  We propose numerical algorithms for recovering parameters in eigenvalue
problems for linear elasticity of transversely isotropic materials.
Specifically, the algorithms are used to recover the elastic constants of a
rotor core. Numerical tests show that in the noiseless setup, two pairs of
bending modes are sufficient for recovering one to four parameters accurately.
To recover all five parameters that govern the elastic properties of electric
engines accurately, we require three pairs of bending modes and one torsional
mode. Moreover, we study the stability of the inversion method against
multiplicative noise; for tests in which the data contained multiplicative
noise of at most $1\%$, we find that all parameters can be recovered with an
error less than $10\%$.
