Natural modes of modified structures

Nomenclature C = matrix of admixture coefficients for mode shape changes / = identity matrix K = symmetric stiffness matrix . £_ = modification vector M = symmetric mass matrix u = modification vector in modal coordinates x — displacement vector z = displacement vector in modal coordinates a. = magnitude of local stiffness modification A = change between baseline and modified structures X = natural frequency of modified structure $ = modal matrix with columns k k = kih mode shape vector i = Ath mode shape vector of modified structure ft = frequency matrix with diagonals co oo = natural frequency of baseline structure