Stability analysis of Rosenbrock-based Real-time compatible method via the energy approach

The focus of this paper is on stability analysis of 2-Stage Rosenbrock-based Real-time integrator for nonlinear structural dynamic problems, but the analysis spans both linear and nonlinear ranges. In linear case, the energy approach is presented to study its energy decaying property and high-frequency dissipation property. To investigate its nonlinear stability, numerical simulations are conducted on a shear-type structure including a pendulum. The theoretical analysis and the numerical simulations, on the one hand, efficiently demonstrate the applicability of the integrator to complicated structural problems; on the other hand, provide favorable approaches to investigate performances of other monolithic integrators.