Laëtitia Duigou

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 Pade 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.

Forced harmonic response of viscoelastic sandwich beams by a reduction method

ABSTRACT The aim of this article is to develop a reduction method to determine the forced harmonic response of viscoelastic sandwich structures at a reasonable computational cost. The numerical resolution is based on the asymptotic numerical method. This type of problem is complex, and its number of degrees of freedom is double the number of the undamped structure, leading to a high computational time. To address the problem, three reduction methods are evaluated, which differ from the projection operator. Numerical tests have been performed in the case of cantilever sandwich beams. The comparison of the results obtained by the reduction order resolution with those given by the full order resolution shows both a good agreement and a significant reduction in computational cost.

Nonlinear Forced Vibrations of Rotating Composite Beams with Internal Combination Resonance

This work deals with forced vibration of nonlinear rotating composite beams with uniform cross-section. Coupling the Galerkin method with the balance harmonic method, the nonlinear intrinsic and geometrical exact equations of motion for anisotropic beams are converted into a static formulation, which is treated with the continuation method; the asymptotic numerical method, where power series expansions and Pade approximants are used to represent the generalized vector of displacement and the frequency. Response curves are obtained and the nonlinearity is studied for various angular speed. Internal resonance flexion-flexion is found and the angular speed effect on the coupling between modes is investigated.