Accuracy of Time Integration Procedures for Seismic Response of Linear Oscillators

Abstract eng:
The goodness of time integration algorithms commonly used in earthquake engineering is characterized in this paper by the ratios of their transfer function to the ones corresponding to the exact integration operator. This approach permits to appraise very easily how the different components of the seismic action are affected by the oscillator and to quantify the adequacy of the integration scheme as the excitation frequency approaches the Nyquist frequency. Using this methodology, the effects of various temporal algorithms (recursive digital filters) on the accuracy of the seismic response of linear systems are investigated, both for Duhamel integral methods and for time-stepping methods. Analytical solutions are applied to several examples of discrete and continuum linear systems to elucidate the influence on the overall error of the unknown variation of the input motion between sampling points, as well as the uneven distortion of the frequencies introduced by the integration process.

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