Resonances and resonant frequencies for a class of nonlinear systems

Peng, Z.K.; Lang, Zi–Qiang; Billings, S.A.

doi:10.1016/j.jsv.2006.09.012

Cited by 55 publications

(31 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Even though the HBM can reveal sub-resonance phenomenon, for example the maximum at Figure 1 (b), it cannot account for this nonlinear phenomenon. However, the NOFRFs can give a theoretical explanation for both the appearances of super-harmonics and sub-resonance; more details can be found in reference [35]. In addition, comparative studies using numerical methods have shown the HBM can capture the well-known jump phenomenon, but it will suffer from the computational limits.…”

Section: Conclusion and Remarksmentioning

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

Self Cite

112

View full text Add to dashboard Cite

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.

show abstract

Section: Conclusion and Remarksmentioning

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

Self Cite

112

View full text Add to dashboard Cite

show abstract

“…In this section, an example illustrating the efficacy of the proposed spectrum constrained NMPC approach for damping resonance frequencies in constrained nonlinear systems is presented. In practice, many oscillatory dynamical systems can be modelled as linear resonators with a nonlinear restoring force [9]. Therefore, we consider the constrained nonlinear system 8 > > > > > > > < > > > > > > > :…”

Section: Numerical Examplementioning

confidence: 99%

Constrained Spectrum Control

Hours

Zeilinger

Linares

et al. 2015

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

Abstract-A novel Nonlinear Model Predictive Control (NMPC) scheme is proposed in order to shape the harmonic response of constrained nonlinear systems. The salient ingredient is the short-time Fourier transform (STFT) of the system's output signal, which is constrained in an NMPC problem, leading to the novel formulation of so-called spectrum constraints. Recursive feasibility and asymptotic stability of the proposed NMPC scheme with such spectrum constraints are guaranteed by means of an appropriate ellipsoidal terminal invariant set. The efficacy of the proposed approach is demonstrated on a nonlinear vibration damping problem.

show abstract

“…However, according to our experiences, in practical applications, because the method will make use of the nonlinear effect, therefore, it might be better to choose an excitation frequency that can make the nonlinear effect significant, for example, one half of a resonant frequency where the second harmonic component often reaches a maximum. More information about the resonances in nonlinear systems can be found in [28].…”

Section: Conclusion and Remarksmentioning

confidence: 99%

Linear parameter estimation for multi-degree-of-freedom nonlinear systems using nonlinear output frequency-response functions

Peng

Lang

Billings

2007

Mechanical Systems and Signal Processing

Self Cite

View full text Add to dashboard Cite

Abstract:The Volterra series approach has been widely used for the analysis of nonlinear systems. Based on the Volterra series, a novel concept named Nonlinear Output Frequency Response Functions (NOFRFs) was proposed by the authors. This concept can be considered as an alternative extension of the classical frequency response function for linear systems to the nonlinear case. In this study, based on the NOFRFs, a novel algorithm is developed to estimate the linear stiffness and damping parameters of multidegree-of-freedom (MDOF) nonlinear systems. The validity of this NOFRF based parameter estimation algorithm is demonstrated by numerical studies.

show abstract

Resonances and resonant frequencies for a class of nonlinear systems

Cited by 55 publications

References 31 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

Constrained Spectrum Control

Linear parameter estimation for multi-degree-of-freedom nonlinear systems using nonlinear output frequency-response functions

Contact Info

Product

Resources

About