Design of Ultrasonic Transducer - Numerical Singularity and Negative Eigen Value Warnings

[Throwawaynerd]

Hi all,

I am designing ultrasonic transducer in Abaqus. I have performed modal analysis on the model and now I am performing harmonic analysis. During modal analysis I got several warnings of Numerical Singularity at different nodes of the bolt but in the subsequent iterations those warnings disappeared but the warning message of one node appeared till the end of simulation. The warning message reads as: "Solver problem. Numerical singularity when processing node BOLT-1.48 D.O.F. 1 ratio = 135.419E+09."

Then I performed Harmonic Analysis (steady state dynamic, direct) on the same model, I am getting warning messages of Negative Eigen Value like this: "The system matrix has 25 negative eigenvalues."

1- Can anyone suggest me where am I making mistake(s)?
2- Should I worry about the results and their reliability?

Thanks in anticipation.

 

[FEA way]

What are the boundary conditions ? The model can be underconstrained. It should be visible in the initial mode shapes in the eigenfrequency extraction step.

 

[Throwawaynerd]

I have electrical potential for the PZT material and Tie constraint between the bolt and front mass of the transducer.

 

[FEA way]

I was talking about mechanical (displacement) boundary conditions. Are there none in your model ?

 

[Throwawaynerd]

There is no mechanical displacement besides the excitation of PZT stacks that is generating mechanical vibration.
When I play with the mesh, this numerical singularity is appeared at some other location. Like in my previous model of the same design but with different mesh has a numerical singularity at electrode. Now, I am not sure if that is because of design or it is something numerical.

 

[FEA way]

Then the negative eigenvalue messages can be normal but you should check the results carefully anyway.

 

[Throwawaynerd]

FEA Way, thank you for your time and input.