Païdoussis MP, Li GX, Rand RH (1991) Chaotic motions of a constrained pipe conveying fluid:
comparison between simulation, analysis, and experiment. ASME J Appl Mech 58(2):559–565
Païdoussis MP, Semler C (1993) Nonlinear dynamics of a fluid-conveying cantilevered pipe with
an intermediate spring support. J Fluids Struct 7:269–298
Panovko YG, Gubanova II (1965) Stability and oscillations of elastic systems; paradoxes, fallacies
and new concepts. Consultants Bureau, New York
Parker TS, Chua LO (1989) Practical numerical algorithms for chaotic systems. Springer-, New
York
Pearson CE (1974) Handbook of applied mathematics. Van Nostrand Reinhold Co., New York
Pecora LM, Caroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821–824
Pedersen P (1986) Quantitative dynamic stability. Doctoral dissertation, Technical University of
Denmark
Peeters M, Kerschen G, Golinval JC (2011) Dynamic testing of nonlinear vibrating structures
using nonlinear normal modes. J Sound Vib 330(3):486–509
Peter S, Riethmüller R, Leine RI (2016) Tracking of backbone curves of nonlinear systems using
phase-locked-loops. In: Kerschen G (ed) Nonlinear dynamics, vol 1. Conference proceedings
of the society for experimental mechanics series. Springer, Cham
Peterson I (1990) Rock and roll bridge. Sci News 137(November):344–346
Pilipchuk VN (1988) Transformation of the vibratory-systems by means of a pair of non-smooth
periodic-functions (In Ukrainian), Dopovidi Akademii Nauk Ukrainskoi Rsr Seriya
A-Fiziko-Matematichni Ta Technichni Nauki 4:36–38
Pilipchuk VN (2002) Some remarks on non-smooth transformations of space and time for
vibrating systems with rigid barriers. PMM J Appl Math Mech 66:31–37
Poddar B, Moon FC, Murkherjee S (1988) Chaotic motion of an elastic-plastic beam. ASME J
Appl Mech 55(1):185–189
Poincaré H (1899) Les Méthods Nouvelles de la Mécanique Céleste, vol 1–3. Gauthier-Villars,
Paris (in French)
Polyanin AD, Zaitsev VF (2003) Handbook of exact solutions for ordinary differential equations,
2nd edn. Chapman & Hall/CRC, Boca Raton, Florida
Popp K (1992) Some model problems showing stick-slip motion and chaos. In: Friction-induced
vibration, chatter, squeal, and chaos, ASME DE-vol 49, pp 1–12
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2002) Numerical recipes. Cambridge
University Press, Cambridge
Quinn D, Rand R, Bridge J (1995) The dynamics of resonant capture. Nonlinear Dyn 8(1):1–20
Rakaric Z, Kovacic I (2016) Mechanical manifestations of bursting oscillations in slowly rotating
systems. Mech Syst Signal Process 81:35–42
Rayleigh JWS (1877) The theory of sound, vol 1–2, 2nd edn, 1945 re-issue. Dover Publications,
New York
Rebouças GFS, Santos IF, Thomsen JJ (2017) Validation of vibro-impact force models by
numerical simulation, perturbation methods and experiments. J Sound Vib 413:291–307
Rebouças GFS, Santos IF, Thomsen JJ (2019) Unilateral vibro-impact systems—experimental
observations against theoretical predictions based on the coefficient of restitution. J Sound Vib
440:346–371
Rega G, Settimi V, Lenci S (2020) Chaos in one-dimensional structural mechanics. Nonlinear Dyn
102:785–834
Renson L, Gonzalez-Buelga A, Barton DAW, Neild SA (2016) Robust identification of backbone
curves using control-based continuation. J Sound Vib 367:145–158
Renson L, Kerschen G, Cochelin B (2016) Numerical computation of nonlinear normal modes in
mechanical engineering. J Sound Vib 364:177–206
Renson L, Shaw AD, Barton DAW, Neild SA (2019) Application of control-based continuation to
a nonlinear structure with harmonically coupled modes. Mech Syst Signal Process 120:449–
