Hi,
I am trying to estimate the Center of Frequency for a dam.
I have followed the example below, where the geometry was defined, and the shear modulus, bulk modulus, and density properties were assigned to different regions. Then the model was cycled with a horizontal gravimetric force (shear example below).
Based on the results, I adopted a fmin of 1.56 Hz.
Following the completion of seismic deformation, I calculated the velocity response spectra of crest acceleration, with the results shown below.
Is this approach appropriate for estimating the center of frequency in Rayleigh damping? The extent of liquefaction in my model significantly changes when adopting different values, and I am unsure how to verify the appropriate fmin.
Procedure for Determining Natural Frequencies for Crest Acceleration Response Spectra:
Vibration Analysis Without Damping:
Perform a vibration test by displacing the crest in a specific direction.
Avoid applying a horizontal gravity load unless this scenario represents a practical design case.
Time History Recording:
Record the time history of the crest point’s response throughout the vibration test.
Power Spectrum Plotting:
Plot the power spectrum of the recorded time history to identify the dominant natural frequencies.
Typically, the first two natural frequencies are denoted as F1 and F2.
Damping Ratio Design:
Determine the primary damping ratio and the two target frequencies.
For example, set D=5% at f1=F1, and f2=max(3∼5×F1,F2).
Rayleigh Damping Parameters:
Once D, f1, and f2 are defined, calculate the center frequency and its corresponding damping ratio for Rayleigh damping.
Refer to Equations 1 to 8 of the Rayleigh Damping documentation. Pay special attention to the distinction between frequency and angular frequency in these equations (omega = 2pi*f):
D = 0.5(alpha/omega1 + beta/omega1)
D = 0.5(alpha/omega2 + beta/omega2)
With the above two relationship, we can calculate alpha & beta, then we can obtain f_min and Xi_min.
The inputs for Rayleigh damping are f_min and Xi_min.
