Fast eigenvalue sensitivity calculations for special structures of system matrix derivatives

In this paper a possible application is presented of a general rank-1 matrix formula to the eigenvalue sensitivity evaluation which reduces the sensitivity expressions to elegant, very fast and recursive formulas with substantial savings in computer resources. The rank-1 matrix formula allows for re-arranging terms in multi-product forms involving vectors and matrices. The formula is applicable to rank-1 matrices of special structures which may constitute derivatives of the system state matrix with respect to parameters of interest. In such cases, the use of the rank-1 formula yields exact non-approximate solutions which are identical to those obtained by other conventional formulas. The applicability of the rank-1 formula is believed to cover a wide variety of practical engineering systems pertaining to sound and vibration. (C) 1997 Academic Press Limited.