tdehaeze/digital-brain
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Update Content - 2024-12-17

Browse Source
This commit is contained in:
Thomas Dehaeze
2024-12-17 15:23:12 +01:00
parent ba5c203e48
commit f0d28899bf
6 changed files with 210 additions and 209 deletions
Download Patch File Download Diff File Expand all files Collapse all files

36
content/phdthesis/li01_simul_fault_vibrat_isolat_point.md
View File

@@ -24,13 +24,13 @@ Year
### Flexure Jointed Hexapods {#flexure-jointed-hexapods}
A general flexible jointed hexapod is shown in Figure [1](#figure--fig:li01-flexure-hexapod-model).
A general flexible jointed hexapod is shown in [1](#figure--fig:li01-flexure-hexapod-model).
<a id="figure--fig:li01-flexure-hexapod-model"></a>
{{< figure src="/ox-hugo/li01_flexure_hexapod_model.png" caption="<span class=\"figure-number\">Figure 1: </span>A flexure jointed hexapod. {P} is a cartesian coordinate frame located at, and rigidly attached to the payload's center of mass. {B} is the frame attached to the base, and {U} is a universal inertial frame of reference" >}}
Flexure jointed hexapods have been developed to meet two needs illustrated in Figure [2](#figure--fig:li01-quet-dirty-box).
Flexure jointed hexapods have been developed to meet two needs illustrated in [2](#figure--fig:li01-quet-dirty-box).
<a id="figure--fig:li01-quet-dirty-box"></a>
@@ -43,7 +43,7 @@ On the other hand, the flexures add some complexity to the hexapod dynamics.
Although the flexure joints do eliminate friction and backlash, they add spring dynamics and severely limit the workspace.
Moreover, base and/or payload vibrations become significant contributors to the motion.
The University of Wyoming hexapods (example in Figure [3](#figure--fig:li01-stewart-platform)) are:
The University of Wyoming hexapods (example in [3](#figure--fig:li01-stewart-platform)) are:
- Cubic (mutually orthogonal)
- Flexure Jointed
@@ -87,7 +87,7 @@ J = \begin{bmatrix}
\end{bmatrix}
\end{equation}
where (see Figure [1](#figure--fig:li01-flexure-hexapod-model)) \\(p\_i\\) denotes the payload attachment point of strut \\(i\\), the prescripts denote the frame of reference, and \\(\hat{u}\_i\\) denotes a unit vector along strut \\(i\\).
where (see [1](#figure--fig:li01-flexure-hexapod-model)) \\(p\_i\\) denotes the payload attachment point of strut \\(i\\), the prescripts denote the frame of reference, and \\(\hat{u}\_i\\) denotes a unit vector along strut \\(i\\).
To make the dynamic model as simple as possible, the origin of {P} is located at the payload's center of mass.
Thus all \\({}^Pp\_i\\) are found with respect to the center of mass.
@@ -140,7 +140,7 @@ Equation <eq:hexapod_eq_motion> can be rewritten as:
\end{split}
\end{equation}
If the hexapod is designed such that the payload mass/inertia matrix written in the base frame (\\(^BM\_x = {}^B\_PR \cdot {}^PM\_x \cdot {}^B\_PR\_T\\)) and \\(J^T J\\) are diagonal, the dynamics from \\(u\_1\\) to \\(y\\) are decoupled (Figure [4](#figure--fig:li01-decoupling-conf)).
If the hexapod is designed such that the payload mass/inertia matrix written in the base frame (\\(^BM\_x = {}^B\_PR \cdot {}^PM\_x \cdot {}^B\_PR\_T\\)) and \\(J^T J\\) are diagonal, the dynamics from \\(u\_1\\) to \\(y\\) are decoupled ([4](#figure--fig:li01-decoupling-conf)).
<a id="figure--fig:li01-decoupling-conf"></a>
@@ -152,7 +152,7 @@ Alternatively, a new set of inputs and outputs can be defined:
u\_2 = J^{-1} f\_m, \quad y = J^{-1} (l - l\_r)
\end{equation}
And another decoupled plant is found (Figure [5](#figure--fig:li01-decoupling-conf-bis)):
And another decoupled plant is found ([5](#figure--fig:li01-decoupling-conf-bis)):
\begin{equation} \label{eq:hexapod\_eq\_motion\_decoup\_2}
\begin{split}
@@ -200,13 +200,13 @@ The control bandwidth is divided as follows:
### Vibration Isolation {#vibration-isolation}
The system is decoupled into six independent SISO subsystems using the architecture shown in Figure [6](#figure--fig:li01-vibration-isolation-control).
