A Relationship Between Defective Systems and Unit-Rank Modification of Classical Damping

1999 ◽  
Vol 122 (2) ◽  
pp. 180-183 ◽  
Author(s):  
Uwe Prells ◽  
Michael I. Friswell
Keyword(s):  
Mathematical Modeling ◽  
Mechanical Systems ◽  
Viscous Damping ◽  
Common Assumption ◽  
Damping Matrix ◽  
Linearly Independent ◽  
Rank One ◽  
Strong Motivation ◽  
Repeated Eigenvalue

A common assumption within the mathematical modeling of vibrating elastomechanical system is that the damping matrix can be diagonalized by the modal matrix of the undamped model. These damping models are sometimes called “classical” or “proportional.” Moreover it is well known that in case of a repeated eigenvalue of multiplicity m, there may not exist a full sub-basis of m linearly independent eigenvectors. These systems are generally termed “defective.” This technical brief addresses a relation between a unit-rank modification of a classical damping matrix and defective systems. It is demonstrated that if a rank-one modification of the damping matrix leads to a repeated eigenvalue, which is not an eigenvalue of the unmodified system, then the modified system is defective. Therefore defective systems are much more common in mechanical systems with general viscous damping than previously thought, and this conclusion should provide strong motivation for more detailed study of defective systems. [S0739-3717(00)00602-4]

Some Remarks on the Identification of Damping Parameters at the Boundary of Vibrating Systems

1995 ◽  
Vol 48 (11S) ◽  
pp. S107-S110
Author(s):  
Peter Hagedorn ◽  
Ulrich Pabst
Keyword(s):  
Mathematical Modeling ◽  
Modal Analysis ◽  
Mechanical Systems ◽  
Experimental Modal Analysis ◽  
Steel Beam ◽  
Modal Data ◽  
Stiffness And Damping ◽  
Parameter Values ◽  
Vibrating Systems

In many cases, vibrating mechanical systems permit a reliable mathematical modeling with parameter values which are reasonably well known beforehand, except for the joints between different subsystems and at the boundaries. The boundary stiffness, which is often assumed as infinite, and the damping at the boundary, which is frequently ignored, are typically not well known. In this note, we discuss the identification of the boundary stiffness and damping parameters from modal data. As an example, we treat an elastic steel beam, for which an experimental modal analysis had been carried out in our laboratory.

Applied Problems of Marine Mechanical Systems Technical Condition Estimation

2017 ◽  
Author(s):  
Неменко ◽  
Aleksandra Nemenko ◽  
Никитин ◽  
Mihail Nikitin
Keyword(s):  
Mathematical Modeling ◽  
Time Series ◽  
Mechanical Systems ◽  
Technical Condition ◽  
Technical Diagnostics ◽  
Operational Parameters ◽  
Physical Processes ◽  
Minimum Loss ◽  
Condition Estimation

We consider the problems of technical diagnostics of marine mechanical systems such as machinery and other mechanisms. We propose effective techniques of mathematical modeling concerning physical processes during operation of these systems, machines and mechanisms. We describe algorithms of time series far forecast for operational parameters, ways of time series composition with minimum loss of accuracy and application of all of this for the prevention of breakdowns and other accidents.

Perpetual points in natural mechanical systems with viscous damping: A theorem and a remark

2020 ◽  
pp. 095440622093483
Author(s):  
Fotios Georgiades
Keyword(s):  
Rigid Body ◽  
Mechanical Systems ◽  
Dissipative Systems ◽  
Viscous Damping ◽  
Ongoing Research ◽  
Rigid Body Motions ◽  
Gyroscopic Effects ◽  
Nonlinear Mechanical Systems ◽  
Stiffness And Damping ◽  
Perpetual Points

Perpetual points have been defined recently and their role in the dynamics of mechanical systems is ongoing research. In this article, the nature of perpetual points in natural dissipative mechanical systems with viscous damping, but excepting any externally applied load, is examined. In linear dissipative systems, a theorem and its inverse are proven stating that the perpetual points exist if the stiffness and damping matrices are positive semi-definite and they coincide with the rigid body motions. In nonlinear dissipative natural mechanical systems with viscous damping excepting any external load, the existence of perpetual points that are associated with rigid body motions is shown. Also, an additional type of perpetual points due to the added dissipation is shown that exists, and this type of perpetual points, at least in principle can be used for identification of dissipation in nonlinear mechanical systems. Further work is needed to understand the nature of this additional type of perpetual points. In all the examined examples the perpetual points when they exist, they are not just a few points, but they are forming manifolds in state space, the Perpetual Manifolds, and their geometric characteristics worth further investigation. The findings of this article are applied in all mechanical systems with no gyroscopic effects on their motion, e.g. cars, airplanes, trucks, rockets, robots, etc. and can be used as part of the elementary studies for basic design of all mechanical systems. This work paves the way for new design processes targeting stable rigid body motions eliminating any vibrations in mechanical systems.

