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Hall/CRC
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model two d.o.f. mechanical system performing snap-through motion. Nonlinear Dyn 16
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Nonlinear Dyn 60:639–650
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(7823):31–32
Sorokin VS, Thomsen JJ (2015a) Eigenfrequencies and eigenmodes of a beam with periodically
continuously varying spatial properties. J Sound Vib 347:14–26
Sorokin VS, Thomsen JJ (2015b) Vibration suppression for strings with distributed loading using
spatial cross-section modulation. J Sound Vib 335:66–77
Sorokin VS, Thomsen JJ (2016) Effects of weak nonlinearity on the dispersion relation and
frequency band-gaps of a periodic Bernoulli-Euler beam. Proc Roy Soc A 472
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state chaos. J Sound Vib 152(2):369–372
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structures under parametric excitation. ASME J Appl Mech 56(4):947–952
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chaos in two-well potential systems: superharmonic frequency region. J Sound Vib 152(1):57–
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dynamics. Kluwer, Dordrecht
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beam. ASME J Appl Mech 55(1):190–196
Tcherniak D, Thomsen JJ (1998) Slow effects of fast harmonic excitation for elastic structures.
Nonlinear Dyn 17(3):227–246
Tcherniak DM (1999) The influence of fast excitation on a continuous system. J Sound Vib 227
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References
of unstable periodic orbits. J Comput Nonlinear Dyn 6(1):011005(1–9)
Skiadas CH (ed) (2016) The foundations of chaos revisited: from poincaré to recent advancements.
Springer, Switzerland
Skiadas CH, Skiadas C (eds) (2016) Handbook of applications of chaos theory. Chapman and
Hall/CRC
Smale S (1967) Differential dynamical systems. Bull Am Math Soc 747–817
Sorokin SV, Terentév AV (1998) On Modal interaction, stability and nonlinear dynamics of a
model two d.o.f. mechanical system performing snap-through motion. Nonlinear Dyn 16
(3):239–257
Sorokin VS, Blekhman II, Thomsen JJ (2010) Motions of elastic solids in fluids under vibration.
Nonlinear Dyn 60:639–650
Sorokin VS, Blekhman II (2020) Vibration overcomes gravity on a levitating fluid. Nature 585
(7823):31–32
Sorokin VS, Thomsen JJ (2015a) Eigenfrequencies and eigenmodes of a beam with periodically
continuously varying spatial properties. J Sound Vib 347:14–26
Sorokin VS, Thomsen JJ (2015b) Vibration suppression for strings with distributed loading using
spatial cross-section modulation. J Sound Vib 335:66–77
Sorokin VS, Thomsen JJ (2016) Effects of weak nonlinearity on the dispersion relation and
frequency band-gaps of a periodic Bernoulli-Euler beam. Proc Roy Soc A 472
(2186):20150751(1–22)
Stephenson A (1908a) On a new type of dynamic stability. Mem Proc Manchester Literary Philos
Soc 52(8):1–10
Stephenson A (1908b) On induced stability. Philos Mag 15:233–236
Stephenson A (1909) On induced stability. Philos Mag 17:765–766
Stoker JJ (1950) Nonlinear vibrations. Interscience, New York
Sudor DJ, Bishop SR (1999) Inverted dynamics of a tilted pendulum. Eur J Mech A/Solids
18:517–526
Sugiyama Y, Langthjem MA (2007) Physical mechanism of the destabilizing effect of damping in
continuous non-conservative dissipative systems. Non-Linear Mech 42(1):132–145
Sugiyama Y, Langthjem MA, Katayama K (2019) Dynamic stability of columns under
nonconservative forces—theory and experiment. Springer Nature, Cham, Switzerland
Sugiyama Y, Langthjem MA, Ryo B-J (1999) Realistic follower forces. J Sound Vib 225(4):770–
782
Sung CK, Yu WS (1992) Dynamics of a harmonically excited impact damper: bifurcations and
chaotic motion. J Sound Vib 158(2):317–329
Szemplinska-Stupnicka W (1992) A discussion on necessary and sufficient conditions for steady
state chaos. J Sound Vib 152(2):369–372
Szemplinska-Stupnicka W, Plaut RH, Hsieh J-C (1989) Period doubling and chaos in unsymmetric
structures under parametric excitation. ASME J Appl Mech 56(4):947–952
Szemplinska-Stupnicka W, Rudowski J (1992) Local methods in predicting the occurrence of
chaos in two-well potential systems: superharmonic frequency region. J Sound Vib 152(1):57–
72
Tabarrok B, Rimrott FPJ (1994) Variational methods and complementary formulations in
dynamics. Kluwer, Dordrecht
Tang DM, Dowell EH (1988) On the threshold force for chaotic motions for a forced buckled
beam. ASME J Appl Mech 55(1):190–196
Tcherniak D, Thomsen JJ (1998) Slow effects of fast harmonic excitation for elastic structures.
Nonlinear Dyn 17(3):227–246
Tcherniak DM (1999) The influence of fast excitation on a continuous system. J Sound Vib 227
(2):343–360
512
References