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Acta Mechanica
Erschienen in: Acta Mechanica 7/2019

26.04.2019 | Original Paper

On the analysis of nonlinear dynamic behavior of an isolation system with irrational restoring force and fractional damping

verfasst von: Y. Y. Dong, Y. W. Han, Z. J. Zhang

Erschienen in: Acta Mechanica | Ausgabe 7/2019

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Abstract

An archetypal isolation system with rational restoring force and fractional damping is proposed and investigated based on the nonlinear mechanism of geometric kinematics. The equations of motion of this nonlinear isolator subject to nonlinear damping and external excitation are derived based on the Lagrange equation. For the free vibration system, the nonlinear irrational restoring force, nonlinear stiffness behaviors, and fractional damping are investigated to show the complex transitions of multi-stability. For the forced vibration system, the analytical expressions of force transmissibility of the nonlinear isolator with single-well potential under the perturbation of viscous damping and harmonic forcing are formulated by applying the harmonic balance method. The shock response spectra of the perturbed system subject to half-sine input are evaluated by the maximum responses. The Melnikov analysis and empirical method are employed to determine the analytical criteria of chaotic thresholds for the homoclinic orbit of the perturbed system with symmetric double-well characteristics. The numerical simulations are carried out to demonstrate periodic solutions, periodic doubling bifurcation, and chaotic solutions. The maximum displacements have been obtained to show the isolation characteristics in the case of chaotic vibration.
Vorheriger Artikel A correspondence between compressible and incompressible plane elastostatics
Nächster Artikel Analysis of high-frequency ANCF modes: Navier–Stokes physical damping and implicit numerical integration
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Literatur
1.
Lei, Z.X., Zhang, L.W., Liew, K.M.: Modeling large amplitude vibration of matrix cracked hybrid laminated plates containing CNTR-FG layers. Appl. Math. Model. 55, 33–48 (2018)MathSciNetCrossRef
2.
Harris, C.M., Paez, T.L.: Shock and Vibration Handbook, 6th edn. McGraw-Hill, New York (2009)
3.
Ibrahim, R.A.: Recent advances in non-linear passive vibration isolators. J. Sound Vib. 314, 371–452 (2008)CrossRef
4.
Liu, C.C., Jing, X.J., Daley, S.: Recent advances in micro-vibration isolation. Mech. Syst. Signal Process. 56, 55–80 (2015)CrossRef
5.
Fulcher, B.A., Shahan, D.W., Haberman, M.R.: Analytical and experimental investigation of buckled beams as negative stiffness elements for passive vibration and shock isolation systems. J. Vib. Acoust. 136, 031009 (2014)CrossRef
6.
Yang, C., Yuan, X.W., Wu, J.: The research of passive vibration isolation system with broad frequency field. J. Vib. Control 19, 1348–1356 (2013)CrossRef
7.
Zhang, L.W., Zhang, Y., Liew, K.M.: Modeling of nonlinear vibration of graphene sheets using a meshfree method based on nonlocal elasticity theory. Appl. Math. Model. 49, 691–704 (2017)MathSciNetCrossRef
8.
Xu, D.L., Yu, Q.P., Zhou, J.X.: Theoretical and experimental analyses of a nonlinear magnetic vibration isolator with quasi-zero-stiffness characteristic. J. Sound Vib. 1332, 3377–3389 (2013)CrossRef
9.
Zhou, N., Liu, K.A.: Tunable high-static-low-dynamic stiffness vibration isolator. J. Sound Vib. 329, 1254–1273 (2010)CrossRef
10.
Zhang, W., Zhao, J.B.: Analysis on nonlinear stiffness and vibration isolation performance of scissor-like structure with full types. Nonlinear Dyn. 86, 17–36 (2016)CrossRef
11.
