Associated Linear Equations for Volterra operators

Feijoo, J.A. Vázquez; Worden, Keith; Stanway, R.

doi:10.1016/j.ymssp.2004.03.003

Cited by 39 publications

(22 citation statements)

References 7 publications

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“…Eq. 7 can be expanded in Volterra series, by resorting to associated linear equations (ALEs) [15], the first of which is the equation of motion of the underlying linear system; having posed the Wen parameter n=1, the best cubic polynomial was found to contain only the r x 2 and 2 r x terms, hence: A proper choice for the order of the Volterra series expansion has the advantage of suppressing distortions due to measurement or integration; in this case the order 7 was found to be sufficient to adequately approximate the system response. Fig.…”

Section: Numerical Examplementioning

confidence: 99%

Instantaneous Identification of Bouc-Wen-Type Hysteretic Systems from Seismic Response Data

Ceravolo

Demarie

Erlicher³

2007

KEM

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Abstract. This paper presents a technique for identification of non-linear hysteretic systems subjected to non-stationary loading. In the numerical simulations, a Bouc-Wen model was chosen for its ability to represent the properties of a wide class of real hysteretic systems. The parameters of the model are computed instantaneously by approximating the internal restoring force surface through an "ad hoc" polynomial basis. Instantaneous estimates result from time-varying spectra of the response signals. A numerical application of interest to earthquake engineering is finally reported.

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Section: Numerical Examplementioning

confidence: 99%

Instantaneous Identification of Bouc-Wen-Type Hysteretic Systems from Seismic Response Data

Ceravolo

Demarie

Erlicher³

2007

KEM

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“…The method is based on the harmonic probing method (14), (15) . In the proposed method, it is assumed that the nonlinear system to be identified is a nonlinear vibration system shown in Fig.1.…”

Section: Nonlinear Parameter Estimation From Volterra Kernelsmentioning

confidence: 99%

“…In order to solve this problem, we estimate parameters which represent the nonlinear characteristics of the system from the Volterra kernels identified by the M-sequence correlation method. The estimation method is based on the harmonic probing method (14), (15) and nonlinear parameters are calculated from high-order…”

Section: Introductionmentioning

confidence: 99%

Identification of Nonlinear Parameters by Using M-sequence and Harmonic Probing Method

Harada

Toyozawa

Shigaki

et al. 2008

JSDD

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Many classes of nonlinear systems can be represented by Volterra kernels. The authors have recently developed a method for identification of Volterra kernels of nonlinear systems by using M-sequence and correlation technique. In this paper, the authors propose a new method for identification of nonlinear mechanical systems by use of Volterra kernels. The nonlinear mechanical systems are approximated to a nonlinear vibrating system which consists of a mass, a dumper, a linear spring and nonlinear and springs. Then, the parameters, which represent the nonlinear springs are calculated by use of the Volterra kernels. From the results of computer simulation and experiment, the parameters that represent the nonlinear characteristics of the nonlinear mechanical systems can be identified by the proposed method.

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“…However, from Equation (5) it can be seen that the GFRF is multidimensional [19] [20], which makes it difficult to measure, display and interpret the GFRFs in practice. Feijoo, Worden and Stanway [27]- [29] demonstrated that the Volterra series can be described by a series of associated linear equations (ALEs) whose corresponding associated frequency response functions (AFRFs) are easier to analyze and interpret than the GFRFs. According to Equation (6), the NOFRF )…”

Section: Nofrfs Under General Inputsmentioning

confidence: 99%

Resonances and resonant frequencies for a class of nonlinear systems

Peng

Lang

Billings

2007

Journal of Sound and Vibration

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Abstract:Resonant phenomena for a class of nonlinear systems, which can be described by a SDOF model with a polynomial type nonlinear stiffness, are investigated using Nonlinear Output Frequency Response Functions (NOFRFs). The concepts of resonance and resonant frequencies are proposed for the first time for a class of nonlinear systems.The effects of damping on the resonances and resonant frequencies are also analyzed.These results produce a novel interpretation of energy transfer phenomena in this class of nonlinear systems and show how the damping effect influences the system resonant frequencies and amplitudes. The results are important for the design and fault diagnosis of mechanical systems and structures which can be described by the SDOF nonlinear model.

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Associated Linear Equations for Volterra operators

Cited by 39 publications

References 7 publications

Instantaneous Identification of Bouc-Wen-Type Hysteretic Systems from Seismic Response Data

Instantaneous Identification of Bouc-Wen-Type Hysteretic Systems from Seismic Response Data

Identification of Nonlinear Parameters by Using M-sequence and Harmonic Probing Method

Resonances and resonant frequencies for a class of nonlinear systems

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