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Journal Article•DOI•

Conditions revisited for asymptotic stability of pervasive damped linear systems

Wolfhard Kliem1, Alexei A. Mailybaev, Christian Pommer1•
Technical University of Denmark1
22 Nov 2006-Journal of Sound and Vibration (Elsevier)-Vol. 298, Iss: 1, pp 471-474
TL;DR: In this paper, the authors reveal the importance of Moran's criterion for suppression of oscillations by incomplete damping in systems with multiple eigenfrequencies and provide extensions to the case of indefinite damping.
About: This article is published in Journal of Sound and Vibration.The article was published on 2006-11-22. It has received 8 citations till now. The article focuses on the topics: Damping matrix & Stability theory.
Citations
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Journal Article•DOI•
Brake comfort – a review

[...]

Carlo Cantoni, Riccardo Cesarini, Giampiero Mastinu1, G. Rocca1, Roberto Sicigliano •
Polytechnic University of Milan1
06 Aug 2009-Vehicle System Dynamics
TL;DR: In this article, a review of state-of-the-art studies on brake vibration and noise is presented, focusing on the still-open questions that appear crucial from the perspective of a leading brake manufacturer.
Abstract: Several state of the art papers and even books on brake vibration and/or noise have been presented in the literature. Many of them have analytically and sharply accounted for the impressive amount of research undertaken on this topic. This state of the art review focuses on the still-open questions that appear crucial from the perspective of a leading brake manufacturer. The paper deals with the phenomena of brake vibration and/or noise, the experimental and theoretical methods for studying such phenomena, and the actions that are identified to be necessary to definitely solve the addressed problem. Key topics are the modelling of friction, the modelling of the dynamics of the brake as a non-linear system subjected to deterministic or random (parametric) excitation, the proper modelling of the contact between the disc and the pad, and the experimental validation of the mathematical models.

86 citations

Journal Article•DOI•
Stability of linear gyroscopic systems: A review

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Peter Lancaster1•
University of Calgary1
01 Aug 2013-Linear Algebra and its Applications
TL;DR: In this article, the effects of adding viscous damping to the preceding models are considered, including parameter dependent systems and the so-called Thomson, Tait, Chetaev circle of ideas.

46 citations

Journal Article•DOI•
A note on the damped vibrating systems

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Ranislav M. Bulatovic
01 Jan 2006-Theoretical and Applied Mechanics
TL;DR: In this article, the presence of pure imaginary eigenvalues of the partially damped vibrating systems is treated and the number of such eigen values is determined using the rank of a matrix which is directly related to the system matrices.
Abstract: The presence of pure imaginary eigenvalues of the partially damped vibrating systems is treated. The number of such eigenvalues is determined using the rank of a matrix which is directly related to the system matrices.

5 citations

Cites background from "Conditions revisited for asymptotic..."

  • ...Also, it should be mentioned that the paper [1] rediscovered an old criterion for asymptotic stability of the system [3], as was recently stressed in [4]....

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  • ...Since D and K commute there exists an orthogonal matrix such that both D and K are orthogonally congruent to diagonal matrices [4]....

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Journal Article•DOI•
Pervasive damping in mechanical systems and the role of gyroscopic forces

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Jan Awrejcewicz1, Nataliya Losyeva2, Volodymyr Puzyrov2•
Lodz University of Technology1, Donetsk National University2
01 Apr 2019-Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik

4 citations

Journal Article•DOI•
On the residual motion in damped vibrating systems

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Ranislav M. Bulatovic1•
University of Montenegro1
01 Jan 2013-Theoretical and Applied Mechanics
TL;DR: In this article, linear vibrating systems with symmetric positive definite matrices and damping matrices are studied, in which the inertia and stiffness matrix are symmetric and the damping matrix is symmetric====== positive semi-definite, respectively.
Abstract: In this paper, linear vibrating systems, in which the inertia and stiffness matrices are symmetric positive definite and the damping matrix is symmetric positive semi-definite, are studied. Such a system may possess undamped modes, in which case the system is said to have residual motion. Several formulae for the number of independent undamped modes, associated with purely imaginary eigenvalues of the system, are derived. The main results formulated for symmetric systems are then generalized to asymmetric and symmetrizable systems. Several examples are used to illustrate the validity and application of the present results.

3 citations

Cites background from "Conditions revisited for asymptotic..."

  • ... Since rankR m rankRjj = ≤ , the next result recently formulated in [5] follows directly from Theorem 4....

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  • ...Also, it should be mentioned that the paper [2] rediscovered an old criterion for asymptotic stability of the system [4], as was recently stressed in [5]....

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References
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Journal Article•DOI•
Equations of Mathematical Physics

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Vidar Thomée, Vasilii S Vladimirov
01 Apr 1972-Mathematics of Computation

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Journal Article•DOI•
Equations of Mathematical Physics

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Vibrations and Stability of Multiple Parameter Systems

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Stabilität und Matrizen

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Peter C. Müller, Thomas K. Caughey1•
California Institute of Technology1
01 Jan 1977-Journal of Applied Mechanics

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"Conditions revisited for asymptotic..." refers background in this paper

  • ...The aim of our letter is to draw attention of the readers to Moran’s result, which seems to be forgotten (even though it was mentioned in classical textbooks [2,10])....

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  • ...Pervasive damping was also recognized by Müller [2] as essential for an extension of the Thomson–Tait–Chetayev stability criterion....

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  • ...Au th or 's pe rs on al co py example, control theory provides the rank condition [2]...

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  • ...Pervasive damping was also recognized by Müller [2] as essential for an extension of the Thomson–Tait–Chetayev stability criterion....

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Book•
Gyrodynamics and Its Engineering Applications

[...]

Ronald N. Arnold, Leonard Maunder
10 May 2014

71 citations

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