Estimating the “effective period” of bilinear systems with linearization methods, wavelet and time-domain analyses: From inelastic displacements to modal identification

This paper revisits and compares estimations of the effective period of bilinear systems as they result from various published equivalent linearization methods and signal processing techniques ranging from wavelet analysis to time domain identification. This work has been mainly motivated from the modal identification studies which attempt to extract vibration periods and damping coefficients of structures that may undergo inelastic deformations. Accordingly, this study concentrates on the response of bilinear systems that exhibit low to moderate ductility values (bilinear isolation systems are excluded) and concludes that depending on the estimation method used, the values of the “effective period” are widely scattered and they lie anywhere between the period-values that correspond to the first and the second slope of the bilinear system. More specifically, this paper shows that the “effective period” estimated from the need to match the spectral displacement of the equivalent linear system with the peak deformation of the nonlinear system may depart appreciably from the time needed for the nonlinear system to complete one cycle of vibration. Given this wide scattering the paper shows that for this low to moderate ductility values (say μ<10) the concept of the “effective period” has limited technical value and shall be used with caution and only within the limitations of the specific application.

► The paper revisits published methods that estimate the effective period of the bilinear systems. ► The study concentrates on the response of bilinear systems that exhibit low to moderate ductility values. ► Depending on the estimation method used the values of the effective period are widely scattered.