Computational Mechanics New advances in the forced response computation of periodicstructures using the wave finite element ( WFE ) method
The wave finite element (WFE) method is investigated to describe the harmonic forced response of onedimensional periodic structures like those composed of com plex substructures and encountered in engineering applica tions. The dynamic behavior of these periodic structures is analyzed over wide frequency bands where complex spatial dynamics, inside the substructures, are likely to occu r. Within the WFE framework, the dynamic behavior of periodic structures is described in terms of numerical wave modes. Their computation follows from the consideration of the finite element model of a substructure that involves a large number of internal degrees of freedom. Some rules of thumb of the WFE method are highlighted and discussed to circumvent numerical issues like ill-conditioning and i stabilities. It is shown for instance that an exact analytic relation needs to be considered to enforce the coherence between positive-going and negative-going wave modes. Besides, a strategy is proposed to interpolate the frequency r esponse functions of periodic structures at a reduced number of discrete frequencies. This strategy is proposed to tackl e the problem of large CPU times involved when the wave modes are to be computed many times. An error indicator is formulated which provides a good estimation of the level of accuracy of the interpolated solutions at intermediate poi nts. Adaptive refinement is carried out to ensure that this error indicator remains below a certain tolerance threshold. Numerical experiments highlight the relevance of the propose d approaches.
Finite element prediction of wave motion in structural waveguides.
A method is presented by which the wavenumbers for a one-dimensional waveguide can be predicted from a finite element (FE) model. The method involves postprocessing a conventional, but low order, FE model, the mass and stiffness matrices of which are typically found using a conventional FE package. This is in contrast to the most popular previous waveguide/FE approach, sometimes termed the spectral finite element approach, which requires new spectral element matrices to be developed. In the approach described here, a section of the waveguide is modeled using conventional FE software and the dynamic stiffness matrix formed. A periodicity condition is applied, the wavenumbers following from the eigensolution of the resulting transfer matrix. The method is described, estimation of wavenumbers, energy, and group velocity discussed, and numerical examples presented. These concern wave propagation in a beam and a simply supported plate strip, for which analytical solutions exist, and the more complex case of a viscoelastic laminate, which involves postprocessing an ANSYS FE model. The method is seen to yield accurate results for the wavenumbers and group velocities of both propagating and evanescent waves.
Wave finite elements for low and mid-frequency description of coupled structures with damage
This paper focuses on wave propagation in complex elastic structures along with a precise account of guided waves. A numerical finite element based approach named wave finite element (WFE) is further developed. Diffusion matrix prediction model (DMM) through a full numerical scheme is proposed and extended. The applicability of the WFE for the low and mid-frequency description of coupled systems is considered. Analysis of coupled structures through a notch is also treated numerically and the numerical experiments given prove the interest of the WFE for structural wave studies such as damage detection through guided waves.