scholarly journals Some Elements of Operational Modal Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Rune Brincker
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Modal Analysis ◽  
Mode Shape ◽  
Fourier Integral ◽  
Operational Modal Analysis ◽  
Difficult Case ◽  
Domain Identification ◽  
Spectral Density Matrix ◽  
Random Responses

This paper gives an overview of the main components of operational modal analysis (OMA) and can serve as a tutorial for research oriented OMA applications. The paper gives a short introduction to the modeling of random responses and to the transforms often used in OMA such as the Fourier series, the Fourier integral, the Laplace transform, and the Z-transform. Then the paper introduces the spectral density matrix of the random responses and presents the theoretical solutions for correlation function and spectral density matrix under white noise loading. Some important guidelines for testing are mentioned and the most common techniques for signal processing of the operating signals are presented. The algorithms of some of the commonly used time domain and frequency domain identification techniques are presented and finally some issues are discussed such as mode shape scaling, and mode shape expansion. The different techniques are illustrated on the difficult case of identifying the three first closely spaced modes of the Heritage Court Tower building.

Analysis of Instabilities in Railway Vehicles Employing Operational Modal Analysis

2015 ◽  
Author(s):  
Lara Erviti Calvo ◽  
Gorka Agirre Castellanos ◽  
Germán Gimenez
Keyword(s):  
Numerical Model ◽  
Modal Analysis ◽  
Mode Shape ◽  
Operational Modal Analysis ◽  
Mode Shapes ◽  
Correct Identification ◽  
Unstable Condition ◽  
Static Tests ◽  
Railway Vehicles ◽  
Damping Rate

The application of Operational Modal Analysis (OMA) in the railway sector opens a broad field of opportunities. The validation of the numerical model employed in the design phase is usually performed employing data obtained in static tests. The drawback is that some suspension parameters, such as dampers, only have an influence in the dynamic behavior and not in the static behavior. Because of that, the use of the mode shapes identified from track measurements in combination with the static tests leads to a more accurate validation of the numerical model. Apart from that, most passenger comfort and dynamic problems are associated to slightly damped modes. A correct identification of the modal parameters can be used as a continuous design improvement tool to improve the comfort and dynamic characteristics of future designs. Another valuable application of OMA techniques is the identification of the mode shapes corresponding to instabilities, due to the safety impact that they have. In railway vehicles, instabilities are associated to mode shapes that present a damping rate which decreases with the increase of the running speed. Above a certain speed value, the excitation coming from track cannot be damped by the vehicle and it reaches an unstable condition. This unstable condition leads to high acceleration levels experienced by the passengers and high interaction forces between the wheel and the rail that may lead to safety hazards. The speed above which the vehicle is unstable is known as critical speed, and has to be greater than the maximum speed of the vehicle with a reasonable safety margin. The use of OMA techniques allows identifying the mode shape that causes the instability. This paper presents the application of OMA techniques to measurements performed on a passenger vehicle, in which the speed was increased until the vehicle was unstable. The mode shape that caused the instability was identified as well as its corresponding natural frequency and damping rate.

scholarly journals Modal Participation Estimated from the Response Correlation Matrix

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Rune Brincker ◽  
Sandro D. R. Amador ◽  
Martin Juul ◽  
Manuel Lopez-Aenelle
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Correlation Matrix ◽  
Analytical Form ◽  
Mode Shapes ◽  
Transformation Matrices ◽  
Spectral Density Matrix ◽  
Spectral Density Functions ◽  
Input Load ◽  
The Time Domain

In this paper, we are considering the case of estimating the modal participation vectors from the operating response of a structure. Normally, this is done using a fitting technique either in the time domain using the correlation function matrix or in the frequency domain using the spectral density matrix. In this paper, a more simple approach is proposed based on estimating the modal participation from the correlation matrix of the operating responses. For the case of general damping, it is shown how the response correlation matrix is formed by the mode shape matrix and two transformation matrices T1 and T1 that contain information about the modal parameters, the generalized modal masses, and the input load spectral density matrix Gx. For the case of real mode shapes, it is shown how the response correlation matrix can be given a simple analytical form where the corresponding real modal participation vectors can be obtained in a simple way. Finally, it is shown how the real version of the modal participation vectors can be used to synthesize empirical spectral density functions.

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