Frequency-Domain Assessment of Integration Schemes for Earthquake Engineering Problems

Although numerical integration is a technique commonly employed in many time-dependent problems, usually its accuracy relied on a time interval small enough. However, taking into account that time integration formulae can be considered to be recursive digital filters, in this research a criterion based on transfer functions has been employed to characterize a wide range of integration algorithms from a frequency approach, both in amplitude and in phase. By adopting Nyquist’s criterion to avoid the aliasing phenomena, a total of seven integration schemes have been reviewed in terms of accuracy and distortion effects on the frequency content of the signal. Some of these schemes are very well-known polynomial approximations with different degrees of interpolation, but others have been especially defined for solving earthquake engineering problems or have been extracted from the digital signal processing methodology. Finally, five examples have been developed to validate this frequency approach and to investigate its influence on practical dynamic problems. This research, focused on earthquake and structural engineering, reveals that numerical integration formulae are clearly frequency-dependent, a conclusion that obviously has a relevant interest in all dynamic engineering problems, even when they are formulated and solved in the time-domain.