Optimization Procedure to Correct Stiffness and Flexibility Matrices Using Vibration Tests

Abstract

Nomenclature Lagrange function for the flexibility matrix weighted norm of the errors between the given and the optimal flexibility matrix Lagrange function for the stiffness matrix weighted norm of the errors between the given and the optimal stiffness matrix unity matrix given stiffness matrix mass matrix M» //element of TV //element of N~* Nq general-coordinates vector measured mode shape /th measured_mode shape normalized 7} transpose of [ • ] = optimal flexibility matrix = (/ element of W orthogonal mode shape matrix = (/ element of X optimal stiffness matrix -ij element of Y = matrices of Lagrange multipliers = ij element of 0y and 0W , respectively = matrix of Lagrange multipliers = given flexibility matrix = matrices of Lagrange multipliers = ij element of A^ and A^ , respectively = measured frequency matrix = //element of Q y»(i* w