Numerical calculations of elastic modes frequencies for parametric oscillatory instability in Advanced LIGO interferometer

We discuss the importance of accurate numerical calculation of elastic modes in the mirrors of Advanced LIGO to enable precise predictions of the problem of parametric oscillatory instability. We propose accuracy estimations through use of analytical solutions based on Chree-Lamb modes. Small deviations from cylindrical test mass shape may produce splitting of non-axial symmetric elastic modes into doublets. This splitting may increase the possibility of parametric oscillatory instability.