I have a question regarding the determination of mass and stiffness damping parameters of Rayleigh Damping. In Plaxis, I need to determine the target frequencies to calculate the mass and stiffness damping parameters. In the Plaxis manual, it is written that the the first target frequency is first natural frequency of the soil deposit and the second target frequency is the predominant frequency of the input motion over the natural frequency of the soil. So if my input motion is a sinusoidal harmonic motion with a frequency of 100 Hz, so the predominant frequency is 100 Hz? Or do I just the first frequency as 1 Hz and the second target frequency is 100 Hz? Thank you.
Dear A. Moussa,
Several different methodologies have been proposed in the literature to calibrate Rayleigh damping coefficients. In the PLAXIS Reference manual, the methodology originally proposed by Hudson et al. (1994) is described.
According to this proposal, and as you described, the first target frequency should correspond to the natural frequency of the soil deposit and the second target frequency should correspond to the odd integer immediately above the value given by the ratio of the predominant frequency of the input signal to the natural frequency of the soil deposit. In your case, according to what you described, since the natural frequency of the soil deposit is 1 Hz and the predominant frequency of the input signal is 100 Hz.
Therefore, the first target frequency, f1, should be set to 1 Hz and the second target frequency, f2, set to 101 Hz (odd integer closest to 100 / 1).
I have one question, let the predominant frequency of the input signal is 1.5 Hz and natural frequency of soil deposits is 1.7, according to Hudson et al. (1994)
F1=1.7Hz
F2= ?
1.5/1.7= 0.88
F2=1
Is it right ?
my point is F2 is less than F1.
Does work Hudson et al. (1994) principle in this case?
I believe my colleague already responded to the post you made on the same topic here: Damping
Dear Stefanos,
I am applying the 3 components of an earthquake in x, y and z direction at the same time to my soil profile. how can I define the final f2 value to introduce to Rayleigh damping? because each of motions in x, y and z direction have different predominant frequencies. in my case f1=0.97 HZ. and predominant freq. in x dirextion=12.5 HZ, in y direction=3.57HZ and in z direction 4.54HZ. I will be appreciate if you help me.
I think this answer is not valid for Plaxis 2D. Because if we set F2 lower than F1, Plaxis 2D gives an error. What should we do in this situation?
Thank you.
Consider swapping F1 and F2 so that F1 < F2.
With kind regards,
Dennis Waterman