The impulse response of a band-limited vibrator with rate-independent hysteretic damping

Abstract

The linear rate-independent damping model is non-causal. But its mathematical form is so attractive that this model and its enhancements are still considered as contemporary research. The linear band-limited hysteretic vibrator (LBLHV) is one such suggested modification for suppressing the non-causality effect. However, its response properties have not been delineated. One of the properties, the unitary impulse response function, will be investigated systematically by the residue theorem here. It was shown that, first, the LBLHV is still non-causal, and the asymptotic rate of the impulse response precursor (IRP) is O(1/t) as time approaches negative infinity. Second, the IRP is no longer monotonic, but composed of two oscillating components. Third, the response at t = 0 can be set to zero by appropriately combining the lower and upper limits of the pass band.