Rapid Controllable Damper Design for Complex Structures with a Hybrid Reduced-Order Modeling/Simulation Approach

Evaluating controllable damping designs typically requires simulation of the resulting inherently nonlinear closed-loop system because linear design strategies cannot always be reliably used. These analyses typically require many simulations, each a function evaluation in a parameter study or optimization. For complex structural models, these simulations can require significant computational resources. Further, complex structural models requiring repeated solutions of high-order Riccati equations for each function evaluation further exacerbate the computational burden. This paper demonstrates that a reduced-order model for designing the control strategy, resulting in a low-order control law, coupled with the full model of the original system, falls in the class of systems that are mostly linear but with very localized nonlinearities. For such systems, the authors have previously developed an approach that reduces the equations of motion to a low-order nonlinear Volterra integral equation that can be rapidly solved for each function evaluation. The proposed approach is evaluated using two numerical examples, a moderate-order seismically excited isolated building and a high-order wind-excited building, showing that exploiting the localized nature of the nonlinearities can speed up the computations by a factor of approximately 200, and further gains are achieved for the high-order example by basing the dynamic control strategies on reduced-order models but evaluating them with the full system model. The result is a strategy for complex structures that reduces the computation time for a typical controllable damping design parameter study from more than a year to less than a day, making these design studies computationally tractable.