Application of the momentum equations of motion to pseudo–dynamic testing

Four major advantages can be found if a step–by–step integration method is used to solve the momentum equations of motion in performing a pseudo–dynamic test. The first is that less error propagation is shown and the second is that the external momentum–dependent effect of an impulse can be more easily reflected when compared with the use of the force equations of motion. The third is that the rapid changes of dynamic loading can be smoothed out by time integration of the external force and consequently can be easily captured. The fourth advantage is that the detailed variation of resistance within each time–step will be thoroughly taken into account through the time integration of restoring–force and the linearization errors will then be drastically reduced or even eliminated. As a result, more accurate pseudo–dynamic test results can be obtained if the momentum equations of motion are applied. In addition to the four major advantages of using the momentum equations of motion, improved pseudo–dynamic results can be further obtained if a dissipative integration algorithm is employed to perform the step–by–step integration. This is because the favourable numerical dissipation can effectively suppress the spurious growth of high–frequency responses, while the lower modes are integrated very accurately. In this study, the integral form of the γ–function dissipative explicit method is chosen to confirm all the advantages both numerically and experimentally.