Maximum response of a slow-variant mechanical system during transition through a resonance

摘要

A new approach to the estimation of the maximum transient response of a mechanical system with slow-variant natural frequencies and linear viscous damping is worked out. Based on the modal decomposition, the vibration response of a system is modeled using a set of simple vibrators with slow-variant natural frequencies. The passage through a resonance which is induced by a sweep of the excitation frequency during runup or run-down is studied. Exact asymptotic formulas for the maximum transient response and the corresponding excitation frequency are derived analytically, starting from the first Krylov-Bogoliubov approximation. The obtained formulas are tested numerically and compared to known approximations.