Accuracy of time history analysis of impulses

It was found that a very small time step might be needed in the step-by-step solution of the shock response from an impulse. In fact, this time step might be much smaller than the time step needed for accurate representation of the impulse and negligible period distortion. In this study, it is analytically verified that this difficulty arises from the discontinuity in the external force. In addition, a technique used to estimate the relative amplitude error caused by this discontinuity is also developed. In fact, the numerical accuracy of the shock response from a linear impulse is thoroughly explored in terms of both amplitude and period. Analytical results show that the numerical accuracy might be entirely dominated by amplitude distortion for an impulse with significant discontinuity in the external force. However, it is generally controlled by period distortion if there is no discontinuity in the external force. It is also found that amplitude distortion is not significantly affected by viscous damping. Guidelines for obtaining an accurate shock response from an impulse are proposed and thoroughly verified, through numerical examples.