Felt material (Felt)
Nonlinear felt material used in piano-hammer. The model is that found in [1] eq. (11). It includes a nonlinear restoring force and a nonlinear damper as follows:
\begin{equation*}
e_{total}\left(c, \dot c\right) = e_{elastic}(c) + e_{damper}\left(c, \dot c\right),
\end{equation*}
with
\begin{equation*}
e_{elastic}(c) = F \,c ^B,
\end{equation*}
and
\begin{equation*}
e_{damper}\left(c, \dot c\right) = \frac{A \, L}{B} c^{B-1} \,\dot c,
\end{equation*}
where \(c = \frac{\max (q, 0)}{L}\) is the crush of the hammer with contraction \(q\in\mathbb R\).
Felt material (Felt)
Nonlinear felt material used in piano-hammer. The model is that found in [1] eq. (11). It includes a nonlinear restoring force and a nonlinear damper as follows:
\begin{equation*}
e_{total}\left(c, \dot c\right) = e_{elastic}(c) + e_{damper}\left(c, \dot c\right),
\end{equation*}
with
\begin{equation*}
e_{elastic}(c) = F \,c ^B,
\end{equation*}
and
\begin{equation*}
e_{damper}\left(c, \dot c\right) = \frac{A \, L}{B} c^{B-1} \,\dot c,
\end{equation*}
where \(c = \frac{\max (q, 0)}{L}\) is the crush of the hammer with contraction \(q\in\mathbb R\).
Power variables
flux: Velocity \(v\) (m/s)
effort: Force \(f\) (N)
Arguments
- label : str
- Felt label.
- nodes : ('N1', 'N2')
- Nodes associated with the component terminals with positive flux N1->N2.
- parameters : keyword arguments
- Component parameters.
| Key | Description | Unit | Default |
|---|---|---|---|
| L | Height at rest | m | 0.01 |
| F | Elastic characteristic force | N | 10.0 |
| A | Damping coefficient | N.s/m | 100.0 |
| B | Hysteresis coefficient | d.u. | 2.5 |
Usage
felt = Felt('felt', ('N1', 'N2'), L=0.01, F=10.0, A=100.0, B=2.5)
Netlist line
mechanics_dual.felt felt ('N1', 'N2'): L=0.01; F=10.0; A=100.0; B=2.5;
Example
>>> # Import dictionary
>>> from pyphs.dictionary import mechanics_dual
>>> # Define component label
>>> label = 'felt'
>>> # Define component nodes
>>> nodes = ('N1', 'N2')
>>> # Define component parameters
>>> parameters = {'L': 0.01, # Height at rest (m)
... 'F': 10.0, # Elastic characteristic force (N)
... 'A': 100.0, # Damping coefficient (N.s/m)
... 'B': 2.5, # Hysteresis coefficient (d.u.)
... }
>>> # Instanciate component
>>> component = mechanics_dual.Felt(label, nodes, **parameters)
>>> # Graph dimensions
>>> len(component.nodes)
3
>>> len(component.edges)
2