Analysis of non-stationary structural systems by using a band-variable filter

One of the main tools used to study the dynamic response of structural systems is certainly the Fourier Transform. This tool is very useful and reliable to investigating the response of a stationary system, i.e. a generic system that does not changes its characteristics over time. Conversely, the Fourier Transform is no longer reliable if the main goal is to study the evolution of the dynamic response of a system whose features rapidly vary with time. To this regard, several mathematical tools were developed to analyze time-variable dynamic responses. Soil and buildings, subject to transient forcing such as an earthquake, may change their characteristics over time with the initiation of nonlinear phenomena. This paper proposes a new methodology to approach the study of non-stationary response of soil and buildings: a band-variable filter based on S-Transform. In fact, with the possibility of changing the bandwidth of each filtering window over time, it becomes possible to extract from a generic record only the response of the system focusing on the variation of individual modes of vibration. Practically, it is possible to extract from a generic non-stationary signal only the phase of interest. The paper starts from examples and applications on synthetic signals, then examines possible applications to the study of the non-stationary response of soil and buildings. The last application focuses on the possibility to evaluate the mode shapes over time for both numerical and scaled model subjected to strong motion inputs.