Rhoads JF, Jeffrey F, Miller NJ, Nicholas J, Shaw SW, Feeny BF (2008) Mechanical domain
parametric amplification. ASME J Vib Acoust 130(6):061006(1–7)
Rhoads JF, Shaw SW (2010) The impact of nonlinearity on degenerate parametric amplifiers. Appl
Phys Lett 96(23):234101(1–3)
Romeiras FJ, Bondeson A, Ott E, Antonsen TM, Grebogi C (1987) Quasiperiodically forced
dynamical systems with strange nonchaotic attractors. Physica 26D:277–294
Rosenberg RM (1960) Normal modes of nonlinear dual-mode systems. ASME J Appl Mech 27
(2):263–268
Rosenstein MT, Collins JJ, De Luca CJ (1993) A practical method for calculating largest
Lyapunov exponents from small data sets. Physica D 65:117–134
Ross SS (1984) Construction disasters. McGraw-Hill, New York
Rossikhin YA, Shitikova MV (1995) Analysis of nonlinear free vibrations of suspension bridges.
J Sound Vib 186(3):369–393
Rudowski J, Szemplinska-Stupnicka W (1987) On an approximate criterion for chaotic motion in a
model of a buckled beam. Ing Archiv 57:243–255
Sah SM, McGehee CC, Mann BP (2013) Dynamics of a horizontal pendulum driven by
high-frequency rocking. J Sound Vib 332:6505–6518
Sah SM, Thomsen JJ, Brøns M, Fidlin A, Tcherniak D (2018) Estimating bolt tightness using
transverse natural frequencies. J Sound Vib 431:137–149
Sanders JA, Verhulst F (1985) Averaging methods in nonlinear dynamical systems. Appl Math Sci
59 (Springer, New York)
Sayag MR, Dowell EH (2016) Linear versus nonlinear response of a cantilevered beam under
harmonic base excitation: theory and experiment. ASME J Appl Mech 83(10):101002(1–8)
Schmidt G, Tondl A (2009) Non-Linear vibrations. Cambridge University Press, Cambridge
Schmitt JM, Bayly PV (1998) Bifurcations in the mean angle of a horizontally shaken pendulum:
analysis and experiment. Nonlinear Dynamics 15:1–14
Schuster HG (1989) Deterministic chaos. VCH Verlag, Weinheim
Sethna PR (1967) An extension of the method of averaging. Q Appl Math 25:205–211
Seydel R (2010) Practical bifurcation and stability analysis. Springer, New York
Shabana AA (1996) Theory of vibration I: an introduction. Springer, New York
Shabana AA (1997) Theory of vibration II: discrete and continuous systems. Springer, New York
Shapiro B, Zinn B (1997) High-frequency nonlinear vibrational control. IEEE Trans Autom
Control 42(1):83–90
Shaw SW and Holmes PJ (1983) A periodically forced piecewise linear oscillator. J Sound Vib 90
(l):129–155
Shaw SW, Pierre C (1993) Normal modes for non-linear vibratory systems. J Sound Vib 164
(1):85–124
Sheheitli H, Rand RH (2011) Dynamics of three coupled limit cycle oscillators with vastly
different frequencies. Nonlinear Dyn 64:131–145
Sheheitli H, Rand RH (2012) Dynamics of a mass-spring-pendulum system with vastly different
frequencies. Nonlinear Dyn 70(1):25–41
Shin Y-H, Choi J, Kim SJ, Kim S, Maurya D, Sung T-H, Priya S, Kang C-Y, Song H-C (2020)
Automatic resonance tuning mechanism for ultra-wide bandwidth mechanical energy
harvesting. Nano Energy 77:104986
Shinbrot T, Ott E, Grebogi C, Yorke JA (1990) Using chaos to direct trajectories to targets. Phys
Rev Lett 65(26):3215–3219
Shishkina EV, Blekhman II, Cartmell MP, Gavrilov SN (2008) Application of the method of direct
separation of motions to the parametric stabilization of an elastic wire. Nonlinear Dyn 54:313–
331
Siddiqui SAQ, Golnaraghi MF, Heppler GR (2003) Large free vibrations of a beam carrying a
moving mass. Int J Non-Linear Mech 38:1481–1493
Sieber J, Krauskopf B (2008) Control based bifurcation analysis for experiments. Nonlinear Dyn
51(3):365–377
References
511
parametric amplification. ASME J Vib Acoust 130(6):061006(1–7)
Rhoads JF, Shaw SW (2010) The impact of nonlinearity on degenerate parametric amplifiers. Appl
Phys Lett 96(23):234101(1–3)
Romeiras FJ, Bondeson A, Ott E, Antonsen TM, Grebogi C (1987) Quasiperiodically forced
dynamical systems with strange nonchaotic attractors. Physica 26D:277–294
Rosenberg RM (1960) Normal modes of nonlinear dual-mode systems. ASME J Appl Mech 27
(2):263–268
Rosenstein MT, Collins JJ, De Luca CJ (1993) A practical method for calculating largest
Lyapunov exponents from small data sets. Physica D 65:117–134
Ross SS (1984) Construction disasters. McGraw-Hill, New York
Rossikhin YA, Shitikova MV (1995) Analysis of nonlinear free vibrations of suspension bridges.
