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References
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Thomson WT, Dahleh MD (1998) Theory of vibrations with applications. Prentice-Hall, Upper
Saddle River, NJ
Timoshenko S, Young DH, Weaver W (1974) vibration problems in engineering. Wiley, New
York
Tondl A (1991) Quenching of self-excited vibrations. Elsevier, Amsterdam
Tondl A, Nabergoj R, Ruijgrok M, Verhulst F (2000) Autoparametric resonance in mechanical
systems. Cambridge University Press, Cambridge
Troger H, Steindl A (1991) Nonlinear stability and bifurcation theory. Springer, New York
Tsonis AA (1992) Chaos—from theory to applications. Plenum, New York
Tufillaro NB, Ramshankar R, Gollub JP (1989) Order-disorder transition in capillary ripples. Phys
Rev Lett 62(4):422–425
Tufillaro NB, Abott T, Reilly J (1992) An experimental approach to nonlinear dynamics and
chaos. Addison-Wesley, Redwood City, California
Turkstra TP, Semercigil SE (1993) Elimination of resonance with a switching tensile support.
J Sound Vib 163(2):359–362
Ueha S, Tomikawa Y (1993) Ultrasonic motors: theory and applications. Clarendon Press, Oxford
Vakakis AF (1997) Non-linear normal modes (NNMs) and their applications in vibration theory:
an overview. Mech Syst Signal Process 11(1):3–22
Vakakis AF, Gendelman O (2001) Energy pumping in nonlinear mechanical oscillators: Part II—
resonance capture. Asme J Appl Mech 68(1):42–48
van der Pol B, Strutt MJO (1928) On the stability of the solutions to Mathieu’s equation. Philos
Mag 5:18–38
Verhulst F (1996a) Nonlinear differential equations and dynamical systems. Springer, Berlin
Verhulst F (1996b) Autoparametric resonance, survey and new results. In: Proceedings of the
EUROMECH 2nd European Nonlinear Oscillation Conference, Prague, September 9–13,
1996, vol 1, pp 483–488
Veskos P, Demiris Y (2006) Experimental comparison of the van der Pol and Rayleigh nonlinear
oscillators for a robotic swinging task. In: Proceedings of the AISB 2006 conference,
adaptation in artificial and biological systems, Bristol, pp 197–202
Weast RC (ed) (1981) Handbook of chemistry and physics. CRC Press, Boca Raton
Weibel S, Kaper TJ, Baillieul J (1997) Global dynamics of a rapidly forced cart and pendulum.
Nonlinear Dyn 13:131–170
Wiercigroch M (2000) Modelling of dynamical systems with motion dependent discontinuities.
Chaos, Solitons Fractals 11:2429–2442
Wolf A, Swift JB, Swinney HL, Vastano JA (1985) Determining Lyapunov exponents from a time
series. Physica 16D:285–317
Woodhouse J (1998) Linear damping models for structural vibration. J Sound Vib 215(3):547–569
Wu B, Zhou Y, Lim CW, Sun W (2018) Analytical approximations to resonance response of
harmonically forced strongly odd nonlinear oscillators. Arch Appl Mech 88:2123–2134
Yabuno H, Tsumoto K (2007) Experimental investigation of a buckled beam under high-frequency
excitation. Arch Appl Mech 77:339–351
Yagasaki K, Sakata M, Kimura K (1990) Dynamics of a weakly nonlinear system subjected to
combined parametric and external excitation. ASME J Appl Mech 57(1):209–217
Yim SCS, Lin H (1991) Nonlinear impact and chaotic response of slender rocking objects. J Eng
Mech 117(9):2079–2100
Zak M (1984) Elastic continua in high frequency excitation field. Int J Non-Linear Mech 19
(5):479–487
Zames G, Shneydor NA (1976) Dither in nonlinear systems. IEEE Trans Autom Control 21
(5):660–667
514
References