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• W4362586132 endingPage "117700" @default.
• W4362586132 startingPage "117700" @default.
• W4362586132 abstract "Quasi-periodic responses composed of multiple base frequencies widely exist in science and engineering problems. The multiple harmonic balance (MHB) method is one of the most commonly used approaches for such problems. However, it is limited by low-order estimations due to complex symbolic operations in practical uses. Many variants have been developed to improve the MHB method, among which the time domain MHB-like methods are regarded as crucial improvements because of their high efficiency and simple derivation. But there is still one main drawback remaining to be addressed. The time domain MHB-like methods negatively suffer from non-physical solutions, which have been shown to be caused by aliasing (mixtures of the high-order into the low-order harmonics). Inspired by the collocation-based harmonic balancing framework recently established by our group, we herein propose a reconstruction multiple harmonic balance (RMHB) method to reconstruct the conventional MHB method using discrete time domain collocations. Our study shows that the relation between the MHB and time domain MHB-like methods is determined by an aliasing matrix, which is non-zero when aliasing occurs. On this basis, a conditional equivalence is established to form the RMHB method. Three numerical examples demonstrate that this new method is more robust and efficient than the state-of-the-art methods." @default.
• W4362586132 created "2023-04-06" @default.
• W4362586132 creator A5030789694 @default.
• W4362586132 creator A5052344851 @default.
• W4362586132 creator A5082829077 @default.
• W4362586132 date "2023-06-01" @default.
• W4362586132 modified "2023-10-16" @default.
• W4362586132 title "An efficient multiple harmonic balance method for computing quasi-periodic responses of nonlinear systems" @default.
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• W4362586132 doi "https://doi.org/10.1016/j.jsv.2023.117700" @default.
• W4362586132 hasPublicationYear "2023" @default.
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