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# Questions about First modes of vibration and viscous dampers

## Questions about First modes of vibration and viscous dampers

(OP)
Hi everyone,

I have questions that I hope someone will help me in answering them.

1) is it effective to place a plain viscous damper for vertical mid-span vibrations when located to act horizontally at the roller support of a simply supported beam?

2) why would the periods of the first modes of vibration for buildings are very large (over 5 secs, especially tall buildings)?

3) How should I determine whether a mode of vibration corresponds to a local mode (of a member) or a building mode?

I am very sorry for making this long. Thank you in advance for your kind help.

### RE: Questions about First modes of vibration and viscous dampers

1) I'm not sure I understand your first question... You have a simply supported beam and you want to dampen it's mid span vertical vibrations by putting a horizontal damper at a support?
2) The taller the building, the longer the period it will be. This is because they have a building mass to stiffness ratio.
Also, the natural period increases as you increment the vibration mode, so the first mode always has the longest period.
A very rough rule of thumb is to multiply the number of stories in a building by 0.1 seconds to get the natural period for the first mode shape.
Thus a one story building ~ 0.1 seconds, a fifty story building ~5 seconds.
3) I'm not sure I understand this question either... All modes will affect the entire building.
Maybe you are asking about determining the story shear vs diaphragm shear in the equivalent lateral force method?
The building's story shears will be governed by the first mode of vibration, where all story forces act in the same direction. However, to determine the diaphragm shear, the first mode of vibration does not govern. Read ASCE 7 12.10.1.

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