On the impulse response precursor of an ideal linear hysteretic damper

The model of the ideal linear hysteretic damper has been shown to possess a non-causal impulse response precursor. However, the relevant characteristics of the impulse response precursor (its extremum, monotonicity, and asymptotic property) were not well comprehended in the literature. In this paper, an impulse response precursor expression was derived. It was observed that the impulse response precursor achieves its only extremum, which is negative, at the origin. The impulse response precursor monotonically increases from this extremum to zero while time retraces to the negative infinity. The asymptotic rate of impulse response precursor approaching zero is O(1/t). The non-causal size gets stronger as the loss factor increases. Numerical computation also shows that the non-causal extremum is even deeper than the first trough of the causal portion of the impulse response when the loss factor is greater than 0.77.