Barrier Crossing Due to Transient Excitation

The first‐passage time problem for the response amplitude of a linear lightly damped single‐degree‐of‐freedom oscillator under evolutionary random excitation is considered. A Markovian approximation of the amplitude allows the use of a Fokker‐Planck equation for the formulation of the problem. This equation is solved exactly for the special case of a step function‐modulated stationary excitation. These results are used in determining a solution for the general excitation case via a Galerkin technique. Pertinent digital simulation data demonstrate the reliability and extreme efficiency of the developed solution method.