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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this article, we consider vibrational systems with semi-active dampingthat are described by a second-order model. In order to minimize the influenceof external inputs to the system response, we are optimizing some dampingvalues. As minimization criterion, we evaluate the energy response, that is the$\cH_2$-norm of the corresponding transfer function of the system. Computingthe energy response includes solving Lyapunov equations for different dampingparameters. Hence, the minimization process leads to high computational costsif the system is of large dimension. We present two techniques that reduce theoptimization problem by applying the reduced basis method to the correspondingparametric Lyapunov equations. In the first method, we determine a reducedsolution space on which the Lyapunov equations and hence the resulting energyresponse values are computed approximately in a reasonable time. The secondmethod includes the reduced basis method in the minimization process. Toevaluate the quality of the approximations, we introduce error estimators thatevaluate the error in the controllability Gramians and the energy response.Finally, we illustrate the advantages of our methods by applying them to twodifferent examples.

Semi-active damping optimization of vibrational systems using the reduced basis method