**impedance#
Description#
The impedance boundary condition can be useful, for example, for modeling the presence behind an interface of a material having different wave propagation properties. It can be used to tune the part of reflection and transmission of an incident wave on an interface. The characteristic impedance \(Z\) of a medium is a material property defined as :
where \(\rho\) is the density of the medium and \(c\) is the longitudinal wave speed.
The impedance bc is a Robin condition that links the stress on the boundary with the velocity :
Where \(\vect{n}\) is the unitary outward normal vector to the boundary \(\Gamma_i\). \(\ten{\sigma}\) and \(\vect{v}\) are the stress tensor and the velocity respectively. Numerically, impedance is handled through additional terms in the damping matrix (see calcul dynamic ).
A classical situation where an impedance bc is needed is the hopkinson experiment. An input bar impacts a sample from a side, a wave is generated and propagates though the sample in contact with an output bar on the other side. To simulate the sample/output bar interface without meshing the output bar, an impedance bc can be used with \(Z\) equal to the output bar characteristic impedance.
Here are two special cases to illustrate the role of the impedance in the reflection/transmission behavior of a wave at the interface between two media. Lets take two media having impedances \(Z_1\) and \(Z_2\) respectively and lets consider a wave coming from material 1:
if \(Z_2/Z_1=0\) (medium 2 is void for instance), the wave is totally reflected
if \(Z_2/Z_1=1\), the wave is totally transmitted to medium 2
Syntax#
**impedance bset value
Where bset is the name of the bset where the impedance bc is applied and value is the impedance factor.
Example#
***bc
**impedance
interface 40.e6
An example can be found in $Z7PATH/TESTS/Dynamic_test/INP/impedance.inp.