2ND-ORDER SENSITIVITY ANALYSIS IN VIBRATION AND BUCKLING PROBLEMS

A perturbation approach for the first- and second-order sensitivity an alysis of eigenvalue problems, as they arise in buckling and vibration of structural systems, is presented. A particular feature introduced in the formulation is the dependence of all matrices that model the pr oblem not only on the design parameter, but also on a pre-critical sta te. Thus, the sensitivity of the response of the fundamental path in b uckling problems, or a pre-stressed state, in vibration problems, are introduced in the analysis. Two techniques are considered in this work : the direct and the adjoint methods. First- and second-order sensitiv ity equations for eigenvalues and eigenvectors are obtained, and it is shown that second-order sensitivity of an eigenvalue can be accomplis hed by using only one adjoint problem.