Identification of the Damping Matrix

2001 ◽  
Author(s):  
Menahem Baruch
Keyword(s):  
Frequency Response Function ◽  
Degrees Of Freedom ◽  
Linear Structure ◽  
Dynamic Structure ◽  
Viscous Damping ◽  
Structural System ◽  
Linear Dynamic ◽  
Damping Matrix ◽  
Stiffness Matrices ◽  
Mass Matrices

Abstract Only experiments can provide the data necessary to obtain the damping matrix of a dynamic structural system. In the method proposed here the damping matrix can be separated from the mass and stiffness matrices and obtained in an independent of them way. Two methods are presented. In the first method it is assumed that all the degrees of freedom can be loaded and measured. Several methods for calculation of the damping, mass and stiffness matrices, using the experimental data are presented. In the second method the load is employed only in some chosen points. However, it is assumed again that all the degrees of freedom are measured. In order to identify the damping, stiffness and mass matrices of the structure the measured quantities are forced to comply with the general laws for a linear structure. The structure is idealized to be a linear dynamic structure with viscous damping. The measured quantities are measured during the tests at discrete points of the Frequency Response Function.

Self-Excited Vibrations and Damping in Circulatory Systems

2014 ◽  
Vol 81 (10) ◽  
Author(s):  
Peter Hagedorn ◽  
Manuel Eckstein ◽  
Eduard Heffel ◽  
Andreas Wagner
Keyword(s):  
Transmission Lines ◽  
Mechanical Engineering ◽  
Equations Of Motion ◽  
The Self ◽  
Engineering Systems ◽  
Common Assumption ◽  
Damping Matrix ◽  
Stiffness Matrices ◽  
Ground Resonance ◽  
The Stability

Self-excited vibrations in mechanical engineering systems are in general unwanted and sometimes dangerous. There are many systems exhibiting self-excited vibrations which up to this day cannot be completely avoided, such as brake squeal, the galloping vibrations of overhead transmission lines, the ground resonance in helicopters and others. These systems have in common that in the linearized equations of motion the self-excitation terms are given by nonconservative, circulatory forces. It has been well known for some time, that such systems are very sensitive to damping. Recently, several new theorems concerning the effect of damping on the stability and on the self-excited vibrations were proved by some of the authors. The present paper discusses these new mathematical results for practical mechanical engineering systems. It turns out that the structure of the damping matrix is of utmost importance, and the common assumption, namely, representing the damping matrix as a linear combination of the mass and the stiffness matrices, may give completely misleading results for the problem of instability and the onset of self-excited vibrations. The authors give some indications on improving the description of the damping matrix in the linearized problems, in order to enhance the modeling of the self-excited vibrations. The improved models should lead to a better understanding of these unwanted phenomena and possibly also to designs oriented toward their avoidance.

Particle swarm optimization–based characterization technique of nonproportional viscous damping parameter of a cantilever beam

2021 ◽  
pp. 107754632110105
Author(s):  
Subhajit Das ◽  
Subhajit Mondal ◽  
Shyamal Guchhait
Keyword(s):  
Particle Swarm Optimization ◽  
Objective Function ◽  
Optimization Problem ◽  
Particle Swarm ◽  
Damping Coefficient ◽  
Viscous Damping ◽  
Swarm Optimization ◽  
Damping Matrix ◽  
Damping Parameter ◽  
Gradient Based

A complex eigenvector is a result of nonproportional damping present in a structural system. However, it is difficult to identify the accurate damping matrix considering the modal sparsity and coordinate sparsity. A nonproportional viscous damping parameter identification is formulated as an unconstrained optimization problem in the present study. The damping coefficient of each element is considered as the design variable for the optimization problem. The objective function is defined using the incomplete complex eigenvectors, which are generated because of the presence of external damping devices in the structure. This objective function is then minimized using standard particle swarm optimization to identify the damping coefficient of the damping matrix. The accuracy and efficiency of the particle swarm optimization are investigated by solving a few numerical problems with simulated measured data. The proposed method works well with the incomplete measured modal data. The current methodology performs satisfactorily with and without noisy data. A comparison study is performed with the existing gradient-based method, and the results show that the proposed method performs better than the existing gradient-based method for the present problem with and without noisy measurement data.

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