The system is decoupled into six independent SISO subsystems using the architecture shown in [6](#figure--fig:li01-vibration-isolation-control).
<a id="figure--fig:li01-vibration-isolation-control"></a>
{{< figure src="/ox-hugo/li01_vibration_isolation_control.png" caption="<span class=\"figure-number\">Figure 6: </span>Vibration isolation control strategy" >}}
One of the subsystem plant transfer function is shown in Figure [6](#figure--fig:li01-vibration-isolation-control)
One of the subsystem plant transfer function is shown in [6](#figure--fig:li01-vibration-isolation-control)
<a id="figure--fig:li01-vibration-isolation-control"></a>
@@ -243,7 +243,7 @@ The reason is not explained.
### Pointing Control Techniques {#pointing-control-techniques}
A block diagram of the pointing control system is shown in Figure [8](#figure--fig:li01-pointing-control).
A block diagram of the pointing control system is shown in [8](#figure--fig:li01-pointing-control).
<a id="figure--fig:li01-pointing-control"></a>
@@ -252,7 +252,7 @@ A block diagram of the pointing control system is shown in Figure [8](#figure--f
The plant is decoupled into two independent SISO subsystems.
The decoupling matrix consists of the columns of \\(J\\) corresponding to the pointing DoFs.
Figure [9](#figure--fig:li01-transfer-function-angle) shows the measured transfer function of the \\(\theta\_x\\) axis.
[9](#figure--fig:li01-transfer-function-angle) shows the measured transfer function of the \\(\theta\_x\\) axis.
<a id="figure--fig:li01-transfer-function-angle"></a>
@@ -268,7 +268,7 @@ A typical compensator consists of the following elements:
The unity control bandwidth of the pointing loop is designed to be from **0Hz to 20Hz**.
A feedforward control is added as shown in Figure [10](#figure--fig:li01-feedforward-control).
A feedforward control is added as shown in [10](#figure--fig:li01-feedforward-control).
\\(C\_f\\) is the feedforward compensator which is a 2x2 diagonal matrix.
Ideally, the feedforward compensator is an invert of the plant dynamics.
@@ -284,7 +284,7 @@ The simultaneous vibration isolation and pointing control is approached in two w
1. **Closing the vibration isolation loop first**: Design and implement the vibration isolation control first, identify the pointing plant when the isolation loops are closed, then implement the pointing compensators.
2. **Closing the pointing loop first**: Reverse order.
Figure [11](#figure--fig:li01-parallel-control) shows a parallel control structure where \\(G\_1(s)\\) is the dynamics from input force to output strut length.
[11](#figure--fig:li01-parallel-control) shows a parallel control structure where \\(G\_1(s)\\) is the dynamics from input force to output strut length.
<a id="figure--fig:li01-parallel-control"></a>
@@ -302,16 +302,16 @@ However, the interaction between loops may affect the transfer functions of the
The dynamic interaction effect:
- Only happens in the unity bandwidth of the loop transmission of the first closed loop.
- Affect the closed loop transmission of the loop first closed (see Figures [12](#figure--fig:li01-closed-loop-pointing) and [13](#figure--fig:li01-closed-loop-vibration))
- Affect the closed loop transmission of the loop first closed (see [12](#figure--fig:li01-closed-loop-pointing) and [13](#figure--fig:li01-closed-loop-vibration))
As shown in Figure [12](#figure--fig:li01-closed-loop-pointing), the peak resonance of the pointing loop increase after the isolation loop is closed.
As shown in [12](#figure--fig:li01-closed-loop-pointing), the peak resonance of the pointing loop increase after the isolation loop is closed.
The resonances happen at both crossovers of the isolation loop (15Hz and 50Hz) and they may show of loss of robustness.
<a id="figure--fig:li01-closed-loop-pointing"></a>
{{< figure src="/ox-hugo/li01_closed_loop_pointing.png" caption="<span class=\"figure-number\">Figure 12: </span>Closed-loop transfer functions \\(\theta\_y/\theta\_{y\_d}\\) of the pointing loop before and after the vibration isolation loop is closed" >}}
The same happens when first closing the vibration isolation loop and after the pointing loop (Figure [13](#figure--fig:li01-closed-loop-vibration)).
