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

In his paper, we present order reduction techniques for nonlinearquasi-periodic systems subjected to external excitations. The order reductiontechniques presented here are based on the Lyapunov-Perrone (L-P)Transformation. For a class of non-resonant quasi-periodic systems, the L-Ptransformation can convert a linear quasi-periodic system into a lineartime-invariant one. This Linear Time-Invariant (LTI) system retains thedynamics of the original quasi-periodic system. Once this LTI system isobtained, the tools and techniques available for analysis of LTI systems can beused, and the results could be obtained for the original quasi-periodic systemvia the L-P transformation. This approach is similar to using theLyapunov-Floquet (L-F) transformation to convert a linear time-periodic systeminto an LTI system and perform analysis and control.  Order reduction is a systematic way of constructing dynamical system modelswith relatively smaller states that accurately retain large-scale systems'essential dynamics. In this work, reduced-order modeling techniques fornonlinear quasi-periodic systems subjected to external excitations arepresented. The methods proposed here use the L-P transformation that makes thelinear part of transformed equations time-invariant. In this work, two orderreduction techniques are suggested. The first method is simply an applicationof the well-known Guyan like reduction method to nonlinear systems. The secondtechnique is based on the concept of an invariant manifold for quasi-periodicsystems.  The 'quasi-periodic invariant manifold' based technique yields' reducibilityconditions.' These conditions help us to understand the various types ofresonant interactions in the system. These resonances indicate energyinteractions between the system states, nonlinearity, and external excitation.

Order Reduction of Nonlinear Quasi-periodic Systems Subjected to External Excitations