mode participation factor

[rk_19]

hi, I am trying to calculate mode participation factors for a frame structure. the consistent mass matrix approach is used. I got the Eigen values, vectors, checked orthogonality - all ok. for calculating the mode participation, gamma=L/M, L is the coeff vector = [transpose(phi)]*[m]*[r]. how do I calculate the vector r. I went through few books/web which says r is the influence vector which represent displacement at nodes due to unit displacement at ground. how do I calculate this when doing modal analysis for free vibration problem.
thanks,

 

[Shu Jiang PEng SE]

"r" is one modal shape vector (you can get it from the modal analysis) which is corresponding to the modal participation factor you need to calculate.

 

[rk_19]

Hi, I was writing the fe code in Fortran for performing modal analysis. I crosschecked the Eigen values/vectors with third party software and they are matching... are u telling that 'r' is the mode shape vector??... in my eqn, phi represents normalized Eigen vector.. I refered some materials and it reads 'r' as influence vector representing displacement at a node due to unit displacement at ground. I am not clear with this statement

 

[Shu Jiang PEng SE]

YES. I am wrong. r is a displacement vector that expresses the displacement of each structure degree of freedom due to static application of a unit support displacement.

 

[rk_19]

So, how do I calculate that.

 

[Shu Jiang PEng SE]

Think you can find your answer in chapter 26 of "dynamics of structures, 3rd edition" by Ray W. Clough.