(NTU "KhPI", 2016) Plaksiy, Kateryna Yu.; Mikhlin, Yuri V.
Dynamics of the dissipative spring-pendulum system under periodic external excitation in the vicinity of
external resonance and simultaneous external and internal resonances is studied. Analysis of the system
resonance behaviour is made on the base of the concept of nonlinear normal vibration modes (NNMs), which is
generalized for systems with small dissipation. The multiple scales method and subsequent transformation to
the reduced system with respect to the system energy, an arctangent of the amplitudes ratio and a difference of
phases of required solutions are applied. Equilibrium positions of the reduced system correspond to nonlinear
normal modes. So-called Transient nonlinear normal modes (TNNMs), which exist only for some certain levels
of the system energy are selected. In the vicinity of values of time, corresponding to these energy levels, these
TNNMs temporarily attract other system motions. Interaction of nonlinear vibration modes under resonance
conditions is also analysed. Reliability of obtained analytical results is confirmed by numerical and numerical-analytical
simulation.
