How Does a PTMD Dissipate Energy Back into the Building?

[no_drama_llama_77]

TL;DR Summary

How do buildings dissipate kinetic energy into pendulum tuned mass dampers (PTMD)? Please read for more details.

"What is a tuned mass damper" by practical engineering
From 6:36 to 7:07How does the energy of the pendulum tuned mass damper (PTMD) dissipate energy back into the building? Intuitively, it seems like it's momentum or resonance, where the PTMD is in phase with the motion of the building and thus there is an increase in amplitude of the oscillation, but what is the correct scientific explanation for this phenomenon?I understand that the PTMD should be 'tuned' to the natural frequency of the structure to oscillate out of phase with the structure and thus damp the system, but why is it from 6:36 to 7:07 that even though the PTMD is 'tuned' to the correct frequency (i.e., the natural frequency of the building), the system was unable to damp without Coulomb damping due to the tightening of the screw (shown after 7:07)? And how is the kinetic energy of the structure dissipated into the PTMD if the PTMD moves out of phase with the structure?

Thank you

 

[jrmichler]

The building by itself is a simple single degree of freedom (1 DOF) spring mass system. It has a single natural frequency, and minimal damping. Adding a second spring and mass (the TMD) adds another natural frequency. A typical TMD has mass that is a fraction of the mass of the building with natural frequency close to that of the building, so the two natural frequencies of the 2 DOF system are close to the original natural frequency of the 1 DOF system. The lower natural frequency of the 2 DOF system is below the original 1 DOF natural frequency, the higher natural frequency of the 2 DOF system is above the original natural frequency of the 1 DOF system.

An undamped TMD is useful when a system has a single frequency excitation at its natural frequency. It moves the natural frequency to two frequencies, neither of which align with the excitation. Since the system is no longer at the excitation frequency, it does not resonate.

A damped TMD is used when there is a broad range of excitation frequencies AND where it is not possible to connect a damper directly from the vibrating object to ground. In a multi-DOF spring-mass-damper system, a damper anywhere in the system reduces vibration in the entire system. A crude way of putting it: Vibration energy transfers to the tuned mass, the damper takes energy out of the tuned mass, which sucks vibration energy from the original mass.

As alluded to in the video, there is an optimal amount of damping. Zero damping removes zero energy, so does not reduce vibration. Infinite damping locks the tuned mass in place, with the result that the mass is added to the mass of the structure. Again, there is no reduction in vibration. Somewhere in between, there is an optimal amount of damping to get the best vibration reduction.

Viscous damping is taught in basic vibration courses because it is easy to analyze. Coulomb damping is more difficult to analyze because closed form solutions are either difficult or impossible. Coulomb damping is easily analyzed using numerical methods.

I once built some TMD's to control a machine vibration. The TMD spring was a two inch diameter steel bar about two feet long, and the mass was a piece of steel of about 40 lbs. The optimal damping turned out to exactly the amount of damping achieved by grabbing the tuned mass with both hands using a "death grip". Since the machine needed four TMD's, the R&D tests needed four helpers. Unfortunately, by the time we proved that TMD's would control the vibration, the design had been changed to a thicker machine frame and a passive TMD would no longer do the job. So we went to an active vibration control system that did do the job.

 

[no_drama_llama_77]

An undamped TMD is useful when a system has a single frequency excitation at its natural frequency.

What do you mean by undamped TMD? Aren't TMDs meant to damp oscillations of the structure/building? For example, if referring to the video, does an undamped TMD (pendulum tuned mass damper in this case) mean simple harmonic oscillation?

Zero damping removes zero energy, so does not reduce vibration. Infinite damping locks the tuned mass in place, with the result that the mass is added to the mass of the structure. Again, there is no reduction in vibration.

What does infinite damping mean in this case? If there's infinite damping, shouldn't there be a great reduction in vibration?
From the video, the pendulum tuned mass damping had damping and was tuned to the correct frequency, by why wasn't it able to "suck the vibration energy from the original mass"?

Thank you very much for your reply and help!

 

[jrmichler]

The definition of a viscous damper is $Force = C * V$, where F is force in $lbs$, C is the damping coefficient with units of $lb-sec/ft$, and V is the velocity in $ft/sec$. Damping force opposes velocity. If there is no velocity, there is no damping force. If the damping coefficient is zero, there is no damping force. If the damping coefficient is very large, a small velocity has a very large force. If the damping coefficient is infinite, any microscopically small velocity has an infinite force. In that case, the damper is effectively a rigid link.

Here is a schematic of a spring-mass system with a damped TMD:

M1 is the mass of the system, K1 is its spring constant. M2, K2, and C2 are the tuned mass mass, spring, and damper. The damper is attached to the tuned mass because there is no practical way to attach a damper to the system (building in this case).

You will need to spend some time studying the schematic while studying Post #2 to wrap your mind around the concepts of zero damping, optimal damping, and infinite damping and how they affect the overall system. Good search term for general background is spring mass damper system.

 

[no_drama_llama_77]

The definition of a viscous damper is $Force = C * V$, where F is force in $lbs$, C is the damping coefficient with units of $lb-sec/ft$, and V is the velocity in $ft/sec$. Damping force opposes velocity. If there is no velocity, there is no damping force. If the damping coefficient is zero, there is no damping force. If the damping coefficient is very large, a small velocity has a very large force. If the damping coefficient is infinite, any microscopically small velocity has an infinite force. In that case, the damper is effectively a rigid link.

Here is a schematic of a spring-mass system with a damped TMD:
View attachment 271426
M1 is the mass of the system, K1 is its spring constant. M2, K2, and C2 are the tuned mass mass, spring, and damper. The damper is attached to the tuned mass because there is no practical way to attach a damper to the system (building in this case).

You will need to spend some time studying the schematic while studying Post #2 to wrap your mind around the concepts of zero damping, optimal damping, and infinite damping and how they affect the overall system. Good search term for general background is spring mass damper system.

I'll try to consolidate my knowledge on this. Thank you!