Wave finite elements in guided elastodynamics with internal fluid

Abstract

This paper presents a general formulation which addresses the issue of wave propagation in guided elastodynamic structures filled with acoustic fluid. The formulation is based on a finite element description of periodic systems. It leads to a general spectral problem, whose eigenvalues and eigenvectors are related to the free propagating wave properties. The formulation incorporates many simplified elastodynamic models of an analytical nature. Here, the formulation is stated for a fluid-structure guided medium. The free and forced frequency response of such elasto-acoustic system is fully formulated in the wave space. Reduction of the wave basis is discussed. Numerical simulations and comparisons with classic simplified theories clearly shows the pertinence of the proposed formulation. Moreover, it is clearly shown that, unlike most of the existing theories, the proposed formulation is not low frequency limited.

New advances in the forced response computation of periodic structures using the wave finite element (WFE) method

“…Previous works made on the WFE topic have been carried out to assess the guided wave propagation along straight elastic waveguides [23,15], fluid-filled pipes [16,11] and truss beams [20]. Besides, the WFE method has been applied to describe the plane wave propagation in infinite twodimensional structures [10].…”

Wave transmission through two-dimensional structures by the hybrid FE/WFE approach

“…For simple cases such as slender connected beams, analytical solutions can be 10 obtained for the reflection and transmission coefficients [4,5]. However, developing analytical models that describe the dynamic behaviour of more complicated structures comprised of plates and different type of joints can be a very difficult task.…”

“…Therefore, for such complicated structures, and particularly at high frequencies, the wave and finite element (WFE) method can be used. The WFE 15 method for waveguides has been used to predict the free [6] and forced [7] response and to study different type of structures, such as thin-walled structures [8], laminated plates [6], fluid filled pipes [9,10] etc. It has also been extended to two-dimensional plane [11,12] and cylindrical structures [13].…”

A Wave Finite Element Strategy to Compute the Dynamic Flexibility Modes of Structures With Cyclic Symmetry and Its Application to Domain Decomposition

“…The WFE method is nothing else but a transfer matrix method which, once combined with the Bloch theorem, provides wave modes which propagate along periodic structures, i.e., structures composed of identical substructures along a straight or circumferential direction (see [3,4,5,6,7,8,9,10,11]). The WFE method has been further used to describe the dynamic response of periodic structures.…”