The engineering merit of the "Effective Period" of bilinear isolation systems

This paper examines whether the "effective period" of bilinear isolation systems, as defined invariably in most current design codes, expresses in reality the period of vibration that appears in the horizontal axis of the design response spectrum. Starting with the free vibration response, the study proceeds with a comprehensive parametric analysis of the forced vibration response of a wide collection of bilinear isolation systems subjected to pulse and seismic excitations. The study employs Fourier and Wavelet analysis together with a powerful time domain identification method for linear systems known as the Prediction Error Method. When the response history of the bilinear system exhibits a coherent oscillatory trace with a narrow frequency band as in the case of free vibration or forced vibration response from most pulselike excitations, the paper shows that the "effective period" = $T_{eff}$ of the bilinear isolation system is a dependable estimate of its vibration period; nevertheless, the period associated with the second slope of the bilinear system = $T_2$ is an even better approximation regardless the value of the dimensionless strength,$Q/(K_2u_y)=1/{\alpha}-1$, of the system. As the frequency content of the excitation widens and the intensity of the acceleration response history fluctuates more randomly, the paper reveals that the computed vibration period of the systems exhibits appreciably scattering from the computed mean value. This suggests that for several earthquake excitations the mild nonlinearities of the bilinear isolation system dominate the response and the expectation of the design codes to identify a "linear" vibration period has a marginal engineering merit.