13. Damped free vibration

Questions and discussion for this lecture live here. Fire away by hitting Reply below :fire:

Greetings, Dr Sean hope you are doing great.

As you said underdamped system is more commonly observed in civil engineering structures. Could you explain in brief what does critically damped, underdamped, and over-damped systems mean in real life structures ?? How does it affect the structure ? Which one is most preferred and why ?

Also, as we go up, the stiffness of our structure reduces. Could you state the reason ? In this case, how tall buildings achieve required stiffness ?/

Also, how does time period affect the structure at the time of extreme events like earthquake ?? Is more time period good or bad for the structure say, at the time of resonance. For eg. I read that every structure vibrates/oscillates at its own natural frequency and undergo resonance at different times.

This means if we consider say, we have three building models and we apply base excitation using the shake table. Not all three building models will oscillate at the same time. Each structure will oscillate only after reaching the resonance and the resonance time will be different for each of them.

Could you explain the above phenomenon ?


As you mention, critically damped and over-damped systems are not common in civil/structural engineering. In fact they are so uncommon that I would struggle to think of a practical example. They are mentioned here more for completeness as they emerge from the mathematics of the system. They are best understood simply by looking at the free vibration response - i.e. that is the most visual and easily interpretable description of these damping regimes. There really isn’t a lot more to it than that…from a civil engineering point of view. A mechanical engineer may have more to say however!

Regarding tall buildings, stiffness of a flexural element, a tall building in this case, is inversely proportional to length - hence the taller the building, the lower the stiffness.

Structures have multiple modes of vibration which means there are multiple frequencies that the building could resonate at. The building’s response to ground motion will depend on the frequency distribution within the ground motion and how these frequencies compare with the building’s inherent modal frequencies. We cover this topic in more detail in my MDoF dynamics course.

Hope that helps.