Determination of eigenfunction and frequency response function of constrained dynamic system

Structural modification needs to prescribe some structural frequencies and mode shapes. This study derives the eigenfuction and frequency response function matrix of constrained dynamic system based on measured test data. The modified eigenfunction is derived by utilizing the measured modal data of the actual system as constraints to govern a part of the behavior of modified system and minimizing cost functions of the difference between analytical and corrected parameter matrices with them. It is shown that the modified eigenfunction incorporates the modified parameter matrices. The frequency response function matrix modified by measured constraints is also derived by minimizing a cost function of the dynamic strain energy to be expressed by dynamic stiffness matrix and the difference between analytical and measured modal displacements. The validity of the proposed methods is demonstrated in applications