Computation of eigenvalue and eigenvector derivatives for a general complex-valued eigensystem

Aa, Novikov; Morsche, H. G. ter; Mattheij, R.M.M.

doi:10.13001/1081-3810.1203

Cited by 83 publications

(62 citation statements)

References 8 publications

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“…Instead, in this paper one computes these expressions using the properties of the derivatives of eigenvalues demonstrated by Van der Aa et al [40] . Denoting Λ the eigenvector matrix of B, and ξ the localization vector containing the index of the 2n Floquet exponentsλ among the eigenvalues λ, i.e.,λ i = λ ξ i " the eigenvalues derivatives can be computed as…”

Section: Tracking Of Bifurcationsmentioning

confidence: 99%

The Harmonic Balance Method for Bifurcation Analysis of Nonlinear Mechanical Systems

Detroux

Renson

Masset

et al. 2016

Nonlinear Dynamics, Volume 1

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Because nowadays structural engineers are willing to use or at least understand nonlinearities instead of simply avoiding them, there is a need for numerical tools performing analysis of nonlinear large-scale structures. Among these techniques, the harmonic balance (HB) method is certainly one of the most commonly used to study finite element models with reasonably complex nonlinearities. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. For this reason, the present paper proposes to extend the method to the detection and tracking of codimension-1 bifurcations in the system parameters space. As an application, the frequency response of a spacecraft is studied, together with two nonlinear phenomena, namely quasiperiodic oscillations and detached resonance curves. This example illustrates how bifurcation tracking using the HB method can be employed as a promising design tool for detecting and eliminating such undesired behaviors.

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Section: Tracking Of Bifurcationsmentioning

confidence: 99%

The Harmonic Balance Method for Bifurcation Analysis of Nonlinear Mechanical Systems

Detroux

Renson

Masset

et al. 2016

Nonlinear Dynamics, Volume 1

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show abstract

“…Based on the eigenvalue derivation theory (Van Der Aa et al, 2007), the derivative of the eigenvalue θ i with respect to ε is…”

Section: Convergence Proofmentioning

confidence: 99%

A robust distributed system incremental cost estimation algorithm for smart grid economic dispatch with communications information losses

Zhang

Rahbari-Asr

Chow

2016

Journal of Network and Computer Applications

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“…It can be shown from [22] that writing S in function of the parameter a gives the nth-order eigenvalue derivative as…”

Section: Derivation Of the Kld Analytical Modelmentioning

confidence: 99%

Incipient fault detection and diagnosis based on Kullback–Leibler divergence using principal component analysis: Part II

2015

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Computation of eigenvalue and eigenvector derivatives for a general complex-valued eigensystem

Cited by 83 publications

References 8 publications

The Harmonic Balance Method for Bifurcation Analysis of Nonlinear Mechanical Systems

The Harmonic Balance Method for Bifurcation Analysis of Nonlinear Mechanical Systems

A robust distributed system incremental cost estimation algorithm for smart grid economic dispatch with communications information losses

Incipient fault detection and diagnosis based on Kullback–Leibler divergence using principal component analysis: Part II

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