xyzr algorithm specialized for eigenvibration problem of bored and laminated objects

We can determine elastic properties of an object from its eigenvibration frequencies, as long as a numerical calculation algorithm is available for the eigenvibration frequencies. The xyz algorithm developed by Visscher et al. is an extremely versatile method applicable even for anisotropic, inhomogeneous, and irregular-shaped objects, with the exception of bored and laminated systems. I examined the characteristics and performance of the original xyz algorithm, and succeeded in developing the xyzr algorithm for bored and laminated sphere and cylinder. The accuracy and convergency of the xyzr algorithm are examined by comparison with analytical solutions; the method is accurate enough for us to develop a new experimental technique to obtain the elastic properties of soft materials accommodated in a solid container.