Analysing non-linear systems in the frequency domain--I. The transfer function

Zhang, H.; Billings, S.A.

doi:10.1006/mssp.1993.1031

Cited by 35 publications

(20 citation statements)

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“…For a nonlinear system, the dynamical properties are determined by the GFRFs n H (n= 1,…,N). However, from equation (16) it can be seen that the GFRF is multidimensional [7][8], which can make the GFRFs difficult to measure, display and interpret in practice. According to equation (17), the NOFRF )…”

Section: Nonlinear Output Frequency Response Functions Under General mentioning

confidence: 99%

Non-linear output frequency response functions of MDOF systems with multiple non-linear components

Peng¹,

Lang²,

Billings³

2007

International Journal of Non-Linear Mechanics

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Abstract:In engineering practice, most mechanical and structural systems are modeled as Multi-Degree-of-Freedom (MDOF) systems. When some components within the systems have nonlinear characteristics, the whole system will behave nonlinearly. The concept of Nonlinear Output Frequency Response Functions (NOFRFs) was proposed by the authors recently and provides a simple way to investigate nonlinear systems in the frequency domain. The present study is concerned with investigating the inherent relationships between the NOFRFs for any two masses of nonlinear MDOF systems with multiple nonlinear components. The results reveal very important properties of the nonlinear systems. One significant application of the results is to detect and locate faults in engineering structures which make the structures behave nonlinearly.

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Section: Nonlinear Output Frequency Response Functions Under General mentioning

confidence: 99%

Non-linear output frequency response functions of MDOF systems with multiple non-linear components

Peng¹,

Lang²,

Billings³

2007

International Journal of Non-Linear Mechanics

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“…However, the GFRFs are multidimensional functions [29] [30], which can be much more complicated than the linear FRF and can be difficult to measure, display and interpret in practice. Recently, a novel concept known as Nonlinear Output Frequency Response Functions (NOFRFs) was proposed by the authors [31].…”

Section: Introductionmentioning

confidence: 99%

Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis

Peng

Lang

Billings

et al. 2008

Journal of Sound and Vibration

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112

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By using the Duffing oscillator as a case study, this paper shows that the harmonic components in the nonlinear system response to a sinusoidal input calculated using the Nonlinear Output Frequency Response Functions (NOFRFs) are one of the solutions obtained using the Harmonic Balance Method (HBM). A comparison of the performances of the two methods shows that the HBM can capture the well-known jump phenomenon, but is restricted by computational limits for some strongly nonlinear systems and can fail to provide accurate predictions for some harmonic components.Although the NOFRFs cannot capture the jump phenomenon, the method has few computational restrictions. For the nonlinear damping systems, the NOFRFs can give better predictions for all the harmonic components in the system response than the HBM even when the damping system is strongly nonlinear.

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“…Moreover, spectral analysis can be performed for nonlinear system through their NARMAX representation by computing the generalised frequency response functions (GFRFs) (Billings and Tsang, 1989a,b, Billings et al, 1990, Chua and Ng, 1979a,b, Jones, 2007, Lee and Chang, 2009, Zhang and Billings, 1993.…”

Section: The Narmax Identification Methodologymentioning

confidence: 99%

Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits

Florescu¹

2017

Springer Theses

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To my family iii The third problem addressed in this work is given by the need of developing neuromorphic engineering circuits that perform mathematical computations in the spike domain.In this respect, this thesis developed a new representation between the time encoded input and output of a linear filter, where the TEM is represented by an ideal IF neuron. A new practical algorithm is developed based on this representation. The proposed algorithm is significantly faster than the alternative approach, which involves reconstructing the input, simulating the linear filter, and subsequently encoding the resulting output into a spike train.

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Analysing non-linear systems in the frequency domain--I. The transfer function

Cited by 35 publications

References 0 publications

Non-linear output frequency response functions of MDOF systems with multiple non-linear components

Non-linear output frequency response functions of MDOF systems with multiple non-linear components

Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis

Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits

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