When a damper is attached to a bridge, its tuned to the bridges natural frequency. I dont get how will that allow for maximum transfer of energy? And also how will heavily damped systems prevent energy from going back to the system? I thought energy is just lost with damping.
I'm not a structural engineer, but as I understand it, catastrophic collapses of bridges were often due to loading that caused the bridge to oscillate at its natural frequency. Dampers tuned to the natural frequency allow the oscillation energy to be safely dissipated as heat. The dissipated heat will not naturally flow back to the structure causing it to again oscillate (in violation of the second law of thermodynamics).
This responds to your follow up questions.
but I don't get how is energy transferred to the damper in the first place?
In a similar way as a shock absorber in the suspension of a car works. Without the shock absorber, the car would bounce up and down on its suspension springs at the natural frequency of the springs. The shock absorber is basically a cylinder with hydraulic fluid and the fluid absorbs the oscillation energy.
plus what has natural frequency to do with the amount of energy thats transferred?
Let’s say the bridge is subjected to very strong, but intermittent, cross winds. The bridge may begin to oscillate if the frequency of the winds matches the natural oscillation frequency of the bridge structure. That’s the only frequency that will cause the bridge to fail. So it only makes sense to design the damper so that it absorbs energy at that natural oscillating frequency. If the damper is too “stiff”, it will not give at all and simply be another rigid part of the bridge structure. If the damper is too “soft”, it will simply oscillate along with the bridge and not dissipate any energy.
Hope this helps.
Disclaimer: I'm not a structural engineer, so in practice this may be different for bridges specifically. This is more about the general nature of vibrations and damping.
When designing mass-spring damper systems (which you could model the bridge as a complex version of) the natural frequency of the system is a critical factor. The damper system is designed to dissipate high amounts of energy at the natural frequency of the bridge. This is because at the natural frequency, an undamped system, or a system with inadequate damping, will continue to increase in the amplitude of oscillations. A very famous example is the Tacoma Narrows Bridge, where the wind travelling across the bridge oscillated it at the resonant frequency, and the damping in place was insufficient to dissipate enough energy.
Essentially, in each period of the periodic motion, if the dampers are unable to dissipate more energy than is added to the system, the total energy of the oscillations will continue to increase until something bad happens (like a bridge collapse).
The purpose of the dampers is to prevent the energy from staying in the bridge system, and instead dissipates it as other forms of energy (generally heat, possibly some sound). The energy isn't completely gone, it just needs to be taken away from the bridge oscillations, so that the potential energy of the bridge due to oscillations doesn't resonate out of control.
Also note that I talked about "the" resonant frequency of the bridge; but in practice it would have multiple resonant frequencies; and possibly some resonances between parts that also need to be accounted for. Treating the bridge like a simple mass-spring-damper system (as I've done here) is a good first approximation; but in practice it is more complex.