A numerical model for vibro-acoustic problems with sheared mean flows

A model based on Galbrun's equation is proposed to address the problem of vibro-acoustic interactions in sheared flows. The use of a displacement-pressure mixed formulation of Galbrun's equation greatly simplifies the coupling condition formulations and avoids the problem of non-zero frequency spurious modes encountered with displacement-based acoustic formulations. This model is applied to duct acoustics. Comparisons with analytical models demonstrate the accuracy of the method. The effects of mean flow shear on acoustic wave propagation in elastic ducts are then illustrated

A mixed finite element method for acoustic wave propagation in moving fluids based on an Eulerian-Lagrangian description

A nonstandard wave equation, established by Galbrun in 1931, is used to study sound propagation in nonuniform flows. Galbrun's equation describes exactly the same physical phenomenon as the linearized Euler's equations (LEE) but is derived from an Eulerian–Lagrangian description and written only in term of the Lagrangian perturbation of the displacement. This equation has interesting properties and may be a good alternative to the LEE: only acoustic displacement is involved (even in nonhomentropic cases), it provides exact expressions of acoustic intensity and energy, and boundary conditions are easily expressed because acoustic displacement whose normal component is continuous appears explicitly. In this paper, Galbrun's equation is solved using a finite element method in the axisymmetric case. With standard finite elements, the direct displacement-based variational formulation gives some corrupted results. Instead, a mixed finite element satisfying the inf-sup condition is proposed to avoid this problem. A first set of results is compared with semianalytical solutions for a straight duct containing a sheared flow (obtained from Pridmore–Brown's equation). A second set of results concerns a more complex duct geometry with a potential flow and is compared to results obtained from a multiple-scale method (which is an adaptation for the incompressible case of Rienstra's recent work)

Cross section shape optimization of wire strands subjected to purely tensile loads using a reduced helical model

This paper introduces a shape optimization of wire strands subjected to tensile loads. The structural analysis relies on a recently developed reduced helical finite element model characterized by an extreme computational efficacy while accounting for complex geometries of the wires. The model is extended to consider interactions between components and its applicability is demonstrated by comparison with analytical and finite element models. The reduced model is exploited in a design optimization identifying the optimal shape of a 1 + 6 strand by means of a genetic algorithm. A novel geometrical parametrization is applied and different objectives, such as stress concentration and area minimization, and constraints, corresponding to operational limitations and requirements, are analyzed. The optimal shape is finally identified and its performance improvements are compared and discussed against the reference strand. Operational benefits include lower stress concentration and higher load at plastification initiation