The Isolation Limits Of Stochastic Vibration

Abstract

The limits on the active isolation of stochastic vibrations are explored. These limits are due to the restricted actuator stroke available for vibration isolation. A one-degree-of-freedom system is analyzed using an ideal actuator, resulting in a kinematic representation. The problem becomes one of finding the minimum acceleration trajectory within a pair of stochastic walls. These walls arise from the constraints on actuator stroke. The wall motion is characterized by an ergodic, stationary, zero-mean, Gaussian random process with known power spectral density. The geometry of the wall trajectories is defined in terms of their significant extrema and zero crossings. This geometry is used in defining a composite trajectory which has a mean square acceleration lower than that on the optimal r.m.s. acceleration path satisfying the stochastic wall inequality constraints. The optimal control problem is solved on a return path yielding the mean square acceleration in terms of the distributions of significant maxima and first-passage time of the wall process. This provides an estimate of the stochastic vibration isolation limit. Two methods of Monte Carlo simulation for obtaining the first-passage time moment are discussed. The methodology is applied to an example isolation problem to find a lower bound on the root-mean-square acceleration given the disturbance power spectral density.