The Calculation of Eigensolution derivatives for Nonviscously damped systems using Nelson's method

A method to calculate the derivatives of the eigenvalues and eigenvectors of multiple-degree-of-freedom damped linear dynamic systems with respect to arbitrary design parameters is presented. In contrast to the traditional viscous damping model, a more general non-viscous damping model is considered in this paper. The non-viscous damping model is such that the damping forces depend on the past history of velocities via convolution integrals over given kernel functions. Due to the general nature of the damping, eigensolutions are generally complex valued and eigenvectors do not satisfy the classical orthogonality relationship. The proposed method to calculate the eigenvector derivative depends only on the eigenvector concerned. Numerical examples are provided to illustrate the derived results.