PrescribeInitialEquilibrium IconPrescribeInitialEquilibrium
Sets the initial velocity and acceleration of a connected flange to zero.
This component is used to define an initial equilibrium state for a mechanical system connected via its flange. It ensures that at the beginning of the simulation, the velocity v and acceleration a of the connected element are both zero. This is achieved through the equations:
\[\begin{align*} v(0) &= 0\\ a(0) &= 0 \end{align*}\]
Additionally, the component ensures that the force flange.f at the connection point is zero. The velocity and acceleration are locally defined as derivatives of the flange's position s:
\[v = \frac{d(\text{flange.s})}{dt}\]
\[a = \frac{dv}{dt}\]
This effectively means that the connected mechanical component starts from a standstill with no initial forces applied through this specific constraint.
Usage
TranslationalComponents.PrescribeInitialEquilibrium()
Connectors
flange- This connector represents a mechanical flange with position and force as the potential and flow variables, respectively. (Flange)
Variables
| Name | Description | Units |
|---|---|---|
v | Velocity associated with the flange's motion. | m/s |
a | Acceleration associated with the flange's motion. | m/s2 |
Behavior
\[ \begin{align} \mathtt{flange.f}\left( t \right) &= 0 \\ v\left( t \right) &= \frac{\mathrm{d} \mathtt{flange.s}\left( t \right)}{\mathrm{d}t} \\ a\left( t \right) &= \frac{\mathrm{d} v\left( t \right)}{\mathrm{d}t} \end{align} \]
Source
"""
Sets the initial velocity and acceleration of a connected flange to zero.
This component is used to define an initial equilibrium state for a mechanical
system connected via its `flange`. It ensures that at the beginning of the
simulation, the velocity `v` and acceleration `a` of the connected element
are both zero. This is achieved through the equations:math \begin{align} v(0) &= 0\
a(0) &= 0 \end{align}
Additionally, the component ensures that the force `flange.f` at the connection
point is zero. The velocity and acceleration are locally defined as derivatives
of the flange's position `s`:
math v = \frac{d(\text{flange.s})}{dt}
math a = \frac{dv}{dt}
This effectively means that the connected mechanical component starts from a
standstill with no initial forces applied through this specific constraint.
"""</span>
<span class="hljs-keyword">component</span> PrescribeInitialEquilibrium
<span class="hljs-comment">"Mechanical connection point (flange)."</span>
<span class="hljs-symbol">flange</span> = <span class="hljs-link"><a href="https://help.juliahub.com/dyad/dev/stdlib/Dyad/connectors/Flange.html">Flange</a></span>() {"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}
<span class="hljs-comment">"Velocity associated with the flange's motion."</span>
<span class="hljs-keyword">variable</span> <span class="hljs-symbol">v</span>::<span class="hljs-link"><a href="https://help.juliahub.com/dyad/dev/stdlib/Dyad/types/Velocity.html">Velocity</a></span>
<span class="hljs-comment">"Acceleration associated with the flange's motion."</span>
<span class="hljs-keyword">variable</span> <span class="hljs-symbol">a</span>::<span class="hljs-link"><a href="https://help.juliahub.com/dyad/dev/stdlib/Dyad/types/Acceleration.html">Acceleration</a></span>
<span class="hljs-keyword">relations</span>
<span class="hljs-keyword">initial</span> v = 0
<span class="hljs-keyword">initial</span> a = 0
flange.f = 0
v = der(flange.s)
a = der(v)
<span class="hljs-keyword">metadata</span> {
"Dyad": {
"labels": [
{"label": "initial v = 0", "x": 500, "y": 150, "rot": 0},
{"label": "initial a = 0", "x": 500, "y": 800, "rot": 0}
],
"icons": {"default": "dyad://TranslationalComponents/Position.svg"}
}
}
<span class="hljs-keyword">end</span></code></pre>
Flattened Source
"""
Sets the initial velocity and acceleration of a connected flange to zero.
This component is used to define an initial equilibrium state for a mechanical
system connected via its `flange`. It ensures that at the beginning of the
simulation, the velocity `v` and acceleration `a` of the connected element
are both zero. This is achieved through the equations:math \begin{align} v(0) &= 0\
a(0) &= 0 \end{align}
Additionally, the component ensures that the force `flange.f` at the connection
point is zero. The velocity and acceleration are locally defined as derivatives
of the flange's position `s`:
math v = \frac{d(\text{flange.s})}{dt}
math a = \frac{dv}{dt}
This effectively means that the connected mechanical component starts from a
standstill with no initial forces applied through this specific constraint.
"""</span>
<span class="hljs-keyword">component</span> PrescribeInitialEquilibrium
<span class="hljs-comment">"Mechanical connection point (flange)."</span>
<span class="hljs-symbol">flange</span> = <span>Flange</span>() {"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}
<span class="hljs-comment">"Velocity associated with the flange's motion."</span>
<span class="hljs-keyword">variable</span> <span class="hljs-symbol">v</span>::<span>Velocity</span>
<span class="hljs-comment">"Acceleration associated with the flange's motion."</span>
<span class="hljs-keyword">variable</span> <span class="hljs-symbol">a</span>::<span>Acceleration</span>
<span class="hljs-keyword">relations</span>
<span class="hljs-keyword">initial</span> v = 0
<span class="hljs-keyword">initial</span> a = 0
flange.f = 0
v = der(flange.s)
a = der(v)
<span class="hljs-keyword">metadata</span> {
"Dyad": {
"labels": [
{"label": "initial v = 0", "x": 500, "y": 150, "rot": 0},
{"label": "initial a = 0", "x": 500, "y": 800, "rot": 0}
],
"icons": {"default": "dyad://TranslationalComponents/Position.svg"}
}
}
<span class="hljs-keyword">end</span></code></pre>
Test Cases
No test cases defined.
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