S-Transform: A Band-Variable Filter to Extract the Nonlinear Dynamic Behaviour of Soil and Structures.

The Fourier transform is certainly one of the main tools used to study the dynamic response of systems. This integral transformation is very useful and reliable if one wants to investigate the response of a stationary system, i.e. a system that doesn't changes its characteristics over time. On the contrary, when the study on the evolution of the dynamic response of a system whose characteristics vary with time is required, the Fourier transform is no longer reliable. In this regard, several mathematical tools to analyze time-variable dynamic responses were developed. Soil and buildings, subject to transient forcing such as an earthquake, may change their characteristics over time with initiation of non-linear phenomena. In most of cases, both for soil and buildings, abandoning the linear elastic field could represent a problem. This paper proposes a new methodology to approach the study of non-stationary response of soil and buildings: a band-variable filter based on the S-Transform. In fact, thanks to the possibility of change the bandwidth over time, it becomes possible to extract from a generic signal only the response of the system focusing on the variation of individual modes of vibration. In this paper, possible applications of the band variable filter to study the non-stationary response of soil and buildings have been proposed.