English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Structural damping is known to be approximately rate-independent in manycases. Popular models for rate-independent dissipation are hysteresis models;and a highly popular hysteresis model is the Bouc-Wen model. If such hystereticdissipation is incorporated in a refined finite element model, then themathematical model includes the usual structural dynamics equations along withnonlinear nonsmooth ordinary differential equations for a large number ofinternal hysteretic states at Gauss points, to be used within the virtual workcalculation for dissipation. For such systems, numerical integration becomesdifficult due to both the distributed non-analytic nonlinearity of hysteresisas well as the very high natural frequencies in the finite element model. Herewe offer two contributions. First, we present a simple semi-implicitintegration approach where the structural part is handled implicitly based onthe work of Pich\'e, and where the hysteretic part is handled explicitly. Acantilever beam example is solved in detail using high mesh refinement.Convergence is good for lower damping and a smoother hysteresis loop. For aless smooth hysteresis loop and/or higher damping, convergence is observed tobe roughly linear on average. Encouragingly, the time step needed for stabilityis much larger than the time period of the highest natural frequency of thestructural model. Subsequently, data from several simulations conducted usingthe above semi-implicit method are used to construct reduced order models ofthe system, where the structural dynamics is projected onto a small number ofmodes and the number of hysteretic states is reduced significantly as well.Convergence studies of error against the number of retained hysteretic statesshow very good results.

Semi-implicit Integration and Data-Driven Model Order Reduction in Structural Dynamics with Hysteresis