Two-story frame with Bouc-Wen hysteretic links as a multi-degree of freedom nonlinear response simulator

Motivation A diverse variety of engineering and dynamic systems, ranging from control applications and solid mechanics to biology and economics, feature hysteretic phenomena. This commonly encountered nonlinear behavior can be captured and described via diverse numerical models, with the Bouc-Wen representation comprising a common choice within the nonlinear dynamics and vibration engineering community. In this benchmark, the Bouc-Wen model is employed to characterize the response of the nodal connections of a two-story frame structure. The resulting shear frame with hysteretic links is proposed as a multi-degree of freedom nonlinear response simulator. This case study can be seen as an extension to the single degree of freedom 'Hysteretic Benchmark with a Dynamic Nonlinearity' problem already featured in the nonlinear benchmark website (here). Our simulator employs a similar parameterized representation of the Bouc-Wen model for each nonlinear link and builds upon it to also include strength deterioration and stiffness degradation effects in a structure with increased dimensionality. As a result, the featured parametric shear frame serves as a multi-degree of freedom nonlinear response simulator, able to model a wide range of nonlinear effects through the parametrized Bouc-Wen couplings. The provided simulator can be utilized as a benchmark problem to validate methods and tools in structural health monitoring, model reduction, or identification applications.