Influence of viscous damping on the earthquake response of linear structures

Abstract

The influence of viscous damping, expressed in terms of critical damping, on the response spectrum of single degree of freedom linear structures is analyzed. The spectra published by Alford, Housner and Martel are taken as a basis for this analysis, and the results arc confirmed through the standard spectra proposed by Housner and also through mean spectra obtained by Byeroft for linear oscillators subjected to random acceleration pulses. It is concluded that there is a very clear dependence between the magnitude of the response and the damping ratio: for a structure ith given period, the response is proportional to n-O.4 for n > 0.02. A theoretical analysis due to Hudson shows that the response for a structure of given period is proportional to n-0.5. This result can be generalized for structures with several degrees of freedom under the following hypothesis: the earthquake may be represented as a stationary random process known as white noise; there are principal modes of vibration that are orthogonal and their frequencies are all different. The discrepancy between theoretical and experimental results is explained as arising from the finite duration of real earthquakes The findings of Hudson are extended to include the possibility of comparing the responses of undamped and damped oscillators.