Hello,
I am interested in using SfePy for analyzing the resonance modes of a piezoelectric element. I've run an eigenmode analysis according to the given linear elastic example on my mesh with the stiffness matrix applied, and the results seem to agree with measured data, but I'm not certain how to extend this analysis to the multiphysics problem. I've tried driving the element with a periodic boundary condition, but I couldn't see any variation in the response vs. frequency--at least when looking at the maximum stress/strain at each frequency.
Here are the equations--a slight modification of the given multiphysics example:
equations = { '1' : """dw_volume_dot.i.volume(resonator.density, vv, dv/dt) + dw_lin_elastic.i.volume(resonator.D, w, u) - dw_piezo_coupling.i.volume(resonator.coupling, w, phi) = 0""", '2' : """dw_piezo_coupling.i.volume(resonator.coupling, u, psi) + dw_diffusion.i.volume(resonator.dielectric, psi, phi) = 0""", '3' : """dw_volume_dot.i.volume(resonator.density, w, du/dt) = dw_volume_dot.i.volume(resonator.density, vv, v)""" }
I thought that perhaps the problem was the lack of a second order time derivative term, which is the reason for the third equation, but adding it didn't seem to help.
I've noticed that the linear elastic terms don't seem to oscillate when stretched and released, perhaps this is at the root of the problem? or perhaps I'm mistaken in what I expect to see...
Any help regarding piezoelectric modelling or harmonic oscillation would be appreciated.
Thanks!
Nolan