On the numerical damping of time integrators for coupled mechatronic systems

The generalized-α time integrator is considered for the simulation of mechatronic systems. In this context, the fundamental concept of numerical damping is analysed for coupled sets of first and second-order differential–algebraic equations. First, it appears that the algebraic variables do not influence the spectral properties of the dynamic variables. Second, we demonstrate that the coupling between the dynamic variables does not influence the high-frequency spectral response, so that the numerical damping can be determined as usual from elementary characteristic polynomials. Those results are exploited to assess the stability properties of the scheme and to select an algorithm with optimal damping properties.