The same happens when first closing the vibration isolation loop and after the pointing loop ([13](#figure--fig:li01-closed-loop-vibration)).
The first peak resonance of the vibration isolation loop at 15Hz is increased when closing the pointing loop.
<a id="figure--fig:li01-closed-loop-vibration"></a>
@@ -328,7 +328,7 @@ Thus, it is recommended to design and implement the isolation control system fir
### Experimental results {#experimental-results}
Two hexapods are stacked (Figure [14](#figure--fig:li01-test-bench)):
Two hexapods are stacked ([14](#figure--fig:li01-test-bench)):
- the bottom hexapod is used to generate disturbances matching candidate applications
- the top hexapod provide simultaneous vibration isolation and pointing control
@@ -338,7 +338,7 @@ Two hexapods are stacked (Figure [14](#figure--fig:li01-test-bench)):
{{< figure src="/ox-hugo/li01_test_bench.png" caption="<span class=\"figure-number\">Figure 14: </span>Stacked Hexapods" >}}
First, the vibration isolation and pointing controls were implemented separately.
Using the vibration isolation control alone, no attenuation is achieved below 1Hz as shown in figure [15](#figure--fig:li01-vibration-isolation-control-results).
Using the vibration isolation control alone, no attenuation is achieved below 1Hz as shown in [15](#figure--fig:li01-vibration-isolation-control-results).
<a id="figure--fig:li01-vibration-isolation-control-results"></a>
@@ -349,7 +349,7 @@ The simultaneous control is of dual use:
- it provide simultaneous pointing and isolation control
- it can also be used to expand the bandwidth of the isolation control to low frequencies because the pointing loops suppress pointing errors due to both base vibrations and tracking
The results of simultaneous control is shown in Figure [16](#figure--fig:li01-simultaneous-control-results) where the bandwidth of the isolation control is expanded to very low frequency.
The results of simultaneous control is shown in [16](#figure--fig:li01-simultaneous-control-results) where the bandwidth of the isolation control is expanded to very low frequency.
<a id="figure--fig:li01-simultaneous-control-results"></a>

56
content/phdthesis/verbaan15_robus.md
View File

@@ -82,17 +82,17 @@ As damping concept, a **viscous fuild damper** is chosen due to the following pr
The guild applied is Rocol Kilopoise 0868 and is chosen based on the extremely high viscosity of 220 Pas.
In order to measure the damping the measurement bench shown in Figure [1](#figure--fig:verbaan15-tmd-mech-system) is used.
The measured FRF are shown in Figure [1](#figure--fig:verbaan15-obtained-damping-bench).
In order to measure the damping the measurement bench shown in [3](#figure--fig:verbaan15-tmd-mech-system) is used.
The measured FRF are shown in [4](#figure--fig:verbaan15-obtained-damping-bench).
The measurement clearly shows that the damper mechanism is over-critically damped.
<a id="figure--fig:verbaan15-tmd-mech-system"></a>
{{< figure src="/ox-hugo/verbaan15_tmd_mech_system.png" caption="<span class=\"figure-number\">Figure 1: </span>Damper test setup to measure the damping characteristics" >}}
{{< figure src="/ox-hugo/verbaan15_tmd_mech_system.png" caption="<span class=\"figure-number\">Figure 3: </span>Damper test setup to measure the damping characteristics" >}}
<a id="figure--fig:verbaan15-obtained-damping-bench"></a>
{{< figure src="/ox-hugo/verbaan15_obtained_damping_bench.png" caption="<span class=\"figure-number\">Figure 1: </span>Obtained damping results" >}}
{{< figure src="/ox-hugo/verbaan15_obtained_damping_bench.png" caption="<span class=\"figure-number\">Figure 4: </span>Obtained damping results" >}}
## Linear viscoelastic characterisation of an ultra-high viscosity fluid {#linear-viscoelastic-characterisation-of-an-ultra-high-viscosity-fluid}
@@ -101,11 +101,11 @@ The measurement clearly shows that the damper mechanism is over-critically dampe
> This design is flexure based to minimize parasitic nonlinear forces.
> Design and the damping mechanism are elaborated and a model is presented that describes the dynamic behavior.
The damper shown in Figure [1](#figure--fig:verbaan15-damper-parts) can be used as a sliding plate rheometer to measure the linear viscoelastic properties of ultra-high viscosity fluids in the frequency range 10Hz to 10kHz.
