Some features of the acceleration impulse response function

Impulse response functions (IRFs) and frequency response functions (FRFs) are fundamental quantities that describe the dynamic behaviour of a linear vibrating system in the time and frequency domains respectively. The acceleration IRF is of particular concern in this paper, because unlike the displacement and velocity IRFs it contains a Delta function as well as a decaying oscillation. The origin of this Delta function is shown to be due to the causality constraint rather than the system. To illustrate the characteristics of the IRFs and FRFs, simulations are presented for a single-degree-of-freedom system, and are supported by some laboratory experimental work. The acceleration IRF is partitioned into the impulse component (Delta function for the simulations) and the oscillatory component. They are separately transformed to the frequency domain to illustrate their effects in the accelerance FRFs for both simulated and measured data.