Time-Dependent resonance frequency study, thermal stress study of a nanostring resonator -- no eigenpair solution

Hello,

I am interested in determining the effect of a time-dependent thermal distribution on the resonance frequency of a nanostring.

My geometry is a nanostring (thus, ill-conditioned) with an initial gaussian temperature distribution.

I've used the thermal stress physics, which includes Solid Mechanics and Heat Transfer in Solids with and added all multiphysics. Also, I have included Initial Stress and Strain as well as thermal expansion. So far, I have been able to obtain individually 1. a stationary solution and determined eigenmodes of mechanical motion from a pre-stressed analysis study 2. a time dependent solution of heat dissipation in the unmoving string (matches well the analytical solution)

I would like to combine these studies to determine how the resonance frequency shifts over time as heat dissipates from the center of the string to the edges. So, I am using the Time-Dependent Modal study with Direct solvers.

My problem is that every time I try to perform this study, I see "No eigenpair solution detected."

So, I've tried coupling solutions from the stationary study to the Eigenfrequency step of the Time-Dependent Modal study as initial conditions and as solutions. This did not work, telling me something about the solver not being able to work with thermal vectors. I have also played around with Fully Coupled and Segregated Step features. I have also tried including Thermoelasticity physics to no avail. I even tried "plucking" the string as an initial condition.

Would one of these issues be the case: a. my study choice is incorrect (my gut says I need to find resonance frequencies, not eigenfrequencies) b. better meshing is needed c. my solution coupling is incorrect (do I need segregation?) d. my heat dissipates too quickly (on the order of the period of oscillation) e. I need to iterate with Livelink in Matlab, i.e. to take solutions of heat dissipation at every time step and feed it into the stationary study?

Thanks a million for your help, and I'd appreciate any advice on what would be the next step in determining the solutions?