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Thomas Dehaeze
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content/zettels/tuned_mass_damper.md
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@@ -19,6 +19,17 @@ The TMD then has large internal damping such that the energy is dissipated (i.e.
{{< youtube qDzGCgLu59A >}}
## How to properly apply a TMD? {#how-to-properly-apply-a-tmd}
Few questions:
- What damping mechanism to use?
Eddy current damping?
Viscous damping?
- How to optimize parameters of the TMD (i.e. mass, stiffness and damping)?
- Where to fix the TMD to the structure?
## Tuned Mass Damper Optimization {#tuned-mass-damper-optimization}
The optimal parameters of the tuned mass damper can be roughly estimated as follows:
@@ -100,18 +111,18 @@ The following mass ratios are tested:
mus = [0.01, 0.02, 0.05, 0.1];
```
The obtained transfer functions are shown in Figure [3](#figure--fig:tuned-mass-damper-mass-effect).
The obtained transfer functions are shown in Figure [1](#figure--fig:tuned-mass-damper-mass-effect).
<a id="figure--fig:tuned-mass-damper-mass-effect"></a>
{{< figure src="/ox-hugo/tuned_mass_damper_mass_effect.png" caption="<span class=\"figure-number\">Figure 3: </span>Effect of the TMD mass on its efficiency" >}}
{{< figure src="/ox-hugo/tuned_mass_damper_mass_effect.png" caption="<span class=\"figure-number\">Figure 1: </span>Effect of the TMD mass on its efficiency" >}}
The maximum amplification (i.e. \\(\mathcal{H}\_\infty\\) norm) of the transmissibility as a function of the mass ratio is shown in Figure [4](#figure--fig:tuned-mass-damper-effect-mass-ratio).
The maximum amplification (i.e. \\(\mathcal{H}\_\infty\\) norm) of the transmissibility as a function of the mass ratio is shown in Figure [1](#figure--fig:tuned-mass-damper-effect-mass-ratio).
This relation can help to determine the minimum mass of the TMD that will give acceptable results.
<a id="figure--fig:tuned-mass-damper-effect-mass-ratio"></a>
{{< figure src="/ox-hugo/tuned_mass_damper_effect_mass_ratio.png" caption="<span class=\"figure-number\">Figure 4: </span>Maximum amplification due to resonance as a function of the mass ratio" >}}
{{< figure src="/ox-hugo/tuned_mass_damper_effect_mass_ratio.png" caption="<span class=\"figure-number\">Figure 1: </span>Maximum amplification due to resonance as a function of the mass ratio" >}}
## Manufacturers {#manufacturers}
@@ -126,7 +137,11 @@ This relation can help to determine the minimum mass of the TMD that will give a
Possible damping sources:
- Magnetic (eddy current)
- Viscous
- Viscous fluid
| Fuild | Reference |
|----------------------|---------------------------------------------------|
| Rocol Kilopoise 0868 | (<a href="#citeproc_bib_item_2">Verbaan 2015</a>) |
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
<div class="csl-entry"><a id="citeproc_bib_item_1"></a>Elias, Said, and Vasant Matsagar. 2017. “Research Developments in Vibration Control of Structures Using Passive Tuned Mass Dampers.” <i>Annual Reviews in Control</i> 44 (nil): 129–56. doi:<a href="https://doi.org/10.1016/j.arcontrol.2017.09.015">10.1016/j.arcontrol.2017.09.015</a>.</div>