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

Reference

[1]	(1, 2) Antoine Falaize and Thomas Helie. Passive simulation of the nonlinear port-hamiltonian modeling of a rhodes piano. Journal of Sound and Vibration, 2016.