# non-linearly. ! As height ( H ) increases, ( f ) decreases, $ % - - PowerPoint PPT Presentation

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non linearly as height h increases f decreases non

Jun 17, 2023 320 likes •479 views

A Model for Resonance As stiffness ( k ) increases, the resonant frequency ( f ) increases, # non-linearly. ! As height ( H ) increases, ( f ) decreases, $ % & non-linearly. As mass ( M ) increases, ( f ) decreases, non-linearly. So

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A Model for Resonance

! ∝ # $%&

As stiffness (k) increases, the resonant frequency (f) increases, non-linearly. As height (H) increases, (f) decreases, non-linearly. As mass (M) increases, (f) decreases, non-linearly.

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So in terms of our testing of model buildings: The higher the frequency at which the earth shakes, the greater the energy intensity the earthquake produces and thus the greater the force the shaking ground exerts on the buildings. We can use the equation above to predict how much a certain Force will displace x (move away from vertical) a building if we know the stiffness k of that building. So, to minimize the displacement x of a building when it is shaken by an earthquake Force, the building should have as high a stiffness k as practical.

x = Force/ k

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Thus, the resonant frequency decreases to about 0.7 x of the original when the mass is doubled (2X). SOLUTION

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Example 2. If you know the resonant frequency of one building f1, and you increase the height by 2x, what happens to its resonant frequency? Calculate it with this equation. !

" = %

1 '()

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SOLUTION

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Resonance and Building Stiffness

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SOLUTION

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Example 4. If you know the resonant frequency of one building f1, and you increase its mass 3x and you reduce its height to half of its original, what happens to its resonant frequency? !

" = %

1 '()

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SOLUTION Example 4. If you know the resonant frequency of one building f1, and you increase its mass

3x and you reduce its height to half of its original, what happens to its resonant frequency?

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Example 5. If you know the resonant frequency of one building f1, and you increased its resonant frequency to 10x its original f1 by changing the building’s height, how much did you change its height? Calculate it with this equation. "

# = %

1 '()

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Example 5. If you know the resonant frequency of one building f1, and you increased its resonant frequency to

10x its original f1 by changing the building’s height, how much did you change its height? Calculate it with this equation.

SOLUTION