Observations on the effect of numerical dissipation on the nonlinear dynamic response of structural systems

Analysis of highly nonlinear systems subjected to dynamic loads involves continuously changing temporal solution characteristics. This is due to changes in the stiffness, and hence, the periods of vibration, with the consequence of changes in the extent of numerical dissipation (or algorithmic damping). The effect of modal contributions in the time-marching solution procedure is discussed in this paper through the implementation of an α-damping scheme within the frontal solution procedure employed in a generalized dynamic analysis program. As the theoretical background to the effectiveness of such a dissipative scheme is restricted to linear analysis, the interaction between the time integration step size and the finite element idealization errors in the nonlinear range is investigated by means of numerical examples. It is concluded that the use of a numerically dissipative scheme in conjunction with a carefully selected cutoff frequency is essential in acceleration response predictions, particularly where a highly nonlinear response is of interest. It is also shown that the displacement response is much less affected by the spurious higher modes of vibration and that the time required to achieve successful dissipation of the spurious higher mode response may involve the execution of a significant number of time-steps.