A Measure of Non-Proportional Damping

Prells, Uwe; Friswell, Michael I.

doi:10.1006/mssp.1999.1280

Cited by 40 publications

(16 citation statements)

References 11 publications

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“…As a result, system (1) may not be decoupled by classical modal analysis in general. Consequently, much attention has been given to the development of decoupling approximation schemes [5][6][7][8][9][10][11][12][13][14][15][16] for analyzing non-classically damped systems, along with the so-called coupling or non-proportionality indices [17][18][19][20][21][22][23][24][25][26][27][28] that quantify their degree of coordinate coupling. Of course, one may also consider decoupling in the 2n-dimensional state space.…”

Section: Introductionmentioning

confidence: 99%

The decoupling of defective linear dynamical systems in free motion

Kawano¹,

Morzfeld²,

Ma³

2011

Journal of Sound and Vibration

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a b s t r a c tIt was demonstrated in two earlier papers that there exists a real, linear, time-varying transformation that decouples any non-defective linear dynamical system in free vibration in the configuration space. As an extension of this work, the present paper represents the first systematic effort to decouple defective systems. It is shown that the decoupling of defective systems is a rather delicate procedure that depends on the multiplicities of the system eigenvalues. While any defective system can be decoupled with the eigenvalues kept invariant, the geometric multiplicities of these eigenvalues may not be preserved. Several numerical examples are provided to illustrate the theoretical developments.

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Section: Introductionmentioning

confidence: 99%

The decoupling of defective linear dynamical systems in free motion

Kawano¹,

Morzfeld²,

Ma³

2011

Journal of Sound and Vibration

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“…(24) and (25) to determine {T L (1), T R (1)} and then to apply Eqs. (18) and (19). In the latter case, an analytical solution is known for the case where {N L (σ ), N R (σ )} are both constant matrices for all σ .…”

Section: Definition 8 (Isospectral Flows) An Isospectral Flow Is a Tmentioning

confidence: 98%

“…could be used as a measure of the degree to which a second-order system is not classically damped--the degree of non-proportionality [19]. This particular measure is obviously flawed since a scalar multiplication of the system will result in a change to the measure.…”

Section: Definition 6 (Real Systems and Real Spts) A System A(λ) Imentioning

confidence: 99%

General isospectral flows for linear dynamic systems

Garvey

Prells

Friswell

et al. 2004

Linear Algebra and its Applications

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The λ-matrix A(λ) = (A 0 + λA 1 + λ 2 A 2 + · · · λ k A k · · · + λ l A l ) with matrix coefficients {A 0 , A 1 , A 2 . . . A } ∈ C m×n defines a linear dynamic system of dimension (m × n). When m = n, and when det(A(λ)) / = 0 for some values of λ, the eigenvalues of this system are welldefined. A one-parameter trajectory of such a system {A 0 (σ ), A 1 (σ ), A 2 (σ ) . . . A (σ )} is an isospectral flow if the eigenvalues and the dimensions of the associated eigenspaces are the same for all parameter values σ ∈ IR. This paper presents the most general form for isospectral flows of linear dynamic systems of orders ( = 2, 3, 4), and the forms for isospectral flows for even higher order systems are evident from the patterns emerging. Based on the definition of a class of coordinate transformations called structure-preserving transformations, the concept of isospectrality and the associated flows is seen to extend to cases where (m / = n).

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“…Particularly the engineering literature is very rich. For a brief insight we give some selection of some older references: [2][3][4][5], as well as some less old: [6][7][8]. In references [9,10] authors studies topology optimization for the problem of damping optimization.…”

Section: Introductionmentioning

confidence: 98%