, G., McFarland, D.M., Kowtko, J.J., Lee, Y.S., Bergman, L.A., Vakakis, A.F.: Experimental demonstration of transient resonance capture in a system of two coupled oscillators with essential stiffness nonlinearity. J. Sound Vib. 299(4–5), 822–838 (2007)

Gourdon, E., Alexander, N.A., Taylor, C.A., Lamarque, C.H., Pernot, S.: Nonlinear energy pumping under transient forcing with strongly nonlinear coupling: Theoretical and experimental results. J. Sound Vib. 300(3–5), 522–551 (2007)

Lee, Y.S., Vakakis, A.F., Bergman, L.A., Michael, McFarland, D.: Suppression of limit cycle oscillations in the van der Pol oscillator by means of passive non-linear energy sinks. Struct. Control Health Monit. Off. J. Int. Assoc. Struct. Control Monit. Eur. Assoc. Control Struct. 13(1), 41–75 (2006)

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

Ding, H., Cheg, L.Q.: Designs, analysis, and applications of nonlinear energy sinks. Nonlinear Dyn. 100(4), 3061–3107 (2020)

10.

Motato, E., Haris, A., Theodossiades, S., Mohammadpour, M., Rahnejat, H., Kelly, P., Bergman, L.A.: Targeted energy transfer and modal energy redistribution in automotive drivetrains. Nonlinear Dyn. 87(1), 169–190 (2017)

11.

Starosvetsky, Y., Gendelman, O.V.: Dynamics of a strongly nonlinear vibration absorber coupled to a harmonically excited two-degree-of-freedom system. J. Sound Vib. 312(1–2), 234–256 (2008)

12.

Zhou, B., Thouverez, F., Lenoir, D.: A variable-coefficient harmonic balance method for the prediction of quasi-periodic response in nonlinear systems. Mech. Syst. Signal Process. 64, 233–244 (2015)

13.

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

14.

Starosvetsky, Y., Gendelman, O.V.: Response regimes of linear oscillator coupled to nonlinear energy sink with harmonic forcing and frequency detuning. J. Sound Vib. 315(3), 746–765 (2008)

15.

Li, T., Seguy, S., Berlioz, A.: Dynamics of cubic and vibro-impact nonlinear energy sink: analytical, numerical, and experimental analysis. J. Vib. Acoust. 138(3) (2016)

16.

AL-Shudeifat, M.A.: Asymmetric magnet-based nonlinear energy sink. J. Comput. Nonlinear Dyn. 10(1) (2015)

17.

Yao, H., Cao, Y., Zhang, S., Wen, B.: A novel energy sink with piecewise linear stiffness. Nonlinear Dyn. 94(3), 2265–2275 (2018)

18.

Dai, J., Wang, Y., Wei, M., Zhang, W., Zhu, J., Jin, H., Jiang, C.: Dynamic characteristic analysis of the inerter-based piecewise vibration isolator under base excitation. Acta Mech., in press (2022)

19.

Wang, G.X., Ding, H., Chen, L.Q.: Performance evaluation and design criterion of a nonlinear energy sink. Mech. Syst. Signal Process. 169, 108770 (2022)

20.

Vakakis, A.F., Gendelman, O.V., Bergman, L.A., Mojahed, A., Gzal, M.: Nonlinear targeted energy transfer: state of the art and new perspectives. Nonlinear Dyn, in press (2022)

21.

Lee, Y.S., Kerschen, G., Vakakis, A.F., Panagopoulos, P., Bergman, L., McFarland, D.M.: Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment. Phys. D 204(1–2), 41–69 (2005)MathSciNetMATH

22.

Smith, M.C.: Synthesis of mechanical networks: the inerter. IEEE Trans. Autom. Control 47(10), 1648–1662 (2002)MathSciNetMATH

23.

Zhao, Z., Chen, Q., Zhang, R., Pan, C., Jiang, Y.: Energy dissipation mechanism of inerter systems. Int. J. Mech. Sci. 184, 105845 (2020)

24.

