Rayleigh damping in Abaqus

[aliabolhasanpoor]

Dear all friends,

Is there any one who know the unit of w (the natural frequency) and fraction of critical damping in the equations of the Rayleigh damping?

The equations are the followings:

aR=2*w1*w2*(the fraction of critical damping)/(w1+w2)
&
BR=2*(the fraction of critical damping)/(w1+w2)

What is the unit of w? Rad/sec or Hz?

Does the fraction of critical damping substitute in term of percent(%)? (e.g, 0.05 or 5)

I look to hear a positive response from you.

Thank you so much.

 

[bkal]

w in rads/sec, fraction of critical damping is unitles, e.g. 0.05 for 5% damping. You can easily work out expressions for Rayleigh coefficients by using definitions of the critical damping and the Rayleigh damping.

 

[aliabolhasanpoor]

Dear bkal,
Thank you so much for your response. As a consequence, I should substitute those parameters in the above equations in term of units which you pointed out them, do not I?

Would you please introduce me a text book or a resource that refers to that units which you told me, because I want to refer my information to them.

Thank you for your response

Best regards.

 

[bkal]

This is all based on two simple basic dynamics equations which you can find in any textbook:
1. natural frequency of the system,
2. critical damping of a system with viscous damping,

Once you introduce these into a formula for Rayleigh damping, you will end up with a system of two equations with two unknowns (ALPHA and BETA), solution of which gives equations you have quoted.

 

[aliabolhasanpoor]

Dear bkal,
Thank you so much for your response.