The problem is probably related to the choice of the timestep. When you have a fixed time step, the choice is related to the critical time step which depends on the numerical scheme considered. When using finite element modeling it is related to the eigenvalues of the smallest element in the mesh.
As an alternative, you can use a modal solver, e.g. FreeModalTimeProblem, which is based on analytical formula or try to construct the state space matrices from the FE matrices and use it DifferentialEquations.jl which use adaptive time stepping.
That being said, I will check the construction of the FE matrices and make an example in the documentation using FE matrices.