Collocation?based harmonic balance framework for highly accurate periodic solution of nonlinear dynamical system
نویسندگان
چکیده
Periodic dynamical systems ubiquitously exist in science and engineering. The harmonic balance (HB) method its variants have been the most widely-used approaches for such systems, but are either confined to low-order approximations or impaired by aliasing improper-sampling problems. Here we propose a collocation-based framework successfully unify reconstruct HB-like methods. Under this new conditional identity, which exactly bridges gap between frequency-domain time-domain analyses, is discovered introducing novel matrix. Upon enforcing matrix vanish, powerful reconstruction (RHB) that obtains extremely high-order (>100) nonaliasing solutions, previously deemed out-of-reach, range of complex nonlinear including cavitation bubble dynamics, three-body problem two dimensional airfoil dynamics. We show present 2–3 orders magnitude more accurate simultaneously much faster than state-of-the-art method. Hence, it has immediate applications multidisciplinary problems where highly periodic solutions sought.
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ژورنال
عنوان ژورنال: International Journal for Numerical Methods in Engineering
سال: 2022
ISSN: ['0029-5981', '1097-0207']
DOI: https://doi.org/10.1002/nme.7128