The Response of Linear Unstable Systems to Stationary Gaussian Excitation.

摘要

When an unstable, linear mechanical system is perturbed by random ambient disturbances, the dynamical parameters (velocities, pressure) characterizing the system are themselves characterized by statistical and spectral distributions that can be directly evaluated from a statistical and spectral description of the random initial condition. This is a natural extension of the deterministic approach whereby a given initial condition (say, a sinusoidal perturbation) gives rise to a deterministic outcome (say, a time-increasing sinusoidal amplitude). While the deterministic approach is valid only when the initial conditions are known exactly, it must be superseded by a stochastic model when these conditions are known only in a statistical sense. This model is successfully applied to the breakup of liquid jets where turbulence is assumed to provide the random disturbance. (Author)