Question

What is the theory behind an "Under-damped free Vibration" and how do we apply that knowledge in the real world [20]

Answer 1

● First you have to know about the damped free vibration

Damped Free Vibrations: Damper is present in the system which is used to absorb the vibrations. But the members doesn't undergo any external force which means the system is under natural vibrations and this can also be called free vibrations.

There are two cases :-

Under damped and over damped

● So now the Under damped Case:- The free vibration of an under damped system is oscillatory but not periodic.

The vibration would be periodic if the amplitude will not decreasing with time.Even though the amplitude decaying with cycles, the member takes the same time to execute each cycle.

● You can apply this knowledge in real world in:-

1. In tall buildings which are in seismic regions by building damping systems to protect them during earthquakes.
2. Suspension Bridges, particularly cable stayed structures, have oscillation issues in the wind. Their enegy can absorbed by the under dammped free vibration (dampers) mechanism.   
3. Shock absorber.

Thank you.