Tuned mass damper does not reduce the amplitude of vibration?

[gunna]

Hello everyone,

I have a simple question. Lets say a single degree of freedom system (SDOF) which consists of a spring and a mass is excited by an external force. The SDOF system has the eigenfrequency of 0.31 Hz and the external force is a periodic force with the frequency of 0.6 Hz. After decay of the transient effects, the frequency response function of the SDOF system should contain peaks at the system's eigenfrequency of 0.31 Hz and the 0.6 Hz excitation, right?

Now I want to reduce the response at 0.6 Hz induced by the excitation with a tuned mass damper (TMD). The TMD also consists of a spring and a mass, and the eigenfrequency of the TMD is tuned to 0.6 Hz, as it should reduce this frequency. I built this configuration in ANSYS and calculated the SDOFs response under the influence of the TMD and the system's response at 0.6 Hz is even getting bigger.

Am I understanding something wrong? Should a TMD with the tuned eigenfrequency not reduced the system's response at THAT frequency after the decay of the transient effects?

Another thought is the excitation induces resonance in the TMD and thus causing an amplification in the SDOF's system at the excitation frequency...

Best regards

 

[Lnewqban]

Welcome, @gunna !

Shouldn't the oscillation frequency of the TMD be tuned to be similar to the resonant frequency of the object it is mounted to (eigenfrequency of 0.31 Hz)?

 

[jrmichler]

I built this configuration in ANSYS and calculated the SDOFs response under the influence of the TMD and the system's response at 0.6 Hz is even getting bigger.

You have a system with resonant frequency of 0.31 Hz that is excited at 0.6 Hz. The response will be small because the magnitude of the response is determined by the mass of the system and the magnitude of the excitation. Then you added a second system with a resonant frequency of 0.6 Hz. That system is driven at its resonant frequency by the 0.6 Hz excitation, so the amplitude is large. Your system is a simple two DOF system with two distinct natural frequencies that is excited at one of those frequencies. Your two DOF system has no relation to a TMD. TMD theory does not apply to your system.

A TMD does two things:
1) It changes a lightly damped natural frequency to two lightly damped natural frequencies, one higher and the other lower than the original natural frequency. This is useful when there is excitation only at the original natural frequency.

2) Adding a damper to the tuned mass damps vibration of the primary mass at both of the new natural frequencies. This is useful when the excitation is over a range of frequencies.

 

[gunna]

Welcome, @gunna !

Shouldn't the oscillation frequency of the TMD be tuned to be similar to the resonant frequency of the object it is mounted to (eigenfrequency of 0.31 Hz)?

I agree, usually the TMD is tuned to the eigenfrequency of the structure. But in my case I want to mitigate the response at 0.6 Hz, and a TMD should be able to reduce any frequency as long as it is tuned to that specific frequency right?

Best regards

 

[gunna]

You have a system with resonant frequency of 0.31 Hz that is excited at 0.6 Hz. The response will be small because the magnitude of the response is determined by the mass of the system and the magnitude of the excitation. Then you added a second system with a resonant frequency of 0.6 Hz. That system is driven at its resonant frequency by the 0.6 Hz excitation, so the amplitude is large. Your system is a simple two DOF system with two distinct natural frequencies that is excited at one of those frequencies. Your two DOF system has no relation to a TMD. TMD theory does not apply to your system.

A TMD does two things:
1) It changes a lightly damped natural frequency to two lightly damped natural frequencies, one higher and the other lower than the original natural frequency. This is useful when there is excitation only at the original natural frequency.

2) Adding a damper to the tuned mass damps vibration of the primary mass at both of the new natural frequencies. This is useful when the excitation is over a range of frequencies.

I can follow you by saying I just created a 2DOF system with two distinct natural frequencies that is excited at one of those frequencies. But that is what a TMD does, right? Turning a SDOF system into a 2DOF system and by doing so, reduce the SDOF system's response at it's natural frequency.
But since I am not interested at reducing the SDOF's response at it's natural frequency but rather at reducing the SDOF's response at another excitation frequency, the use of a tuned mass damper is not appropiated. Is that what both of you are trying to tell me?

Best regards