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Frequency of Vibration & Resonance

In study of dynamic loadings, the number of complete cycle of waves produced in one second, also referred as frequency, f, of the motion, becomes an important parameter. Frequency simply reflects how soon a cycle of motion repeats.

Frequency, in case of periodic motions, is simply expressed as inverse its Time period;

(6)

Though earthquake induced ground motions are also cyclic in nature, nevertheless, due to its transient nature (Refer Fig-18) it is almost impossible to define a frequency of such motion as in periodic motions that repeat itself after the certain time interval in a similar fashion. However, we could characterize such non-periodic/random motion by its Frequency content.

At a given location, for two dissimilar structures, if the duration of shaking and magnitude of peak ground acceleration during an earthquake are same, it is the frequency content of the ground motion that determines the extent of damage to these structures. So, frequency content of the ground motion is an important parameter along-with the duration and peak magnitude of ground shaking in the study of damages that may inccur in structures with different dynamic behaviors.

Fig-18 (Ground acceleration time history of real earthqauke)

Any structure in its natural state possesses a natural Frequency of vibration/Natural Time period (http://buildingresearch.com.np/services/erd/erd1.php); an inherent property of every structure; that primarily depends on its Stiffness and Mass. If, however, the frequency content of earthquake induced ground motion and building's natural frequency of vibration happens to be in close proximity resonance is said to occur.

A resonated structure could vibrate 2-3 times higher or even more than the unresonating loading conditions. It’s the worst scenario in earthquake resistant design, ERD, in which total collapse of such resonated structure is expected; that had been substantiated in past earthquakes.

It wouldn’t be possible to design structures for such a huge vibrational load generated by resonance; but, structure’s property could be modified to avoid resonance.

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