TY - GEN
T1 - Fundamental and subharmonic resonances in a nonlinear oscillator with bifurcating modes
AU - Vakakis, Alexander F.
PY - 1991
Y1 - 1991
N2 - The fundamental and subharmonic resonances of a discrete oscillator with cubic stiffness nonlinearities and linear viscous damping are examined using a multiple-scales averaging analysis. The system is in a '1-1' internal resonance, i.e., it has two equal linearized eigenfrequencies, and possesses nonlinear normal modes. For weak coupling stiffnesses the internal resonance gives rise to a Hamiltonian Pitchfork bifurcation of normal modes which in turn affects the topology of the fundamental and subharmonic resonance curves. It is shown that the number of resonance branches differs before and after the mode bifurcation, and that jump phenomena are possible between forced modes. Some of the steady state solutions were found to be very sensitive to damping: a whole branch of fundamental resonances was eliminated even for small amounts of viscous damping, and subharmonic steady state solutions were shifted by damping to higher frequencies.
AB - The fundamental and subharmonic resonances of a discrete oscillator with cubic stiffness nonlinearities and linear viscous damping are examined using a multiple-scales averaging analysis. The system is in a '1-1' internal resonance, i.e., it has two equal linearized eigenfrequencies, and possesses nonlinear normal modes. For weak coupling stiffnesses the internal resonance gives rise to a Hamiltonian Pitchfork bifurcation of normal modes which in turn affects the topology of the fundamental and subharmonic resonance curves. It is shown that the number of resonance branches differs before and after the mode bifurcation, and that jump phenomena are possible between forced modes. Some of the steady state solutions were found to be very sensitive to damping: a whole branch of fundamental resonances was eliminated even for small amounts of viscous damping, and subharmonic steady state solutions were shifted by damping to higher frequencies.
UR - http://www.scopus.com/inward/record.url?scp=0026397469&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0026397469&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:0026397469
SN - 0791808998
T3 - American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP
SP - 13
EP - 19
BT - Recent Advances in Structural Mechanics - 1991
PB - Publ by ASME
T2 - Winter Annual Meeting of the American Society of Mechanical Engineers
Y2 - 1 December 1991 through 6 December 1991
ER -