.. _acoustics-vibro_acoustic3d: acoustics/vibro_acoustic3d.py ============================= **Description** Vibro-acoustic problem 3D acoustic domain with 2D perforated deforming interface. *Master problem*: defined in 3D acoustic domain (vibro_acoustic3d.py) *Slave subproblem*: 2D perforated interface (vibro_acoustic3d_mid.py) Master 3D problem - find :math:p (acoustic pressure) and :math:g (transversal acoustic velocity) such that: .. math:: c^2 \int_{\Omega} \nabla q \cdot \nabla p - \omega^2 \int_{\Omega} q p + i \omega c \int_{\Gamma_{in}} q p + i \omega c \int_{\Gamma_{out}} q p - i \omega c^2 \int_{\Gamma_0} (q^+ - q^-) g = 2i \omega c \int_{\Gamma_{in}} q \bar{p} \;, \quad \forall q \;, - i \omega \int_{\Gamma_0} f (p^+ - p^-) - \omega^2 \int_{\Gamma_0} F f g + \omega^2 \int_{\Gamma_0} C f w = 0 \;, \quad \forall f \;, Slave 2D subproblem - find :math:w (plate deflection) and :math:\ul{\theta} (rotation) such that: .. math:: \omega^2 \int_{\Gamma_0} C z g - \omega^2 \int_{\Gamma_0} S z w + \int_{\Gamma_0} \nabla z \cdot \ull{G} \cdot \nabla w - \int_{\Gamma_0} \ul{\theta} \cdot \ull{G} \cdot \nabla z = 0 \;, \quad \forall z \;, - \omega^2 \int_{\Gamma_0} R\, \ul{\nu} \cdot \ul{\theta} + \int_{\Gamma_0} D_{ijkl} e_{ij}(\ul{\nu}) e_{kl}(\ul{\theta}) - \int_{\Gamma_0} \ul{\nu} \cdot \ull{G} \cdot \nabla w + \int_{\Gamma_0} \ul{\nu} \cdot \ull{G} \cdot \ul{\theta} = 0 \;, \quad \forall \ul{\nu} \;, .. image:: /../gallery/images/acoustics-vibro_acoustic3d_g0.png .. image:: /../gallery/images/acoustics-vibro_acoustic3d_p1.png .. image:: /../gallery/images/acoustics-vibro_acoustic3d_p2.png .. image:: /../gallery/images/acoustics-vibro_acoustic3d_w.png :download:source code  .. literalinclude:: /../examples/acoustics/vibro_acoustic3d.py