Modeling periodic and non-periodic response of dynamical systems using an efficient Chebyshev-based time-spectral approach

Ekici, Kivanc; Djeddi, Reza; Li, Hang; Frankel, J. I.

doi:10.1016/j.jcp.2020.109560

Cited by 5 publications

(2 citation statements)

References 42 publications

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“…Regarding that, a more concise and elegant high dimensional harmonic balance (HDHB) method was proposed [22,33] using collocation, where the collocation number equals to the number of unknown Fourier coefficients, which is much less than the sampling rate of the AFT method. The HDHB method is computationally fast [34,35], and a series of modified versions, e.g., the Chebyshev-based Time-spectral Method (C-TSM) [36], the Supplemental-frequency Harmonic Balance (SF-HB) method [37], etc., have been developed for specific problems. However, both the AFT method and the family of HDHB methods are impaired by aliasing when dealing with non-polynomial nonlinear problems [21,32].…”

Section: Introductionmentioning

confidence: 99%

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

Dai¹,

Zipu²,

Wang³

et al. 2022

Preprint

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Periodic dynamical systems ubiquitously exist in science and engineering. The harmonic balance (HB) method and its variants have been the most widely-used approaches for such systems, but are either confined to loworder approximations or impaired by aliasing and improper-sampling problems. Here we propose a collocation-based harmonic balance framework to successfully unify and reconstruct the HB-like methods. Under this framework a new conditional identity, which exactly bridges the gap between frequencydomain and time-domain harmonic analyses, is discovered by introducing a novel aliasing matrix. Upon enforcing the aliasing matrix to vanish, we propose a powerful reconstruction harmonic balance (RHB) method that obtains extremely high-order (>100) non-aliasing solutions, previously deemed outof-reach, for a range of complex nonlinear systems including the cavitation bubble equation and the three-body problem. We show that the present method is 2-3 orders of magnitude more accurate and simultaneously much faster than the state-of-the-art method. Hence, it has immediate applications in multi-disciplinary problems where highly accurate periodic solutions are sought.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Dai¹,

Zipu²,

Wang³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…36 Regarding that, a more concise and elegant high dimensional harmonic balance (HDHB) method was proposed 24,37 using collocation, where the collocation number equals to the number of unknown Fourier coefficients, which is much less than the sampling rate of the AFT method. The HDHB method is computationally fast, 38,39 and a series of modified versions, for example, the Chebyshev-based Time-spectral Method (C-TSM), 40 the Supplemental-frequency Harmonic Balance (SF-HB) method, 41 and so forth, have been developed for specific problems. However, both the AFT method and the family of HDHB methods are impaired by aliasing when dealing with nonpolynomial nonlinear problems.…”

Section: Introductionmentioning

confidence: 99%

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

Dai

Zipu

Wang

et al. 2022

Numerical Meth Engineering

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Periodic dynamical systems ubiquitously exist in science and engineering. The harmonic balance (HB) method and its variants have been the most widely‐used approaches for such systems, but are either confined to low‐order approximations or impaired by aliasing and improper‐sampling problems. Here we propose a collocation‐based harmonic balance framework to successfully unify and reconstruct the HB‐like methods. Under this framework a new conditional identity, which exactly bridges the gap between frequency‐domain and time‐domain harmonic analyses, is discovered by introducing a novel aliasing matrix. Upon enforcing the aliasing matrix to vanish, we propose a powerful reconstruction harmonic balance (RHB) method that obtains extremely high‐order (>100) nonaliasing solutions, previously deemed out‐of‐reach, for a range of complex nonlinear systems including the cavitation bubble dynamics, the three‐body problem and the two dimensional airfoil dynamics. We show that the present method is 2–3 orders of magnitude more accurate and simultaneously much faster than the state‐of‐the‐art method. Hence, it has immediate applications in multidisciplinary problems where highly accurate periodic solutions are sought.

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剝離剪断層に生じる不安定性の拡張ハーモニックバランス解析

Nakamura,

Iwamoto,

Teramoto

et al. 2023

AEROSPACE TECHNOLOGY JAPAN, THE JAPAN SOCIETY FOR AERONAUTICAL

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Modeling periodic and non-periodic response of dynamical systems using an efficient Chebyshev-based time-spectral approach

Cited by 5 publications

References 42 publications

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

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

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

剝離剪断層に生じる不安定性の拡張ハーモニックバランス解析

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