1. If you want to estimate only for the fundamental mode, use logarithmic decrement approach, where one has to vibrate the system and allow it to freely damp out. There is relation exists between this value (delta) to damping ratio (psi).
2. In case of multiple modes, one has to either to impulse test or steady or random vibration tests and capture both force and response signals (accelerations) to build frequency response function (FRF). Using half power point method then one can estimate the damping ratio.
3.Standard books explain these approaches (Theory of vibration with applications by W.T.Thomson; Structural Dynamics-Theory and Computation by Mario Paz).
1. If you want to estimate only for the fundamental mode, use logarithmic decrement approach, where one has to vibrate the system and allow it to freely damp out. There is relation exists between this value (delta) to damping ratio (psi).
2. In case of multiple modes, one has to either to impulse test or steady or random vibration tests and capture both force and response signals (accelerations) to build frequency response function (FRF). Using half power point method then one can estimate the damping ratio.
3.Standard books explain these approaches (Theory of vibration with applications by W.T.Thomson; Structural Dynamics-Theory and Computation by Mario Paz).
Curve fitting is one of the best method used in complex models with very close natural frequencies. I recommend using tools like LMS/ Polytec/ MEScope etc...for accurate results. However, if you are looking for fair results with isolated modes, use half power point method, or single DOF curve fitting.
David Ewin's Book "Modal Testing" is still probably the best overview. As mentioned above, circle fitting the FRFs plotted in the complex plane is well established and works fine for moderately lightly damped systems with decent raw vibration data. Whatever the method, things become tricky when modes are not well separated in frequency and/or when the damping is extremely small (Z20-30%)
Jones, David IG. Handbook of viscoelastic vibration damping. John Wiley & Sons, 2001.
Besides the works cited above, you may find useful the following papers.
Article New concept in modal analysis: The characteristic response f...
Article Structural dynamic identification with modal constant consis...
It is possible to do a time domain identification of the system parameters and then calculate what ever quantity you need. See our papers.
Article Parameter identification for uncertain linear systems with p...
Article Parameter identification of uncertain plants using H∞ method
Conference Paper Adaptive controller design and disturbance attenuation for S...
You can use others time-domain methods to identify exponential decay as
- Hilbert Transform
- ERA method (Eigensystem Realization Analysis)
http://vibrationacoustics.asmedigitalcollection.asme.org/article.aspx?articleid=1469186
http://www.sciencedirect.com/science/article/pii/S0888327001914244
You can compute the auto correlation function from the modal coordinate signal. You will get a free decaying response. By simply using a curve fitting technique you can estimate the damping ratio.
Let me suggest few papers :
1. Y.Z. Wang, X.D. Ding, X.M. Xiong, J.X. Zhang, Comparative analysis of internal friction and natural frequency measured by free decay and forced vibration, Rev. Sc. Instr. vol. 78, 103907 (2007).
2. J. Shui, H. Pei, Y. Liu, Relationship between the internal friction values of the specimen and the vibration system, Rev. Sc. Instr. vol 70, 2060-2064 (1999).
3. Let me comment suggestion of Marcus V. G. de Morais
Hilbert Transform cannot be used explicitely to compute damping due to detrimental effect of ripples (too large estimation errors). This is why I recommend a new, the so-called Hilbert-transform method which yields excellent estimation of damping/log decrement for real signals embedded in noise:
L. B. Magalas, M. Majewski, Hilbert-twin - A novel Hilbert transform-based method
to compute envelope of free decaying oscillations embedded in noise, and the
logarithmic decrement in high-resolution mechanical spectroscopy HRMS, Arch. Metall.Mater. 60, 1092-1098 (2015).
4. Another approach/equations is used to estimate damping ratio for two harmonic signals, etc.
To conclude, damping ratio can be estimated in so many different ways that you should to precise the system your are interested in. In general, however, all listed answers are correct but correspond to quite different situations.
Article Hilbert-twin – A novel Hilbert transform-based method to com...
Dear colleagues,
The accuracy of estimation of the logarithmic decrement is a complex issue.
In general, one can use several classical methods, few different interpolated discrete Fourier transform-based mathods and Hilbert transform (Hilbert-twin method). You can find many useful details in the attached papers.
I should mention that many constraints are emposed on estimation of the logarithmic decrement. For example in the case of time-dependent center of oscillations (Zero-point drift) all classical methods do not work. The parametric methods (OMI Optimization in Multiple Intervals) also exhibit some restrictions. Standard Fourier transform method is not satisfactory.
This is why we are developing a high-resolution method to estimate the logarithmic decrement from exponetially damped sinusoidal signals corrupted by ZPD, dc offset and biased by additive noise. Under such difficult (real experimental) conditions we have to find an optimized solution.
This story will be soon published in a forthcoming paper.
If you have more specific question I would be glad to answer.
Regards,
Leszek Magalas
How many ways are there to determine damping ratio by the force vibration?
ANSWER:
I suggest to use discrete Fourier transform to estimate damping ratio (phase lag between two signals). Discrete signal can be analyzed using directly sine and cosine.
The result depends on signal parameters, sampling frequency, measurement time, stability of the center of oscillations, etc.
The approach should be different to various vibrating systems and the frequency of analyzed signals. Again, your question is pretty general to provide an exact answer.
Regards,
Leszek Magalas
Hi
How can you measure the damping for a highly overdamped case with no oscillations at all regardless of initial conditions?
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