I am performing Transient Dynamic Analysis of a 3-storey structure with isolated footings and 20 m soil column/strata below it. I need to consider Rayleigh Damping in this case. As per Rayleigh Damping, we have to provide two frequencies w1 and w2. Where w2= n w1, n=wi/w1 (n= closest odd integer greater than wi/w1). Here wi is dominant frequency of input earthquake motion, w1 is the fundamental frequency of soil-structure system. In my case wi = 10.17 rad/sec, w1 = 13.18 rad/sec, then n= 0.77. The nearest odd integer greater than n is 1. which we can't consider while solving Rayleigh Damping as w2 should be greater than w1.
Hello Divyesh Rohit
The natural frequencies used to construct the Rayleigh damping matrix for the structural frame is obtained from the solution of the normal frame eigenvalue problem
|Kg - M*wi2| = 0 where | | stands for determinant, Kg = global stiffness matrix for the frame, M = the frame mass matrix.
Thus w1 and w2, that are used to construct the damping matrix, are natural frequencies of the frame and are in no way related to the dominant frequency of the earthquake excitation. In addition, a 3-storey frame will have at least 3 degrees of freedom when a lumped mass approach is used. In that case, the damping matrix needs to be at least 3 by 3 instead of 2 by 2 so that w3 needs to be considered also.
hello
for obtain Rayleigh ratio (Alpha and Beta) you don't need to frequency of Earthquake record, there are independent from earthquake record ,
you must to Analysis your complete model to obtain inherent frequencies of your model and then calculate Alpha and Beta
Hi All,
In my case I am doing soil-structure interaction, in which during Rayleigh damping the model should respond to the dominant frequency of the input motion without getting over-damped. Hence , wi (dominant frequency of input motion) is used to determine w1 and w2.
I have used another input motion whose dominant frequency is greater hence no problem. Thanks for your guidance.
Hi Alireza,
Here we are doing soil-structure interaction (SSI) and in this case the damping in soil and structure is not frequency dependent. Also for time-history analysis in SSI the model needs to respond to dominant frequency of earthquake. Hence to find the Rayleigh Frequencies we need dominant frequency of input earthquake motion.
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