initial v = 0initial a = 0PrescribeInitialEquilibrium Icon

PrescribeInitialEquilibrium

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

NameDescriptionUnits
vVelocity associated with the flange's motion.m/s
aAcceleration 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
&nbsp;&nbsp;<span class="hljs-comment">"Mechanical connection point (flange)."</span>
&nbsp;&nbsp;<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}}}}
&nbsp;&nbsp;<span class="hljs-comment">"Velocity associated with the flange's motion."</span>
&nbsp;&nbsp;<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>
&nbsp;&nbsp;<span class="hljs-comment">"Acceleration associated with the flange's motion."</span>
&nbsp;&nbsp;<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>
&nbsp;&nbsp;<span class="hljs-keyword">initial</span> v = 0
&nbsp;&nbsp;<span class="hljs-keyword">initial</span> a = 0
&nbsp;&nbsp;flange.f = 0
&nbsp;&nbsp;v = der(flange.s)
&nbsp;&nbsp;a = der(v)
<span class="hljs-keyword">metadata</span> {
&nbsp;&nbsp;"Dyad": {
&nbsp;&nbsp;&nbsp;&nbsp;"labels": [
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{"label": "initial v = 0", "x": 500, "y": 150, "rot": 0},
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{"label": "initial a = 0", "x": 500, "y": 800, "rot": 0}
&nbsp;&nbsp;&nbsp;&nbsp;],
&nbsp;&nbsp;&nbsp;&nbsp;"icons": {"default": "dyad://TranslationalComponents/Position.svg"}
&nbsp;&nbsp;}
}
<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
&nbsp;&nbsp;<span class="hljs-comment">"Mechanical connection point (flange)."</span>
&nbsp;&nbsp;<span class="hljs-symbol">flange</span> = <span>Flange</span>() {"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}
&nbsp;&nbsp;<span class="hljs-comment">"Velocity associated with the flange's motion."</span>
&nbsp;&nbsp;<span class="hljs-keyword">variable</span> <span class="hljs-symbol">v</span>::<span>Velocity</span>
&nbsp;&nbsp;<span class="hljs-comment">"Acceleration associated with the flange's motion."</span>
&nbsp;&nbsp;<span class="hljs-keyword">variable</span> <span class="hljs-symbol">a</span>::<span>Acceleration</span>
<span class="hljs-keyword">relations</span>
&nbsp;&nbsp;<span class="hljs-keyword">initial</span> v = 0
&nbsp;&nbsp;<span class="hljs-keyword">initial</span> a = 0
&nbsp;&nbsp;flange.f = 0
&nbsp;&nbsp;v = der(flange.s)
&nbsp;&nbsp;a = der(v)
<span class="hljs-keyword">metadata</span> {
&nbsp;&nbsp;"Dyad": {
&nbsp;&nbsp;&nbsp;&nbsp;"labels": [
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{"label": "initial v = 0", "x": 500, "y": 150, "rot": 0},
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{"label": "initial a = 0", "x": 500, "y": 800, "rot": 0}
&nbsp;&nbsp;&nbsp;&nbsp;],
&nbsp;&nbsp;&nbsp;&nbsp;"icons": {"default": "dyad://TranslationalComponents/Position.svg"}
&nbsp;&nbsp;}
}
<span class="hljs-keyword">end</span></code></pre>


Test Cases

No test cases defined.

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