The damper shown in [5](#figure--fig:verbaan15-damper-parts) can be used as a sliding plate rheometer to measure the linear viscoelastic properties of ultra-high viscosity fluids in the frequency range 10Hz to 10kHz.
<a id="figure--fig:verbaan15-damper-parts"></a>
{{< figure src="/ox-hugo/verbaan15_damper_parts.png" caption="<span class=\"figure-number\">Figure 1: </span>Damper parts" >}}
{{< figure src="/ox-hugo/verbaan15_damper_parts.png" caption="<span class=\"figure-number\">Figure 5: </span>Damper parts" >}}
The full damper assembly consists of a mass, mounted on two springs and a damper in parallel configuration.
The mass can make small strokes in the x-direction and is fixed in all other directions.
@@ -114,17 +114,17 @@ The space between the lead springs is used to accommodate for the damping mechan
<a id="figure--fig:verbaan15-tmd-slot-fin-parts"></a>
{{< figure src="/ox-hugo/verbaan15_tmd_slot_fin_parts.png" caption="<span class=\"figure-number\">Figure 1: </span>Exploded view of the damper parts" >}}
{{< figure src="/ox-hugo/verbaan15_tmd_slot_fin_parts.png" caption="<span class=\"figure-number\">Figure 6: </span>Exploded view of the damper parts" >}}
A high-viscosity fluid is applied to create a velocity dependent force.
For this purpose, the sliding plate principle is used which induces a **shear flow**: the fluid is placed between two slot plates and a fin is positioned between these two plates (Figure [1](#figure--fig:verbaan15single-double-fin)).
For this purpose, the sliding plate principle is used which induces a **shear flow**: the fluid is placed between two slot plates and a fin is positioned between these two plates ([7](#figure--fig:verbaan15single-double-fin)).
A **flexible encapsulation** is used to hold the fluid between find and slot part.
To study different damping values with the same fluid, two damper designs with different geometries are used (see Figure [1](#figure--fig:verbaan15single-double-fin)).
To study different damping values with the same fluid, two damper designs with different geometries are used (see [7](#figure--fig:verbaan15single-double-fin)).
<a id="figure--fig:verbaan15single-double-fin"></a>
{{< figure src="/ox-hugo/verbaan15single_double_fin.png" caption="<span class=\"figure-number\">Figure 1: </span>Cross-sectional views of the two different damping mechanims. The single fin (left) and double fin (right)." >}}
{{< figure src="/ox-hugo/verbaan15single_double_fin.png" caption="<span class=\"figure-number\">Figure 7: </span>Cross-sectional views of the two different damping mechanims. The single fin (left) and double fin (right)." >}}
To excite the damper mass, a voice coil is mounted to the hardware.
The damper position is measured with a laser vibrometer.
@@ -151,7 +151,7 @@ t\_c = \frac{10 \rho h^2}{\eta}
\end{equation}
in which \\(\rho\\) describes the fluid density in \\(kg/m^3\\), \\(\eta\\) the dynamic viscosity in \\(Pa s\\) and \\(h\\) the gap width in \\(m\\).
Dimensions are provided in Table [1](#table--tab:single-fin-parameters).
Dimensions are provided in [1](#table--tab:single-fin-parameters).
This estimate results in a frequency above 100kHz.
It shows that high fluid viscosities and small gap widths enable high frequencies without losing homogeneous flow conditions.
@@ -182,12 +182,12 @@ A three mode Maxwell model can accurately describe the behavior.
This chapter presents the results of a robust mass damper implementation on a complex motion stage with realistic natural frequencies to increase the modal damping of flexible modes.
A design approach is presented which results in parameter values for the dampers to improve the modal damping over a specified frequency range.
Figure [1](#figure--fig:verbaan15-stage-undamped) shows a collocated FRF of the stage's corner.
[8](#figure--fig:verbaan15-stage-undamped) shows a collocated FRF of the stage's corner.
The goal is to increase the modal damping of modes 7, 9, 10/11 and 13.
<a id="figure--fig:verbaan15-stage-undamped"></a>
{{< figure src="/ox-hugo/verbaan15_stage_undamped.png" caption="<span class=\"figure-number\">Figure 1: </span>FRF at the stage corner in the z-direction, undamped" >}}
{{< figure src="/ox-hugo/verbaan15_stage_undamped.png" caption="<span class=\"figure-number\">Figure 8: </span>FRF at the stage corner in the z-direction, undamped" >}}
The transfer function \\(T\_i(s)\\) is defined as the contribution of the a single mode \\(i\\) in an input/output transfer function:
@@ -215,13 +215,13 @@ It is known from literature that the efficiency of a TMD depends on the **mass r
It follows that the efficiency of a TMD to damp a certain resonance depends on the position of the damper on the stage in a quadratic sense.
