The focus of this article is on generating spectrum‐compatible acceleration, velocity, and displacement time histories for seismic analysis and design of engineering structures. If a generated acceleration time history is integrated to obtain the corresponding velocity and displacement time histories, it has been found that there are usually drifts in the resulting processes. Such drifts are due to overdeterminacy in the constants of integration. Baseline correction, although widely used, is not a suitable remedial measure to remove drift because it distorts the frequency content and renders the corrected processes no longer mutually consistent.

The objective of this article is to develop an efficient and accurate method for generating drift‐free, consistent, and spectrum‐compatible time histories, which are essential properties for these time histories to be used as seismic input in time history analysis. To ensure drift‐free and consistent behavior, the eigenfunction method is applied to expand the time histories in eigenfunctions of a sixth‐order ordinary differential eigenvalue problem. The influence matrix method considering the influence of one frequency component on all others is capable of achieving perfect spectrum compatibility which has never been accomplished.

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