Frequency domain analysis of time integration operators

Abstract The present paper analyses the error associated with the time integration operators in structural dynamics. It considers the time integration operators as digital recursive filters. The transfer functions of the discretized equations are derived and compared with the transfer function of the differential equation. This leads to a new approach for the accuracy analysis of the time integration operators, which is not restricted to the homogeneous part of the discretized equation. It can therefore be applied to the Duhamel Integral for which, as far as the author is aware, no error analysis has been reported so far. Results are presented for the Newmark's family integration operators. Various assumptions on the variation of the excitation between the sampling points in the Duhamel Integral are also analysed.