The TMD has to be located at the maximum displacement of the mode(s) to be damped.
The damper configuration consists of an inertial mass \\(m\\), a transnational flexible guide designed as a double leaf spring mechanism with total stiffness \\(c\\) and a part that creates the damping force with damping constant \\(d\\) (model shown in Figure [1](#figure--fig:verbaan15-maxwell-fluid-model)).
The damper configuration consists of an inertial mass \\(m\\), a transnational flexible guide designed as a double leaf spring mechanism with total stiffness \\(c\\) and a part that creates the damping force with damping constant \\(d\\) (model shown in [9](#figure--fig:verbaan15-maxwell-fluid-model)).
The velocity dependent damper force is the result of two parameters:
- the fluid's mechanical properties
- the damper geometry
The fluid model is presented in Figure [1](#figure--fig:verbaan15-fluid-lve-model).
The fluid model is presented in [10](#figure--fig:verbaan15-fluid-lve-model).
This figure shows the viscous and elastic properties of the fluid as a function of the frequency.
The damper principle is chosen to be a parallel plate damper based on the shear principle with the viscous fluid in between the two parallel plates.
In case of a velocity difference between these plates, a velocity gradient is created in the fluid causing a specific force per unit of area, which, multiplied by the effective area submerged in the fluid, leads to a damping force.
@@ -241,11 +241,11 @@ In the example, the modal mass is 3.5kg and the damper mass is 110g (useful iner
<a id="figure--fig:verbaan15-maxwell-fluid-model"></a>
{{< figure src="/ox-hugo/verbaan15_maxwell_fluid_model.png" caption="<span class=\"figure-number\">Figure 1: </span>Damper model with multi-mode Maxwell fluid model included" >}}
{{< figure src="/ox-hugo/verbaan15_maxwell_fluid_model.png" caption="<span class=\"figure-number\">Figure 9: </span>Damper model with multi-mode Maxwell fluid model included" >}}
<a id="figure--fig:verbaan15-fluid-lve-model"></a>
{{< figure src="/ox-hugo/verbaan15_fluid_lve_model.png" caption="<span class=\"figure-number\">Figure 1: </span>Storage and loss modulus of the 3 Maxwell mode LVE fluid model" >}}
{{< figure src="/ox-hugo/verbaan15_fluid_lve_model.png" caption="<span class=\"figure-number\">Figure 10: </span>Storage and loss modulus of the 3 Maxwell mode LVE fluid model" >}}
### TMD and RMD optimisation {#tmd-and-rmd-optimisation}
@@ -258,26 +258,26 @@ An algorithm is used to optimize the damping and is used in two cases:
This results in a **robust mass damper** optimal design
The algorithm is first used to calculate the optimal parameters to suppress a **single** resonance frequency.
The result is shown in Figure [1](#figure--fig:verbaan15-tmd-optimization) and shows **Tuned Mass Damper** behavior.
The result is shown in [11](#figure--fig:verbaan15-tmd-optimization) and shows **Tuned Mass Damper** behavior.
For this single frequency, stiffness and damping values can be calculated by hand.
<a id="figure--fig:verbaan15-tmd-optimization"></a>
{{< figure src="/ox-hugo/verbaan15_tmd_optimization.png" caption="<span class=\"figure-number\">Figure 1: </span>Result of the optimization procedure. The cost function is specified between 1kHz and 2kHz. This implies that the first mode is suppressed by the damper." >}}
{{< figure src="/ox-hugo/verbaan15_tmd_optimization.png" caption="<span class=\"figure-number\">Figure 11: </span>Result of the optimization procedure. The cost function is specified between 1kHz and 2kHz. This implies that the first mode is suppressed by the damper." >}}
To obtain broad banded damping, the cost function is redefined between 1 and 4kHz.
Figure [1](#figure--fig:verbaan15-broadbanded-damping-results) presents the resulting bode diagram.
[12](#figure--fig:verbaan15-broadbanded-damping-results) presents the resulting bode diagram.
