On the direct solution of wave propagation for repetitive structures

A 2d Wave Finite Element-Based Superelement Formulation for Acoustic Analysis of Cavities of Arbitrary Shapes

“…Denote as n the number of DOFs on the left (or right) edge of the substructure. Following the WFE framework [4,3], the wave modes are sought as the solutions of an eigenproblem of the form Sφ j = µ j φ j in which S is a 2n × 2n symplectic matrix expressed by…”

“…It makes use of the wave finite element (WFE) method which aims at assessing numerical wave modes traveling along periodic systems [3,4,5]. Within this framework, a so-called hybrid WFE/FE superelement is formulated which consists in a rectangular acoustic domain, with a periodic FE mesh, surrounded by an arbitrary-meshed FE layer with a small width.…”

Model reduction and perturbation analysis of wave finite element formulations for computing the forced response of coupled elastic systems involving junctions with uncertain eigenfrequencies

“…The WFE method requires the mass and stiffness matrices (M, K) of a typical substructure (see Figure 2) to be known; it uses a state vector representation [6] for linking the kinematic variables -i.e. displacements q and forces F -expressed over the left or right cross-section of a substructure k to those expressed over a similar cross-section (either left or right) for an adjacent substructure k − 1.…”

“…In other words, these matrix formulations exhibit sizes that are expected to be much smaller compared to what is encountered when using other types of reduced-order models (e.g. component mode synthesis [7], Krylov subspace techniques [8] or proper orthogonal decom- 1 These wave shapes are provided using a discretization scheme for the cross-section that results from a finite element (FE) modeling of a small substructure [6]. 2 position [9]), yielding extra CPU time savings.…”

“…Here, L c i is a square n i × n i matrix that plays the role of expressing the displacements and forces of each waveguide i in the coordinate system of the coupling junction (x c , y c , z c ) 6 .…”