Response spectrum of incompatible acceleration, velocity and displacement histories by Praveen K. Malhotra, Earthquake Engng Struct. Dyn. 2001; 30(2):279–286

Abstract

The Discussers would like to congratulate the Author for his contribution to the analysis of response spectra. As mentioned in the Original Paper, engineers often pay little attention to incompatibilities in the histories of ground acceleration, displacement, and velocity. As a result, computed response spectra may exhibit erroneous trends at short and long periods. Different techniques have been proposed to treat the problem, focusing primarily on the initial conditions of the oscillator [5,6,8,9,10,11]. The Author proposes an alternative technique: determining response spectra by combining the incompatible time histories using a 'mixing rule' (Equations (6)-(8) in the Original Paper, which allows for the proper asymptotic behaviour to be obtained at extreme periods. The scope of this discussion is three-fold: (i) to present a simplified version of the method, by applying the Author's idea only to initial conditions; (ii) to discuss a more general mixing rule; (iii) to propose alternative ways for estimating the effective frequency of ground motion. These items are presented to further validate the results provided by the Author and offer additional insight into the derivations presented in the Original Paper.