464
510
References
comparison between simulation, analysis, and experiment. ASME J Appl Mech 58(2):559–565
Païdoussis MP, Semler C (1993) Nonlinear dynamics of a fluid-conveying cantilevered pipe with
an intermediate spring support. J Fluids Struct 7:269–298
Panovko YG, Gubanova II (1965) Stability and oscillations of elastic systems; paradoxes, fallacies
and new concepts. Consultants Bureau, New York
Parker TS, Chua LO (1989) Practical numerical algorithms for chaotic systems. Springer-, New
York
Pearson CE (1974) Handbook of applied mathematics. Van Nostrand Reinhold Co., New York
Pecora LM, Caroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821–824
Pedersen P (1986) Quantitative dynamic stability. Doctoral dissertation, Technical University of
Denmark
Peeters M, Kerschen G, Golinval JC (2011) Dynamic testing of nonlinear vibrating structures
using nonlinear normal modes. J Sound Vib 330(3):486–509
Peter S, Riethmüller R, Leine RI (2016) Tracking of backbone curves of nonlinear systems using
phase-locked-loops. In: Kerschen G (ed) Nonlinear dynamics, vol 1. Conference proceedings
of the society for experimental mechanics series. Springer, Cham
Peterson I (1990) Rock and roll bridge. Sci News 137(November):344–346
Pilipchuk VN (1988) Transformation of the vibratory-systems by means of a pair of non-smooth
periodic-functions (In Ukrainian), Dopovidi Akademii Nauk Ukrainskoi Rsr Seriya
A-Fiziko-Matematichni Ta Technichni Nauki 4:36–38
Pilipchuk VN (2002) Some remarks on non-smooth transformations of space and time for
vibrating systems with rigid barriers. PMM J Appl Math Mech 66:31–37
Poddar B, Moon FC, Murkherjee S (1988) Chaotic motion of an elastic-plastic beam. ASME J
Appl Mech 55(1):185–189
Poincaré H (1899) Les Méthods Nouvelles de la Mécanique Céleste, vol 1–3. Gauthier-Villars,
Paris (in French)
Polyanin AD, Zaitsev VF (2003) Handbook of exact solutions for ordinary differential equations,
2nd edn. Chapman & Hall/CRC, Boca Raton, Florida
Popp K (1992) Some model problems showing stick-slip motion and chaos. In: Friction-induced
vibration, chatter, squeal, and chaos, ASME DE-vol 49, pp 1–12
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2002) Numerical recipes. Cambridge
University Press, Cambridge
Quinn D, Rand R, Bridge J (1995) The dynamics of resonant capture. Nonlinear Dyn 8(1):1–20
Rakaric Z, Kovacic I (2016) Mechanical manifestations of bursting oscillations in slowly rotating
systems. Mech Syst Signal Process 81:35–42
Rayleigh JWS (1877) The theory of sound, vol 1–2, 2nd edn, 1945 re-issue. Dover Publications,
New York
Rebouças GFS, Santos IF, Thomsen JJ (2017) Validation of vibro-impact force models by
numerical simulation, perturbation methods and experiments. J Sound Vib 413:291–307
Rebouças GFS, Santos IF, Thomsen JJ (2019) Unilateral vibro-impact systems—experimental
observations against theoretical predictions based on the coefficient of restitution. J Sound Vib
440:346–371
Rega G, Settimi V, Lenci S (2020) Chaos in one-dimensional structural mechanics. Nonlinear Dyn
102:785–834
Renson L, Gonzalez-Buelga A, Barton DAW, Neild SA (2016) Robust identification of backbone
curves using control-based continuation. J Sound Vib 367:145–158
Renson L, Kerschen G, Cochelin B (2016) Numerical computation of nonlinear normal modes in
mechanical engineering. J Sound Vib 364:177–206
Renson L, Shaw AD, Barton DAW, Neild SA (2019) Application of control-based continuation to
a nonlinear structure with harmonically coupled modes. Mech Syst Signal Process 120:449–
464
510
References