J Sound Vib 186(3):369–393
Rudowski J, Szemplinska-Stupnicka W (1987) On an approximate criterion for chaotic motion in a
model of a buckled beam. Ing Archiv 57:243–255
Sah SM, McGehee CC, Mann BP (2013) Dynamics of a horizontal pendulum driven by
high-frequency rocking. J Sound Vib 332:6505–6518
Sah SM, Thomsen JJ, Brøns M, Fidlin A, Tcherniak D (2018) Estimating bolt tightness using
transverse natural frequencies. J Sound Vib 431:137–149
Sanders JA, Verhulst F (1985) Averaging methods in nonlinear dynamical systems. Appl Math Sci
59 (Springer, New York)
Sayag MR, Dowell EH (2016) Linear versus nonlinear response of a cantilevered beam under
harmonic base excitation: theory and experiment. ASME J Appl Mech 83(10):101002(1–8)
Schmidt G, Tondl A (2009) Non-Linear vibrations. Cambridge University Press, Cambridge
Schmitt JM, Bayly PV (1998) Bifurcations in the mean angle of a horizontally shaken pendulum:
analysis and experiment. Nonlinear Dynamics 15:1–14
Schuster HG (1989) Deterministic chaos. VCH Verlag, Weinheim
Sethna PR (1967) An extension of the method of averaging. Q Appl Math 25:205–211
Seydel R (2010) Practical bifurcation and stability analysis. Springer, New York
Shabana AA (1996) Theory of vibration I: an introduction. Springer, New York
Shabana AA (1997) Theory of vibration II: discrete and continuous systems. Springer, New York
Shapiro B, Zinn B (1997) High-frequency nonlinear vibrational control. IEEE Trans Autom
Control 42(1):83–90
Shaw SW and Holmes PJ (1983) A periodically forced piecewise linear oscillator. J Sound Vib 90
(l):129–155
Shaw SW, Pierre C (1993) Normal modes for non-linear vibratory systems. J Sound Vib 164
(1):85–124
Sheheitli H, Rand RH (2011) Dynamics of three coupled limit cycle oscillators with vastly
different frequencies. Nonlinear Dyn 64:131–145
Sheheitli H, Rand RH (2012) Dynamics of a mass-spring-pendulum system with vastly different
frequencies. Nonlinear Dyn 70(1):25–41
Shin Y-H, Choi J, Kim SJ, Kim S, Maurya D, Sung T-H, Priya S, Kang C-Y, Song H-C (2020)
Automatic resonance tuning mechanism for ultra-wide bandwidth mechanical energy
harvesting. Nano Energy 77:104986
Shinbrot T, Ott E, Grebogi C, Yorke JA (1990) Using chaos to direct trajectories to targets. Phys
Rev Lett 65(26):3215–3219
Shishkina EV, Blekhman II, Cartmell MP, Gavrilov SN (2008) Application of the method of direct
separation of motions to the parametric stabilization of an elastic wire. Nonlinear Dyn 54:313–
331
Siddiqui SAQ, Golnaraghi MF, Heppler GR (2003) Large free vibrations of a beam carrying a
moving mass. Int J Non-Linear Mech 38:1481–1493
Sieber J, Krauskopf B (2008) Control based bifurcation analysis for experiments. Nonlinear Dyn
51(3):365–377
References
511