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Optimization of Damping in Self-Excited Mechanical Systems

Jekel, Dominic (2018):
Optimization of Damping in Self-Excited Mechanical Systems.
Darmstadt, Technische Universität, [Online-Edition: https://tuprints.ulb.tu-darmstadt.de/8112],
[Ph.D. Thesis]

Abstract

Self-excited vibrations, such as squealing of disc brakes or galloping of overhead transmission lines, are often accompanied by undesired phenomena. The appearance of self-excitation is ascribed to an instability originating either from negative damping or from non-conservative coupling of motion coordinates. In a linearized description, the stability behavior of such circulatory systems strongly depends on the structure of the damping matrix as well as the relation of all matrices involved. Considering the distinct physical origins of energy dissipation, some of the resulting damping matrices have a stabilizing effect, while others may contribute to destabilization.

In this context, the present thesis addresses two major scientific objectives. First, a deeper understanding is promoted regarding the influence of velocity proportional forces on the stability of linear mechanical systems featuring circulatory and gyroscopic terms. Analytical investigations deliver detailed insights into the required structure of the damping matrix either for stabilization or the avoidance of destabilization. Second, stability is assessed by means of quantitative measures. On this basis, a technique for stability optimization is established. The method relies on decomposing the damping matrix into component matrices which are associated with different physical origins. Suitable variation of these submatrices yields a reduced tendency of self-excitation. Beneficial damping configurations are determined with respect to predefined constraints, as they naturally appear in engineering. The meaningfulness of the obtained results is judged in terms of dependence on parameter fluctuations and technical feasibility. Serving as representative examples, various models of disc brakes and overhead transmission lines are studied numerically at different levels of complexity.

Item Type: Ph.D. Thesis
Erschienen: 2018
Creators: Jekel, Dominic
Title: Optimization of Damping in Self-Excited Mechanical Systems
Language: English
Abstract:

Self-excited vibrations, such as squealing of disc brakes or galloping of overhead transmission lines, are often accompanied by undesired phenomena. The appearance of self-excitation is ascribed to an instability originating either from negative damping or from non-conservative coupling of motion coordinates. In a linearized description, the stability behavior of such circulatory systems strongly depends on the structure of the damping matrix as well as the relation of all matrices involved. Considering the distinct physical origins of energy dissipation, some of the resulting damping matrices have a stabilizing effect, while others may contribute to destabilization.

In this context, the present thesis addresses two major scientific objectives. First, a deeper understanding is promoted regarding the influence of velocity proportional forces on the stability of linear mechanical systems featuring circulatory and gyroscopic terms. Analytical investigations deliver detailed insights into the required structure of the damping matrix either for stabilization or the avoidance of destabilization. Second, stability is assessed by means of quantitative measures. On this basis, a technique for stability optimization is established. The method relies on decomposing the damping matrix into component matrices which are associated with different physical origins. Suitable variation of these submatrices yields a reduced tendency of self-excitation. Beneficial damping configurations are determined with respect to predefined constraints, as they naturally appear in engineering. The meaningfulness of the obtained results is judged in terms of dependence on parameter fluctuations and technical feasibility. Serving as representative examples, various models of disc brakes and overhead transmission lines are studied numerically at different levels of complexity.

Place of Publication: Darmstadt
Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Dynamics and Vibrations
Exzellenzinitiative
Exzellenzinitiative > Graduate Schools
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
Date Deposited: 28 Oct 2018 20:55
Official URL: https://tuprints.ulb.tu-darmstadt.de/8112
URN: urn:nbn:de:tuda-tuprints-81120
Referees: Hagedorn, Prof. Peter and Schweizer, Prof. Bernhard
Refereed / Verteidigung / mdl. Prüfung: 9 October 2018
Alternative Abstract:
Alternative abstract Language
Selbsterregte Schwingungen, wie das Quietschen von Scheibenbremsen oder das Seiltanzen von Freileitungen, werden häufig von unerwünschten Effekten begleitet. Die Entstehung der Selbsterregung wird einer Instabilität zugeschrieben, die entweder von einer negativen Dämpfung oder von einer nicht-konservativen Kopplung der Bewegungskoordinaten herrührt. In einer linearisierten Beschreibung hängt das Stabilitätsverhalten solcher zirkulatorischer Systeme stark von der Struktur der Dämpfungsmatrix sowie vom Zusammenspiel aller beteiligten Matrizen ab. Angesichts der verschiedenen physikalischen Ursprünge von Energiedissipation haben manche der resultierenden Dämpfungsmatrizen eine stabilisierende Wirkung, während andere zur Destabilisierung beitragen können. In diesem Zusammenhang verfolgt die vorliegende Arbeit zwei Hauptziele. Zunächst wird ein tiefergehendes Verständnis gefördert hinsichtlich des Einflusses geschwindigkeitsproportionaler Kräfte auf die Stabilität linearer mechanischer Systeme mit zirkulatorischen und gyroskopischen Termen. Analytische Untersuchungen liefern detaillierte Einblicke in die erforderliche Struktur der Dämpfungsmatrix zur Stabilisierung oder zur Vermeidung von Destabilisierung. Auf Grundlage einer quantitativen Bewertung wird eine Methode zur Stabilitätsoptimierung eingeführt. Das Verfahren beruht auf der Zerlegung der Dämpfungsmatrix in einzelne Komponenten, die ihrem jeweiligen physikalischen Ursprung zugeordnet sind. Eine geeignete Variation dieser Submatrizen verringert die Tendenz zur Selbsterregung. Vorteilhafte Dämpfungskonfigurationen werden unter Berücksichtigung bestimmter Zwangsbedingungen ermittelt. Die Aussagekraft der Ergebnisse wird bezüglich ihrer Abhängigkeit von Parameterschwankungen sowie ihrer technischen Umsetzbarkeit beurteilt. Als repräsentative Beispiele werden Modelle verschiedener Komplexitätsstufen von Scheibenbremsen und Freileitungen numerisch untersucht.German
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