<a id="figure--fig:verbaan15-broadbanded-damping-results"></a>
{{< figure src="/ox-hugo/verbaan15_broadbanded_damping_results.png" caption="<span class=\"figure-number\">Figure 1: </span>Result of the optimization procedure with the cost function specified between 1 and 4kHz. The result is a range of resonances that are suppressed by the dampers." >}}
{{< figure src="/ox-hugo/verbaan15_broadbanded_damping_results.png" caption="<span class=\"figure-number\">Figure 12: </span>Result of the optimization procedure with the cost function specified between 1 and 4kHz. The result is a range of resonances that are suppressed by the dampers." >}}
Results of optimizations for increasing damper mass, in the range from 10 to 250g per damper are shown in Figure [1](#figure--fig:verbaan15-results-fct-mass).
Results of optimizations for increasing damper mass, in the range from 10 to 250g per damper are shown in [13](#figure--fig:verbaan15-results-fct-mass).
<a id="figure--fig:verbaan15-results-fct-mass"></a>
{{< figure src="/ox-hugo/verbaan15_results_fct_mass.png" caption="<span class=\"figure-number\">Figure 1: </span>Optimal damper parameters as a function of the damper mass. The upper graph shows the suppression factor in dB, the second graph shows the natural frequency of the damper in Hz and the lower graph shows the geometrical damping factor in m." >}}
{{< figure src="/ox-hugo/verbaan15_results_fct_mass.png" caption="<span class=\"figure-number\">Figure 13: </span>Optimal damper parameters as a function of the damper mass. The upper graph shows the suppression factor in dB, the second graph shows the natural frequency of the damper in Hz and the lower graph shows the geometrical damping factor in m." >}}
### Damper Design and Validation {#damper-design-and-validation}
@@ -291,7 +291,7 @@ A damper mechanism is design which contains the following properties:
- a geometrical damping factor of 14.3m
- an encapsulation to contain the fluid
Figure [1](#figure--fig:verbaan15-RMD-mechanical-parts) shows an exploded view of the RMD design.
[14](#figure--fig:verbaan15-RMD-mechanical-parts) shows an exploded view of the RMD design.
The mechanism part is monolithically designed and consists of:
1. a mounting side
@@ -302,15 +302,15 @@ The fluid is surrounded by a flexible encapsulation, which prevents it from runn
<a id="figure--fig:verbaan15-RMD-mechanical-parts"></a>
{{< figure src="/ox-hugo/verbaan15_RMD_mechanical_parts.png" caption="<span class=\"figure-number\">Figure 1: </span>Exploded view of the robust mass damper design with different parts indicated" >}}
{{< figure src="/ox-hugo/verbaan15_RMD_mechanical_parts.png" caption="<span class=\"figure-number\">Figure 14: </span>Exploded view of the robust mass damper design with different parts indicated" >}}
<a id="figure--fig:verbaan15-RMD-design-modes"></a>
{{< figure src="/ox-hugo/verbaan15_RMD_design_modes.png" caption="<span class=\"figure-number\">Figure 1: </span>Four lowest natural frequencies and corresponding mode shapes of the RMD while mounted to a stage corner" >}}
{{< figure src="/ox-hugo/verbaan15_RMD_design_modes.png" caption="<span class=\"figure-number\">Figure 15: </span>Four lowest natural frequencies and corresponding mode shapes of the RMD while mounted to a stage corner" >}}
<a id="figure--fig:verbaan15-tmd-side-front-views"></a>
{{< figure src="/ox-hugo/verbaan15_tmd_side_front_views.png" caption="<span class=\"figure-number\">Figure 1: </span>A side view and a front view of the fin and slot parts" >}}
{{< figure src="/ox-hugo/verbaan15_tmd_side_front_views.png" caption="<span class=\"figure-number\">Figure 16: </span>A side view and a front view of the fin and slot parts" >}}
| Dimension | Value | Unit |
|-------------|-------|------|
@@ -321,7 +321,7 @@ The fluid is surrounded by a flexible encapsulation, which prevents it from runn
<a id="figure--fig:verbaan15-damped-undamped-frf"></a>
{{< figure src="/ox-hugo/verbaan15_damped_undamped_frf.png" caption="<span class=\"figure-number\">Figure 1: </span>Measured undamped and damped FRF" >}}
{{< figure src="/ox-hugo/verbaan15_damped_undamped_frf.png" caption="<span class=\"figure-number\">Figure 17: </span>Measured undamped and damped FRF" >}}
### Conclusion {#conclusion}