Dynamic Magnification Factor

 

Dynamic magnification factor (DMF) takes into account the dynamic effect in increasing a system’s response relative to equivalent static response.

We can devise three possible cases based on the value of frequency ratio.

When the force frequency is negligible, a structure becomes stiffness control system, and the structural response is not magnified since the excitation is very slow.

On the other hand, relatively high force frequency when compared to natural frequency of the system yields a mass control system. The response of structure can be reduced by increasing its mass.

When force frequency equals to the natural frequency of the system, resonance occurs. This is not a favourable scenario as the value of DMF can become very high, and makes the structure unsafe.

The following shows the derivation related to dynamic magnification factor. Watch the video above for full details. 

Transformation of steady state response solution 1
Transformation of steady state response solution 2
Transformation of steady state response solution 3
Case 1: frequency ratio approaching zero
Case 1: frequency ratio approaching zero
Case 2: frequency ratio much greater than 1
Case 2: frequency ratio much greater than 1
Case 2: frequency ratio much greater than 1
Case 3: frequency ratio equals to 1
Case 3: frequency ratio equals to 1
Graph of DMF against frequency ratio for various damping ratio

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