Le, T.D., Ahn, K.K.: Experimental investigation of a vibration isolation system using negative stiffness structure. Int. J. Mech. Sci. 70, 99–112 (2013)CrossRef
12.
Schuster, H.G.: Reviews of Nonlinear Dynamics and Complexity. Wiley-VCH, Weinheim (2008)CrossRefMATH
13.
Ruzicka, J.E., Derby, T.F.: Influence of Damping in Vibration Isolation. The Shock Vib. Inf. Center, Washington (1971)
14.
Yang, P., Yang, J.M., Ding, J.N.: Dynamic transmissibility of a complex nonlinear coupling isolator. Tsinghua Sci. Technol. 54, 538–542 (2006)MATH
15.
Paola, M.D., Mendola, L.L., Navarra, G.: Stochastic seismic analysis of structures with nonlinear viscous dampers. Tsinghua Sci. Technol. 133, 1475–1478 (2007)
16.
Lang, Z.Q., Jing, X.J., Billings, S.A., Tomlinson, G.R., Peng, Z.K.: Theoretical study of the effects of nonlinear viscous damping on vibration isolation of SDOF systems. J. Sound Vib. 323, 352–365 (2009)CrossRef
17.
Guo, P.F., Lang, Z.Q., Peng, Z.K.: Analysis and design of the force and displacement transmissibility of nonlinear viscous damper based vibration isolation systems. Nonlinear Dyn. 67, 2671–2687 (2012)MathSciNetCrossRefMATH
18.
Yan, S., Lin, B., Fei, J., Liu, P.: Nonlinear dynamic behavior of a rotor bearing system with non-linear viscous damping suspension. In: ASME International Mechanical Engineering Congress Exposition, Tampa, USA (2017)
19.
Guo, P.F., Lang, Z.Q., Peng, Z.K.: Application of a weakly nonlinear absorber to suppress the resonant vibrations of a forced nonlinear oscillator. J. Vib. Acoust. 134, 044502 (2012)CrossRef
20.
Tang, B., Brennan, M.J.: A comparison of two nonlinear damping mechanisms in a vibration isolator. J. Sound Vib. 332, 510–520 (2013)CrossRef
21.
Zhang, Y., Zhang, L.W., Liew, K.M., Yu, J.L.: Free vibration analysis of bilayer graphene sheets subjected to in-plane magnetic fields. Compos. Struct. 144, 86–95 (2016)CrossRef
22.
Wang, Y., Wang, R.C., Meng, H.D.: Analysis and comparison of the dynamic performance of one-stage inerter-based and linear vibration isolators. Int. J. Appl. Mech. 10, 1850005 (2018)CrossRef
23.
Li, J., Li, S.: Generating ultra wide low-frequency gap for transverse wave isolation via inertial amplification effects. Phys. Lett. A 383, S0375960117311507 (2017)
24.
Chen, Y., Wang, L.: Isolation of surface wave-induced vibration using periodically modulated piles. Int. J. Appl. Mech. 6, 1450042 (2014)CrossRef
25.
Zhou, J.X., Wang, K., Xu, D.L., Ouyang, H.J.: Multi-low-frequency flexural wave attenuation in Euler-Bernoulli beams using local resonators containing negative-stiffness mechanisms. Phys. Lett. A 381, 3141–3148 (2017)CrossRef
26.
Moon, F.C., Gollub, J.P.: Chaotic Vibrations: An Introduction for Applied Scientists and Engineers. Wiley-Interscience, Hoboken (2004)CrossRef
27.
Lim, C.W., Lai, S.K., Wu, B.S.: Accurate higher-order analytical approximate solutions to large-amplitude oscillating systems with a general non-rational restoring force. Nonlinear Dyn. 42, 267–281 (2005)CrossRefMATH
28.
Lim, C.W., Wu, B.S., Sun, W.P.: Higher accuracy analytical approximations to the Duffing-harmonic oscillator. J. Sound Vib. 296, 1039–1045 (2006)MathSciNetCrossRefMATH
29.
Lai, S.K., Lim, C.W., Wu, B.S., Wang, C., Zeng, Q.C., He, X.F.: Newton-harmonic balancing approach for accurate solutions to non-linear cubic–quantic Duffing oscillators. Appl. Math. Model. 33, 852–866 (2009)MathSciNetCrossRefMATH
Metadaten
Titel
On the analysis of nonlinear dynamic behavior of an isolation system with irrational restoring force and fractional damping
verfasst von
Y. Y. Dong
Y. W. Han
Z. J. Zhang
Publikationsdatum
26.04.2019
Verlag
Springer Vienna
Erschienen in
Acta Mechanica / Ausgabe 7/2019
Print ISSN: 0001-5970
Elektronische ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-019-02425-8

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