Nonlinear normal modes, modal interactions and isolated resonance curves
  The objective of the present study is to explore the connection between the nonlinear normal modes of an undamped and unforced nonlinear system and the isolated resonance curves that may appear in the damped response of the forced system. To this end, an energy balancing technique is used to predict the amplitude of the harmonic forcing that is necessary to excite a specific nonlinear normal mode. A cantilever beam with a nonlinear spring at its tip serves to illustrate the developments. The practical implications of isolated resonance curves are also discussed by computing the beam response to sine sweep excitations of increasing amplitudes. 
Robert J. Kuether, Ludovic Renson, Thibaut Detroux, Chiara   Grappasonni, Gaetan Kerschen, Matthew S. Allen
math.DS