Non-stationary frequency response function

Using the Duhamel's integral concept, a non-stationary frequency response function (complete-FRF) for the dynamic response of a single degree of freedom system initially at rest has been developed. Although the procedure is devised to be applied in the frequency domain, this new function is time dependent and can be employed to calculate the transient response of a system in a forced vibration case. The method has been successfully checked with two different cases of loading in the time domain which have either analytical solution or accurate numerical solution using Newmark's algorithm. The method has been compared with the solution obtained from the commonly used steady frequency response function, and a detailed analysis of the four parameters that appear in the complete-FRF function: time, damping ratio, natural period and input frequency is presented. Finally, the proposed non-steady FRF has been applied to the calculation of an elastic displacement response spectrum to confirm the great influence of the natural period of the system and the frequency content of the solicitation in frequency-domain spectral analysis.