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 $10\%$.

翻译：我们提出了用于恢复横向各向同性材料线性弹性特征值问题中参数的数值算法。具体而言，这些算法用于恢复转子铁心的弹性常数。数值测试表明，在无噪声情况下，两对弯曲模态足以精确恢复一至四个参数。为精确恢复控制电机弹性特性的全部五个参数，需要三对弯曲模态和一个扭转模态。此外，我们研究了反演方法对乘性噪声的稳定性；对于数据中包含最多$1\%$乘性噪声的测试，我们发现所有参数均能以小于$10\%$的误差恢复。