Rayleigh Damping Coefficients of a plate
Rayleigh Damping Coefficients of a plate
(OP)
Hello All;
I am working in the vibration analysis field , both theoretical and practical fields.
while working in the theoretical side I needed the Rayleigh Damping Coefficients of a vibrating plate.... I need to calculate (Alpha) and (Beta) of the following equation:
[C]=Beta*[K]+Alpha*[M]
I found in the literatures a method depending on the first natural frequencies from the equation :
Zeta=1/2(Alpha/Omega+Beta*Omega)
the problem is I do not have the (Zeta) to solve the above equtaion simultaneously using two Omega's.
how to calculate the Alpha and Beta ??
Thanks all in advance
I am working in the vibration analysis field , both theoretical and practical fields.
while working in the theoretical side I needed the Rayleigh Damping Coefficients of a vibrating plate.... I need to calculate (Alpha) and (Beta) of the following equation:
[C]=Beta*[K]+Alpha*[M]
I found in the literatures a method depending on the first natural frequencies from the equation :
Zeta=1/2(Alpha/Omega+Beta*Omega)
the problem is I do not have the (Zeta) to solve the above equtaion simultaneously using two Omega's.
how to calculate the Alpha and Beta ??
Thanks all in advance





RE: Rayleigh Damping Coefficients of a plate
What is the material of the plate?
Is it just a single flat piece of material or is it made up of several components bonded together?
These might get you a little closer to an answer.
M
--
Dr Michael F Platten
RE: Rayleigh Damping Coefficients of a plate
Thank you for your response.
I have three boundary conditions (4-edge clamped, 3-edge clamped, 2-edge clamped).
The material is basically Steel (Poison's ratio=0.3,E=200Gpa).
The plate is simple thin plate only.
Is it any way to calculate the constants using the formula above? of course the natural frequincies are known.
Thanks
RE: Rayleigh Damping Coefficients of a plate
Depending on the clamping arrangement, the damping would probably be in the range 1% to 5% critical. You can use your equation to find a rayleigh model that gives you say 2.5% damping across the frequency range of interest.
This will always be an approximation. Real damping is pretty much impossible to predict and for accurate models measured values are usually used.
M
--
Dr Michael F Platten
RE: Rayleigh Damping Coefficients of a plate
I do understand now.
one more question please. Is there any reference talking about this issue ??? maybe I can find some tables or figures concerning this problem.
Best
Ghazwan
RE: Rayleigh Damping Coefficients of a plate
RE: Rayleigh Damping Coefficients of a plate
Thank you for the information.
Do you mean the text "Finite Element Modeling: In Engineering Practice" For Constantine C. Spyrakos ???
because i did not find any thing else for him in books.google.com
Thank you
RE: Rayleigh Damping Coefficients of a plate
page 265 covers a sample calculation although there is a more comprehensive discussion of the coefficients on pages 151-152
RE: Rayleigh Damping Coefficients of a plate
To be honest I could not get the book !!
Is there any other reference?
RE: Rayleigh Damping Coefficients of a plate
Also, try googling the paper "Computation of Rayleigh Damping Coefficients for Large Systems" by Chowdhury and Dasgupta. I havn't had to use it myself, but I guess it might be helpful to you.
RE: Rayleigh Damping Coefficients of a plate
pick two criticals, for example the lowest two and calculate alpha and beta for a given zeta.
RE: Rayleigh Damping Coefficients of a plate
I already downloaded the paper , it is really useful.
thank you
RE: Rayleigh Damping Coefficients of a plate
Thank you again
your tips reflects your background of knowledge.
I wil do it as you said.