Hypersingular Boundary Integral Equation for Harmonic Acoustic Problems in 2.5D Domains with Moving Sources

Authors

  • J. Pizarro-Ruiz Departamento de Mec´anica de Estructuras e Ingenier´ıa Hidr´aulica, ETS de Ingenieros de Caminos, Canales y Puertos, Universidad de Granada, Avenida Fuentenueva s/n, 18002 Granada, Spain
  • Esther Puertas García Departamento de Mec´anica de Estructuras e Ingenier´ıa Hidr´aulica, ETS de Ingenieros de Caminos, Canales y Puertos, Universidad de Granada, Avenida Fuentenueva s/n, 18002 Granada, Spain
  • Rafael Gallego Departamento de Mec´anica de Estructuras e Ingenier´ıa Hidr´aulica, ETS de Ingenieros de Caminos, Canales y Puertos, Universidad de Granada, Avenida Fuentenueva s/n, 18002 Granada, Spain

Keywords:

BEM, 2.5D, Hypersingular, Acoustic barriers, Coincident Boundaries, Moving Sources, Helmholtz Equation.

Abstract

A challenge faced when modeling coincident boundaries by the Boundary Element Method, is to obtain an accurate approximation of integrals which have singular and/or hypersingular kernels. In this paper,we apply a procedure based on regularization of the kernels to compute singular and hypersingular integrals for time harmonic wave problems in two and a half dimensional (2.5D) domains. For this purpose, the Fundamental Solution is described and the study of the terms that arise taking its limit as r → 0 is carried out. These terms lead to Singular Boundary Integral Equation (SBIE) and Hypersingular Boundary Integral Equation (HBIE). Regular terms of SBIE and HBIE are integrated by applying numerical quadratures, whereas singular and hypersingular terms are calculated analytically.Working in 2.5D domains make it easier to compute moving sources.Aprocedure, which leads to a simple change of the frequency of the problem, is described in this paper. Numerical results are presented for acoustic problems with coincident boundaries to demonstrate the accuracy of the proposed formulation.

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Author Biographies

J. Pizarro-Ruiz, Departamento de Mec´anica de Estructuras e Ingenier´ıa Hidr´aulica, ETS de Ingenieros de Caminos, Canales y Puertos, Universidad de Granada, Avenida Fuentenueva s/n, 18002 Granada, Spain

J. Pizarro-Ruiz is a Ph.D student at the University of Granada since 2018. He attended the University of Granada, Spain, where he received his bachelor degree in Civil Engineering in 2016. He continued his studies at this University and obtained Master degree in Structures. Joaqu´ın is working on his doctorate in Civil Engineering at University of Granada. His Ph.D work studies vibrations propagation modeling with Boundary Elements Method in poroelastic soils and spectral analysis of superficial waves, in order to obtain the properties of soils under the sea level.

Esther Puertas García, Departamento de Mec´anica de Estructuras e Ingenier´ıa Hidr´aulica, ETS de Ingenieros de Caminos, Canales y Puertos, Universidad de Granada, Avenida Fuentenueva s/n, 18002 Granada, Spain

Esther Puertas Garc´ıa is permanent lecturer at the University of Granada. She received her Bachelor and Master degrees in Civil Engineering at the University of Granada, and PhD degrees in Civil Engineering from the University of Granada in 2014. She has an extensive teaching, research and professional experience in the Mechanics of Continuous Media and Theory of Structures topics. Her research work concerns the development of computational toolkits for continuum media dynamics. She belongs to the Research Group of Mechanics of Solids and Structures. Her lines of work are based on the study of Integral Equations Methods for advanced applications in Solid Mechanics. She has developed techniques for the analysis of wave propagation problems in two and a half domains.

Rafael Gallego, Departamento de Mec´anica de Estructuras e Ingenier´ıa Hidr´aulica, ETS de Ingenieros de Caminos, Canales y Puertos, Universidad de Granada, Avenida Fuentenueva s/n, 18002 Granada, Spain

Rafael Gallego is full professor at the University of Granada since 1995. He received his Bachelor and Master degrees in Structural and Mechanical Engineering at the University of Sevilla (1987) and got his PhD at the same University in 1990; he was granted a Fulbright postdoctoral scholarship (1990–92) at the Brown University. Among other academic posts, he has been chairman of the Department of Structural and Hydraulic Engineering at the University of Granada since 2000 to 2008 and since 2016 to date. His research work has focused in developing computational models based on Boundary Integral Equations for solid mechanics problem, mainly related to wave propagation in solids, dynamic fracture mechanics and dynamic soil-structure interaction, including resolution of inverse problems to match computational results and experimental ones.

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Published

2019-08-07

How to Cite

Pizarro-Ruiz, J., García, E. P., & Gallego, R. (2019). Hypersingular Boundary Integral Equation for Harmonic Acoustic Problems in 2.5D Domains with Moving Sources. European Journal of Computational Mechanics, 28(1-2), 81–96. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/929

Issue

2019: Vol28 Iss 1-2

Section

Original Article