An efficient numerical method far lhe computation of the frequency response of a vibrating structure as a funclion of its slructural properties is presenled and the resulls are applied to the problem of vihralion reduction. A sensilivity analysis is used to delermine which slructural element changes are mosl responsible for vibration reduction. The usefulness of these methods is demonslrated by numerical results for an elaslic line helicopter model.
NotationC =damping matrix, N-sec/m D =parameter modification matrix E; =stiffness of beam element i, N-m2 F =generalized receptance matrix, m/N G = a squarematrix I =integer set locating nonzero columns of D K =stiffness matrix, N/m M =mass matrix, N-sec2/m N =number of degrees of freedom R =receptance matrix, m/N ajj =jth modal normalization constant f =generalized force vector, N o r N-m f, =vector amplitude of N o r N-m i =imaginary unit d x =response vector, m x, =vector amplitude of unmodified system response, m Xk =response at degree of freedom k, m x, =real part of x,, m X, =imaginary part of x,, m Y O =vector amplitude of modified system response. m '1 1 =time, sec u.W =partitions of vectorx, m m; =sensitivity factor for beam element i 13, = jth eigenvalue 6, = jth left eigenvector 6: =transpose of 6, A, =jth right eigenvector 0 =excitation frequency, s e c '
