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# Relation between modal shapes and structural respone

## Relation between modal shapes and structural respone

(OP)
I want to put my understanding of the above said topic.We have the "n" modal shapes of our building with "n" different frequencies.Each modal shape determined by displacing one of the DOF ,or mass, and finding out the displacement of rest.
Now during earhtquake waves of different frequencies will impart force of different frequencies which may result response of structure in different modes, one after the other.In some modes, ofcourse, a part of structural mass will be active.But for design purposes, only the response which will have maximum participation of mass is important as it will result in maximum base shear.
So is that the reason we combine modes (some of them) to get the dynamic response? Does that mean expressing deformed shape in terms of modal shapes as written in"Ray W. Clough's" book?

I will appreciate Precise replies.
Thanks.
Replies continue below

### RE: Relation between modal shapes and structural respone

I understand that this has a historical explanation, that the actual (linear) vibration shape of the several degrees of freedom case once stated through the physical laws of motion and structural response was found to be mathematically amenable to a (deterministic) solution through the use of component mode shapes; mathematically, the "actual" vibration shape was a precise linear combination of the "notional" vibration modes.

So in my view what primarily lays under the practice of using modes in vibration studies is just a mathematical setup found to be useful to state the response, due that in the physico-mathematical setup of the solution -we are continuously using the results of the work of XIX century people- the whole body of the thought to be feasible linear vibration shapes can be expressed in the space of the modes.

I paste what Anil K. Chopra says about.

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