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

Periodic dynamical systems ubiquitously exist in science and engineering. Theharmonic balance (HB) method and its variants have been the most widely-usedapproaches for such systems, but are either confined to low-orderapproximations or impaired by aliasing and improper-sampling problems. Here wepropose a collocation-based harmonic balance framework to successfully unifyand reconstruct the HB-like methods. Under this framework a new conditionalidentity, which exactly bridges the gap between frequency-domain andtime-domain harmonic analyses, is discovered by introducing a novel aliasingmatrix. Upon enforcing the aliasing matrix to vanish, we propose a powerfulreconstruction harmonic balance (RHB) method that obtains extremely high-order(>100) non-aliasing solutions, previously deemed out-of-reach, for a range ofcomplex nonlinear systems including the cavitation bubble equation and thethree-body problem. We show that the present method is 2-3 orders of magnitudemore accurate and simultaneously much faster than the state-of-the-art method.Hence, it has immediate applications in multi-disciplinary problems wherehighly accurate periodic solutions are sought.

Collocation-based harmonic balance framework for highly accurate periodic solution of nonlinear dynamical system