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Transient, forced vibrations of a mechanical system are considered. Dissipative effects such as material damping, aerodynamic damping and damping at interfaces are taken into account. For the modeling of these effects the set of isolated weakly non-linear single degree of freedom oscillators with damping dependent non-linearities is used. The superposition of their responses approximates the resulting response of the system. The justification of this assumption is discussed. The Krylov-Bogoljubov asymptotic method is applied for the investigation of the transient resonance response. Numerical calculations are provided to demonstrate the validity of the Krylov-Bogoljubov first approximation.

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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 run-up 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.