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Approximation of acoustic black holes with finite element mixed formulations and artificial neural network correction terms.

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Title: Approximation of acoustic black holes with finite element mixed formulations and artificial neural network correction terms.
Authors: Fabra, Arnau1,2 (AUTHOR) arnau.fabra@cimne.upc.edu, Guasch, Oriol1,3 (AUTHOR) oriol.guasch@salle.url.edu, Baiges, Joan1 (AUTHOR) joan.baiges@upc.edu, Codina, Ramon1,2 (AUTHOR) ramon.codina@upc.edu
Source: Finite Elements in Analysis & Design. Nov2024, Vol. 241, pN.PAG-N.PAG. 1p.
Subjects: Artificial neural networks, Acoustic wave propagation, Finite element method, Theory of wave motion, Problem solving, Elastodynamics
Abstract: Wave propagation in elastodynamic problems in solids often requires fine computational meshes. In this work we propose to combine stabilized finite element methods (FEM) with an artificial neural network (ANN) correction term to solve such problems on coarse meshes. Irreducible and mixed velocity–stress formulations for the linear elasticity problem in the frequency domain are first presented and discretized using a variational multiscale FEM. A non-linear ANN correction term is then designed to be added to the FEM algebraic matrix system and produce accurate solutions when solving elastodynamics on coarse meshes. As a case study we consider acoustic black holes (ABHs) on structural elements with high aspect ratios such as beams and plates. ABHs are traps for flexural waves based on reducing the structural thickness according to a power-law profile at the end of a beam, or within a two-dimensional circular indentation in a plate. For the ABH to function properly, the thickness at the termination/center must be very small, which demands very fine computational meshes. The proposed strategy combining the stabilized FEM with the ANN correction allows us to accurately simulate the response of ABHs on coarse meshes for values of the ABH order and residual thickness outside the training test, as well as for different excitation frequencies. • Finite elements for mixed velocity–stress problems in elastodynamics are presented. • An artificial neural network correction term for the discrete problem is introduced. • The correction term allows for accurate problem solving on coarse meshes. • The methodology is tested for acoustic black holes in beams and plates. • Wave propagation inside acoustic black holes is correctly captured on coarse meshes. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Wave propagation in elastodynamic problems in solids often requires fine computational meshes. In this work we propose to combine stabilized finite element methods (FEM) with an artificial neural network (ANN) correction term to solve such problems on coarse meshes. Irreducible and mixed velocity–stress formulations for the linear elasticity problem in the frequency domain are first presented and discretized using a variational multiscale FEM. A non-linear ANN correction term is then designed to be added to the FEM algebraic matrix system and produce accurate solutions when solving elastodynamics on coarse meshes. As a case study we consider acoustic black holes (ABHs) on structural elements with high aspect ratios such as beams and plates. ABHs are traps for flexural waves based on reducing the structural thickness according to a power-law profile at the end of a beam, or within a two-dimensional circular indentation in a plate. For the ABH to function properly, the thickness at the termination/center must be very small, which demands very fine computational meshes. The proposed strategy combining the stabilized FEM with the ANN correction allows us to accurately simulate the response of ABHs on coarse meshes for values of the ABH order and residual thickness outside the training test, as well as for different excitation frequencies. • Finite elements for mixed velocity–stress problems in elastodynamics are presented. • An artificial neural network correction term for the discrete problem is introduced. • The correction term allows for accurate problem solving on coarse meshes. • The methodology is tested for acoustic black holes in beams and plates. • Wave propagation inside acoustic black holes is correctly captured on coarse meshes. [ABSTRACT FROM AUTHOR]
ISSN:0168874X
DOI:10.1016/j.finel.2024.104236