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Variables affecting modal frequency and shape

Variables affecting modal frequency and shape

Variables affecting modal frequency and shape

(OP)
I have modeled a building, applied a horizongal sinusoidal load to the top floor causing the building to vibrate, and am trying to make sense of my results (fundamental frequency and mode shape in particular). I want to make sure that I have the relationships between different variables correct. I know that a structure's frequency depends upon its modal mass and stiffness. I know that the mode shape depends on the frequency. I am a bit hazy when it comes to determining a building's modal mass. I know that the modal mass depends on the participation factor which describes how much a single mode influences the building's movement but does that have anything to do with how the mass is distributed throughout the building?

RE: Variables affecting modal frequency and shape

Not sure if I can give a answer in English. I just look at modal participation based on math:

R_m = sum(Phi_im*M_i)

R_m = participation factor for mode m (note: this is not equal to the mass participation factor given in many programs)

M_i = mass at Joint i
Phi_im = mass normalized mode shape for Joint i for mode m.

This only works for mass normalized mode shapes. But, I would think most programs would give you that already.

RE: Variables affecting modal frequency and shape

Participating mass is based on unit acceleration load on each DOF.

This correspond to seismic loading.

If you have different loading, use load participating ratio instead.

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