This paper presents a non-perturbative method for solving eigenproblems. This method applies to almost all potentials and provides non-perturbative approximations for any energy level. The method converts an eigenproblem into a perturbation problem, obtains perturbation solutions through standard perturbation theory, and then analytically continues the perturbative solution into a non-perturbative solution.

In this work we discuss the numerical challenges involved in the computation of the complex eigenvalues of damped multi-flexible-body problems. Aiming at the highest generality, the candidate method must be able to deal with arbitrary rigid body modes (free-free mechanisms), arbitrary algebraic constraints, and must be able to exploit the sparsity pattern of Jacobians of large systems. We propose a custom implementation of the Krylov-Schur method, proving its robustness and its accuracy in a variety of different complex test cases.

The aim of this paper is to optimize thickness variation function of simply supported and cantilever beams, in terms of maximizing gaps between chosen neighboring frequencies and analyze obtained results. The optimization results are examined in terms of achieving the objective function (related to eigenproblem), but also in terms of their dynamics stiffness (forced vibrations excited by point harmonic load). In the optimization process, a Genetic Algorithm was used. Problems related to structural dynamics were solved by FEM implementation into the algorithm. Sample results were presented, and the developed algorithm was analyzed in terms of result convergence by examining several variable parameters. The authors demonstrated the validity of applying the described optimization tool to the presented problems. Conclusions were drawn regarding the correlation between stiffness and mass distribution in the optimized beams and the natural frequency modes in terms of which they were optimized.