Smith, M.C., Wang, F.C.: Performance benefits in passive vehicle suspensions employing inerters. Veh. Syst. Dyn. 42(4), 235–257 (2004)

25.

Sanches, L., Guimarães, T.A., Marques, F.D.: Nonlinear energy sink to enhance the landing gear shimmy performance. Acta Mech. 232(7), 2605–2622 (2021)MathSciNetMATH

26.

Giaralis, A., Petrini, F.: Wind-induced vibration mitigation in tall buildings using the tuned mass-damper-inerter. J. Struct. Eng. 143(9), 04017127 (2017)

27.

Xu, K., Bi, K., Han, Q., Li, X., Du, X.: Using tuned mass damper inerter to mitigate vortex-induced vibration of long-span bridges: analytical study. Eng. Struct. 182, 101–111 (2019)

28.

Hu, Y., Chen, M.Z., Smith, M.C.: Natural frequency assignment for mass-chain systems with inerters. Mech. Syst. Signal Process. 108, 126–139 (2018)

29.

Zilletti, M.: Feedback control unit with an inerter proof-mass electrodynamic actuator. J. Sound Vib. 369, 16–28 (2016)

30.

Papageorgiou, C., Houghton, N.E., Smith, M.C.: Experimental testing and analysis of inerter devices. J. Dyn. Syst. Meas. Control 131(1) (2009)

31.

Li, C., Liang, M., Wang, Y., Dong, Y.: Vibration suppression using two-terminal flywheel. Part I: modeling and characterization. J. Vib. Control 18(8), 1096–1105 (2012)

32.

De Domenico, D., Deastra, P., Ricciardi, G., Sims, N.D., Wagg, D.J.: Novel fluid inerter based tuned mass dampers for optimised structural control of base-isolated buildings. J. Franklin Inst. 356(14), 7626–7649 (2019)MATH

33.

Ma, R., Bi, K., Hao, H.: Inerter-based structural vibration control: A state-of-the-art review. Eng. Struct. 243, 112655 (2021)

34.

Wagg, D.J.: A review of the mechanical inerter: historical context, physical realisations and nonlinear applications. Nonlinear Dyn. 104(1), 13–34 (2021)MathSciNet

35.

Hu, Y., Chen, M.Z.: Performance evaluation for inerter-based dynamic vibration absorbers. Int. J. Mech. Sci. 99, 297–307 (2015)

36.

Wang, X., Liu, X., Shan, Y., Shen, Y., He, T.: Analysis and optimization of the novel inerter-based dynamic vibration absorbers. IEEE Access 6, 33169–33182 (2018)

37.

Javidialesaadi, A., Wierschem, N.E.: An inerter-enhanced nonlinear energy sink. Mech. Syst. Signal Process. 129, 449–454 (2019)

38.

Zhang, Y.W., Lu, Y.N., Zhang, W., Teng, Y.Y., Yang, H.X., Yang, T.Z., Chen, L.Q.: Nonlinear energy sink with inerter. Mech. Syst. Signal Process. 125, 52–64 (2019)

39.

Zhang, Z., Lu, Z.Q., Ding, H., Chen, L.Q.: An inertial nonlinear energy sink. J. Sound Vib. 450, 199–213 (2019)

40.

Zhang, W., Zhang, H.: Modeling and analysis of nonlinear damping mechanisms in vibrating systems. Int. J. Mech. Sci. 36(9), 829–848 (1994)MATH

41.

Ruzicka, J.E., Derby, T.F.: Vibration isolation with nonlinear damping (1971)

42.

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

43.

Mojahed, A., Moore, K., Bergman, L.A., Vakakis, A.F.: Strong geometric softening-hardening nonlinearities in an oscillator composed of linear stiffness and damping elements. Int. J. Non-Linear Mech. 107, 94–111 (2018)

44.

Liu, Y., Mojahed, A., Bergman, L.A., Vakakis, A.F.: A new way to introduce geometrically nonlinear stiffness and damping with an application to vibration suppression. Nonlinear Dyn. 96(3), 1819–1845 (2019)MATH

45.

