Convergence Analysis of Volterra Series Response of Nonlinear Systems Subjected to Harmonic Excitation

Chatterjee, Animesh; Vyas, Nalinaksh S.

doi:10.1006/jsvi.2000.2967

Cited by 42 publications

(24 citation statements)

References 15 publications

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“…Although the occurrence of jump phenomenon usually indicates a strongly nonlinear behaviour, the inability of the NOFRF to capture the jump phenomenon doesn't mean that NOFRFs cannot handle other cases of strongly nonlinear systems. The case study for the nonlinear damping oscillator (44) shows that the NOFRF can accurately predict the response of this oscillator. As noted in Section 3, the Volterra series can describe the class of nonlinear systems which are stable at zero equilibrium.…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, although it has been claimed that the HBM is able to handle strongly nonlinear systems whose higher order harmonics can make significant contributions to the system responses, in practice, due to computational limits the HBM is still not that powerful for analyzing complex nonlinear systems. That is why the HBM method cannot provide accurate predictions on the nonlinear damping oscillator (44). Moreover, it usually takes quite a long time for the HBM method to find the solutions, and it can be half an hour or even longer.…”

Section: Discussionmentioning

confidence: 99%

“…That is why the NOFRF cannot predict the motion of the Duffing oscillator (40) 1 ω . However, for some damping nonlinear systems like the oscillator (44), although the nonlinear damping can make the system behave strongly nonlinearly, it also makes the system behave more stable at zero equilibrium and thus helps the system to sustain stronger inputs. Figure 10(a) shows the response and its spectrum obtained from a linear oscillator where m, k, c are the same as those used in Case 2.…”

Section: Discussionmentioning

confidence: 99%

“…However, when , the deviation between the results obtained by the two different methods increases with the amplitude for all the first, second and third harmonics. This is because in the region , the contributions of the other higher order harmonics to the response of the nonlinear damping oscillator (44) are too significant to be ignored. On the contrary, Figure 9 shows that, at all amplitudes, the results by the NOFRFs always…”

Section: Figures 3 Andmentioning

confidence: 99%

“…But the NOFRFs does not suffer from the computational limits and can always be implemented in a few seconds. For some nonlinear systems, like the nonlinear damping oscillator (44), the NOFRFs can give much better predictions of the harmonic components compared to the HBM even if such systems are strongly nonlinear. …”

Section: Conclusion and Remarksmentioning

confidence: 99%

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

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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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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Figures 3 Andmentioning

confidence: 99%

Section: Conclusion and Remarksmentioning

confidence: 99%

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

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Lang

Billings

et al. 2008

Journal of Sound and Vibration

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Stiffness Non-Linearity Classification Through Structured Response Component Analysis Using Volterra Series

Chatterjee¹,

Vyas²

2001

Mechanical Systems and Signal Processing

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Analysis and Design of Nonlinear Systems in the Frequency Domain

Zhu

2021

Springer Theses

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Nonlinear system analyses have been widely applied in engineering practice, where the frequency domain approaches have been developed to satisfy the requirement of the analysis and design of nonlinear systems.However, there exist many problems with current techniques including the challenges with the nonlinear system representation using physically meaningful models, and difficulties with the evaluation of the frequency properties of nonlinear systems. In the present work, some new approaches, that have potential to be used to systematically address these problems, are developed based on the NDE (Nonlinear Differential Equation) model and the NARX (Nonlinear Auto Regressive with eXegenous input) model of nonlinear systems.In this thesis, the background of the frequency domain analysis and design of nonlinear systems is introduced in Chapter 1, and the existing approaches are reviewed in Chapter 2. In general, the frequency ABSTRACT II(3) The Output Frequency Response Function (OFRF) in terms of physical parameters of concern is introduced for the NARX Model with parameters of interest for Design (NARX-M-for-D). Moreover, a new concept known as the Associated Output Frequency Response Function (AOFRF) is introduced to facilitate the analysis of the effects of both linear and nonlinear characteristic parameters on the output frequency responses of nonlinear systems.(4) Nonlinear damping can achieve desired isolation performance of a system over both low and high frequency regions and the optimal nonlinear damping force can be realized by closed loop controlled semi-active dampers. Both simulation and laboratory experiments are studied, demonstrating the advantages of the proposed nonlinear damping technologies over both traditional linear damping and more advanced Linear-Quadratic Gaussian (LQG) feedback control which have been used in practice to address building isolation system design and implementation problems. CATALOGUE III AcknowledgementsI would like to thank Prof. Z Q Lang, my supervisor, for his great support and supervision on my PhD study. He has provided a lot of suggestions on my research and writing so that I can complete the project and this PhD thesis.I also want to express my thankfulness to the research and work staffs of the department for their kind help on my study, and also would like to acknowledge the support of Engineering Faculty Scholarship for my PhD study at Sheffield.

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Convergence Analysis of Volterra Series Response of Nonlinear Systems Subjected to Harmonic Excitation

Cited by 42 publications

References 15 publications

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

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

Stiffness Non-Linearity Classification Through Structured Response Component Analysis Using Volterra Series

Analysis and Design of Nonlinear Systems in the Frequency Domain

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