Hi, I have been using comsol to study topics related to piezoelectric materials. I'm modelling a beam with a piezo attached on the top, and an electrical circuit attached to the patch: to do so I used the solid mechanics (solid), electrostatic (es) and circuit (cir) modules. I want to perform the eigenvalue analysis (I want to extract the dispersion using my model as a periodic cell...) it doesn't work and it says that one equation is missing ("Singular matrix. - Detail: There are 1 void equations (empty rows in matrix) for the variable comp1.es.term1.Q0_ode. at coordinates: (0,0), ... "). The implementation is ok for time domain study. Do you have any ideas?
The piezo-shunt is implemented as follows: the bottom face of the piezoelectric patch (attached to the beam) is grounded (es.ground), the upper one is connected to a circuit terminal (es.terminal 1 - type circuit), then a resistor and a inductor (in cir) is connected in series from node 0 (ground) to node 1 which is in turn connected to the terminal (in es) through a "External I - Terminal" connection (selecting terminal 1 for the electric potential).
Please see the attached file for details.
Thanks, Yongchen