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IssuesArchive of Issues2015-3pp.294-304

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R.V. Goldstein, S.V. Kuznetsov, and M.A. Khudyakov, "Study of Forced Vibrations of the Kelvin-Voigt Model with an Asymmetric Spring," Mech. Solids. 50 (3), 294-304 (2015)
Year 2015 Volume 50 Number 3 Pages 294-304
DOI 10.3103/S0025654415030061
Title Study of Forced Vibrations of the Kelvin-Voigt Model with an Asymmetric Spring
Author(s) R.V. Goldstein (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, goldst@ipmnet.ru)
S.V. Kuznetsov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, kuzn-sergey@yandex.ru)
M.A. Khudyakov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, maxim.a.khudyakov@gmail.com)
Abstract We study the damping properties of a modified Kelvin-Voigt system characterized by a spring with different moduli of elasticity and a viscous damper under forced vibrations generated by a harmonic force. We solve the problem by using the Cauchy formalism and by analyzing the properties of the fundamental matrix of the system. The oscillograms, phase portraits, and Poincaré sections corresponding to various parameters of the system are considered.
Keywords spring with different moduli, vibrations, Kelvin-Voigt model, shock-absorbing system
References
1.  S. Maezawa, "Steady Forced Vibrations of Unsymmetrical Piecewise Linear Systems," Bull. Jap. Soc. Mech. Engng 4, 201-229 (1961).
2.  S. W. Shaw and P. J. Holmes, "A Periodically Forced Piecewise Linear Oscillator," J. Sound Vibr. 90, 129-155 (1983).
3.  C. W. Wong, W. S. Zhang, and S. L. Lau, "Periodic Forced Vibration of Unsymmetrical Piecewise-Linear Systems by Incremental Harmonic Balance Method," J. Sound Vibr. 149, 91-105 (1991).
4.  L. Xu, M. W. Lu, and Q. Cao, "Bifurcation and Chaos of a Harmonically Excited Oscillator with Both Stiffness and Viscous Damping Piecewise Linearities by Incremental Harmonic Balance Method," J. Sound Vibr. 264, 873-882 (2003).
5.  G. I. Petrashen', L. A. Molotkov, and P. V. Kraulis, Waves in Layered Homogeneous Isotropic Elastic Media: Contour Integral Method in Nonstationary Problems of Dynamics. (Nauka, Leningrad, 1982) [in Russian].
6.  V. P. Maslov and P. P. Mosolov, "General Theory of the Solutions of the Equations of Motion of an Elastic Medium of Different Moduli," Prikl. Mat. Mekh. 49 (3), 419-437 (1985) [J. Appl. Math. Mech. (Engl. Transl.) 49 (3), 322-336 (1985)].
7.  V. Ph. Zhuravlev and D. M. Klimov, Applied Methods in Theory of Vibrations (Nauka, Moscow, 1988) [in Russian].
8.  O. V. Sadovskaya and V. M. Sadovskii, "Elastoplastic Waves in Granular Materials," Zh. Prikl. Mekh. Tekhn. Fiz. 44 (5), 168-176 (2003) [J. Appl. Mech. Tech. Phys. (Engl. Transl.) 44 (5), 741-747 (2003)].
9.  M. Silveira, B. R. Pontes Jr., and J. M. Balthazar, "Use of Nonlinear Asymmetrical Shock Absorber to Improve Comfort on Passenger Vehicles," J. Sound Vibr. 333, 2114-2129 (2014).
10.  M. Silveira, B. R. Pontes Jr., and J. M. Balthazar, "Vertical and Angular Accelerations with Nonlinear Asymmetrical Shock Absorber in Passenger Vehicles," in ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Vol. 8: 25th Conference on Mechanical Vibration and Noise, Portland, Oregon, USA, August 4-7, 2013.
11.  A. G. Piersol and T. L. Paez, Harris' Shock and Vibration Handbook, 6th ed. (McGraw-Hill Professional, 2010).
12.  J. C. Dixon, The Shock Absorber Handbook, 6th ed. (Wiley, New York, 2007).
13.  F. C. Moon, Chaotic Vibrations. (Wiley, New York, 1987; Mir, Moscow, 1990).
14.  R. C. Hilborn, Chaos and Nonlinear Dynamics, 2th ed. (Oxford Univ. Press, Oxford, 2004).
Received 19 May 2014
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