Extended Wittrick–Williams algorithm for eigenvalue solution of stochastic dynamic stiffness method

This paper proposes an efficient and reliable eigenvalue solution technique for analytical stochastic dynamic stiffness (SDS) formulations of beam built-up structures with parametric uncertainties. The SDS are developed based on frequency-dependent shape functions in conjunction both random-variable random-field structural parameters. overall numerical framework is aimed towards representing the broadband dynamics using very few degrees freedom. a novel approach combining Wittrick–Williams(WW) algorithm, Newton iteration method perturbation to extract eigensolutions from formulations. First, eigenvalues eigenvectors deterministic DS computed by WW algorithm corresponding mode finding technique, which used as initial solution. Then, inverse homotopy proposed update eigenvalues. robustness efficiency guaranteed through several arrangements. Through examples, demonstrated be robust within whole frequency range. provides tool analysis problems relevant free vibration buckling structures.