Touzé, C., Amabili, M.: Nonlinear normal modes for damped geometrically nonlinear systems: application to reduced-order modelling of harmonically forced structures. J. Sound Vib. 298(4–5), 958–981 (2006)

46.

Kong, X., Li, H., Wu, C.: Dynamics of 1-dof and 2-dof energy sink with geometrically nonlinear damping: application to vibration suppression. Nonlinear Dyn. 91(1), 733–754 (2018)

47.

Andersen, D., Starosvetsky, Y., Vakakis, A., Bergman, L.: Dynamic instabilities in coupled oscillators induced by geometrically nonlinear damping. Nonlinear Dyn. 67(1), 807–827 (2012)MathSciNet

48.

Liu, Y., Chen, G., Tan, X.: Dynamic analysis of the nonlinear energy sink with local and global potentials: geometrically nonlinear damping. Nonlinear Dyn. 101(4), 2157–2180 (2020)

49.

Zhang, Y., Kong, X., Yue, C., Xiong, H.: Dynamic analysis of 1-dof and 2-dof nonlinear energy sink with geometrically nonlinear damping and combined stiffness. Nonlinear Dyn. 105(1), 167–190 (2021)

50.

Philip, R., Santhosh, B., Balaram, B.: Dynamics and performance analysis of a nonlinear energy sink with geometric nonlinear damping. In: Advances in Nonlinear Dynamics. pp. 95–104. Springer, Cham (2022)

51.

Kerschen, G., Vakakis, A.F., Lee, Y.S., McFarland, D.M., Bergman, L.A.: Toward a fundamental understanding of the Hilbert-Huang transform in nonlinear structural dynamics. J. Vib. Control 14(1–2), 77–105 (2008)MathSciNetMATH

52.

Raj, P.R., Santhosh, B.: Parametric study and optimization of linear and nonlinear vibration absorbers combined with piezoelectric energy harvester. Int. J. Mech. Sci. 152, 268–279 (2019)

53.

Gendelman, O.V., Gourdon, E., Lamarque, C.H.: Quasiperiodic energy pumping in coupled oscillators under periodic forcing. J. Sound Vib. 294(4–5), 651–662 (2006)

54.

Manevitch, L.: The description of localized normal modes in a chain of nonlinear coupled oscillators using complex variables. Nonlinear Dyn. 25(1), 95–109 (2001)MathSciNetMATH

55.

Tripathi, A., Grover, P., Kalmár-Nagy, T.: On optimal performance of nonlinear energy sinks in multiple-degree-of-freedom systems. J. Sound Vib. 388, 272–297 (2017)

56.

Lee, Y.S., Nucera, F., Vakakis, A.F., McFarland, D.M., Bergman, L.A.: Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments. Phys. D 238(18), 1868–1896 (2009)MATH

Titel: Analytical and numerical investigations on inerter-based NES absorber system with nonlinear damping
verfasst von: Rony Philip
B. Santhosh
Bipin Balaram
Publikationsdatum: 13.09.2022
Verlag: Springer Vienna
Erschienen in: Acta Mechanica / Ausgabe 11/2022
Print ISSN: 0001-5970
Elektronische ISSN: 1619-6937
DOI: https://doi.org/10.1007/s00707-022-03333-0

Premium Partner

Marktübersichten

Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.

Zur Marktübersicht

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Weitere Artikel der Ausgabe 11/2022

On the applicability of Southwell’s method to the determination of the critical force of elastic columns of variable cross sections

Aerothermoelastic analysis of curvilinear fiber variable stiffness laminated panels in supersonic flow

A novel formulation for the weak quadrature element method for solving vibration of strain gradient graded nonlinear nanobeams

A mechanical ramp type of electron–hole semiconducting model with laser pulses and variable thermal conductivity

Thermoelectric conversion efficiency of a two-dimensional thermoelectric plate of finite-size with a center crack

Nonlinear dynamic behavior of a damaged laminated shell structure under time-dependent mechanical loading

Premium Partner

Marktübersichten