Disturbance propagation in structural networks

Flotow, Andreas H. von

doi:10.1016/0022-460x(86)90190-2

Cited by 121 publications

(51 citation statements)

References 12 publications

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“…The main steps of the complex wave vector approach [1,2] are reported. The 2n state vector at the generic point k can be transformed to complex wave vector through the matrix U; whose columns are complex eigenvectors of T; as follows: …”

Section: Appendix a Complex Wave Vector Approachmentioning

confidence: 99%

“…The proposed real wave vector approach is described in Section 3 for generic n-coupled periodic structures. By comparing this approach with the earlier one [1,2], whose main steps are outlined in the appendix, the differences between the two algorithms are highlighted. Afterwards, in Section 4, an illustrative analytical application to a mono-coupled mass spring chain is presented.…”

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confidence: 99%

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Real wave vectors for dynamic analysis of periodic structures

Luongo

Romeo

2005

Journal of Sound and Vibration

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A modified version of the traditional wave vector computational scheme for the dynamic analysis of long undamped periodic structures is presented. First, the consistency of the complex wave vector mathematical formulation is discussed, placing particular emphasis on the real or complex nature of the resulting characteristic equation from which the natural frequencies are derived. It is shown that the rearrangement in terms of complex waves entering the domain, devised to overcome ill-conditioning arising in the transfer matrix formulation, entails as a side effect an ill-posed problem, as it leads to a complex characteristic equation in a real unknown. Next, the proposed approach is described. It provides for transformation of frequency-dependent real transfer matrices for state vectors to real transfer matrices for wave vectors, thus avoiding an ill-conditioned and ill-posed problem. Finally, applications to mono-coupled and bi-coupled structures are illustrated, aiming at comparing the proposed method with the transfer matrix and complex wave vector approaches. (C) 2003 Elsevier Ltd. All rights reserved

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Section: Appendix a Complex Wave Vector Approachmentioning

confidence: 99%

mentioning

confidence: 99%

Real wave vectors for dynamic analysis of periodic structures

Luongo

Romeo

2005

Journal of Sound and Vibration

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“…Miller [5] Rao [4] Maghami [6] Onoda [1] Smith [7] Sepulveda [2] Khot [3] Furuya [9] Skelton [8] Jacques [10,11] Keane [12,13,14] beam [2].…”

Section: * Differing Control Techniquesmentioning

confidence: 99%

“…For further details see the book by Crawley [12], publications by Miller [13] and von Flotow [14], and the theses by MacMartin [15] and McCain [16].…”

Section: Controlled Structures Systems Backgroundmentioning

confidence: 99%

Evolutionary Design of Controlled Structures

Masters

Crawley

1999

Journal of Aircraft

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“…For example, [1,2] used a wave approach to study the vibrations of structural networks composed of simple uniform beams by analytical methods. The first numerical approaches were proposed by [3,4] to approximate the cross-sectional deformations by finite elements.…”

Section: Introductionmentioning

confidence: 99%

Computational Structures Technology

Bull¹

2001

Computational Science, Engineering &Amp; Technology Series

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Classically, waveguides are structures with uniform sections or are periodic along an axis. Vibrations of these waveguides can be described by wave modes and propagation constants relating the displacements and forces in two sections of the waveguide. Here, waveguides of non uniform sections are considered. More precisely, we consider waveguides which have sections with size increasing proportionally to the distance from an origin. This is for instance the case for a domain exterior to a convex body. Using a finite element model of a small section of the guide, the wave finite element method (WFE) can be used to find propagation constants and wave modes relating the displacements and forces at the two extremities of the finite element section. Then, it is shown that the wave modes and propagation constants in a section are simply related to the same quantities in other sections but for different frequencies. From this set of waves, general solutions in the waveguide can be computed. This approach allows an efficient solution by limiting the discretization to a very small part of the waveguide using only classical dynamic stiffness matrices, obtained by any finite element software. This approach can then be used for computing wave radiation in domains exterior to a convex body. The solution is projected onto these waves, allowing a clear separation between incoming and outgoing waves. Keeping only the outgoing part of the solution, wave radiation can be computed. It is shown that the approach is more efficient for high frequencies and can be complementary of the usual methods involving traditional finite or boundary elements.

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Disturbance propagation in structural networks

Cited by 121 publications

References 12 publications

Real wave vectors for dynamic analysis of periodic structures

Real wave vectors for dynamic analysis of periodic structures

Evolutionary Design of Controlled Structures

Computational Structures Technology

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