Limiting performance analysis of shock isolation for transient external disturbances

A single-degree-of-freedom model is used to analyze the limiting performance of a shock isolation system for protecting an object on a moving base from impact pulses undergone by the base. The efficiency of the shock isolation as a function of the shape of the impact pulse is studied. By the shape of the impact pulse, the time history of the impact-induced acceleration of the base is understood. The shock isolator is controlled by a force acting between the object and the base. A constraint is imposed on the absolute value of the control force. The maximum absolute value of the displacement of the object relative to the base is used as the performance index of isolation. It is assumed that the shock pulses have finite durations, do not change in the action direction, and may exceed the maximum value allowed for the object's absolute acceleration in one time interval at most. The change in the velocity of the base due to an impact is assumed to be given. It is shown that if the pulse duration is small enough, then, independently of the pulse shape, the control is performed by a constant force from the beginning of the impact pulse to the instant at which the motion of the object relative to the base stops. A class of shock pulses, within which the optimal control and the performance index do not depend on the pulse shape, is singled out. The minimum value of the maximum displacement of the object relative to the base calculated for the constrained control force is studied as a function of the pulse shape for a number of parametric families of pulses.