Semi-Implicit Integration and Data-Driven Model Order Reduction in Structural Dynamics With Hysteresis

Abstract Structural damping is often empirically rate-independent wherein the dissipative part of stress depends on history deformation but not its rate change. Hysteresis models are popular for dissipation; and a hysteresis model Bouc-Wen model. If such hysteretic dissipation incorporated in refined finite element model, then involves usual structural dynamics equations along with nonlinear nonsmooth ordinary differential large number internal states at Gauss points used within virtual work calculation. For systems, numerical integration difficult due to both distributed nonanalytic nonlinearity as well natural frequencies Here, we offer two contributions. First, present simple semi-implicit approach where handled implicitly based Piché, while explicitly. A cantilever beam example solved detail using high mesh refinement. Convergence good lower smoother loop. less smooth loop and/or higher damping, convergence noted be roughly linear average. Encouragingly, time-step needed stability much larger than time period highest frequency Subsequently, data from several simulations conducted above method construct reduced order system, projected onto few modes significantly well. studies error against retained show very results.