Iterative algorithms for non-linear eigenvalue problems. Application to vibrations of viscoelastic shells

In this paper, two numerical iterative algorithms are developed for the vibrations of damped sandwich structures. These methods associate homotopy, asymptotic numerical techniques and Padé approximants. The first one is a sort of high order Newton method and the second one uses a more or less arbitrary matrix. So one can determine the natural frequencies and the loss factors of viscoelastically damped sandwich structures. To assess their efficiency, a few sandwich beams and plates have been considered. The techniques can be applied to large scale structures, to large damping and to strongly non-linear viscoelastic modulus.