Vibrational analogue of nonadiabatic Landau–Zener tunneling and a possibility for the creation of a new type of energy trap

The problem of irreversible targeted energy transfer is approached in a new way using the analogy between a system of two weakly coupled parametric pendulums or oscillators and nonadiabatic Landau–Zener tunneling in a two-state quantum system. This analogy predicts that efficient irreversible energy transfer is possible between two subsystems if the frequency of at least one of them changes adiabatically slowly with time, thus allowing an internal resonance to occur between them. We also show that evolution equations for the transition of the Landau–Zener tunneling type give a quantitative prediction for the part of the initially imparted energy that is retained asymptotically in the protected classical system. The findings made can be used for designing new types of energy traps for the dynamical protection of various mechanical systems.