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One-dimensional scalar wave propagation in multi-region domains by the boundary element method

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Abstract

Two boundary element method formulations are presented for the analysis of the one-dimensional scalar wave propagation problem in multi-region domains. One of the formulations employs the time-domain fundamental solution; the other, the fundamental solution related to the static problem. The problem domain is constituted of sub-domains with different material properties and, consequently, with different wave propagation velocities. Thus, the sub-region technique, akin to the boundary element method, is used to deal with the non-homogeneous problem. At the end of the article, some examples are presented, illustrating the characteristics of each formulation and their accuracy.

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References

  1. Brebbia CA, Telles JCF, Wrobel LC (1984) Boundary element techniques: theory and application in engineering. Springer, Berlin

    Book  Google Scholar 

  2. Zienkiewicz OC, Morgan K (1983) Finite elements and approximation. Wiley, New York

    MATH  Google Scholar 

  3. Finlayson BA (1972) The method of weighted residuals and variation principles. Academic Press, New York

    MATH  Google Scholar 

  4. Mansur WJ (1983) A time-stepping technique to solve wave propagation problems using the boundary element method. Southampton University, Ph.D. Thesis

  5. Carrer JAM, Costa VL (2015) Boundary element method formulations for the solution of the scalar wave equation in one-dimensional problems. J Braz Soc Mech Sci Eng 37:959–971

    Article  Google Scholar 

  6. Houbolt JC (1950) A recurrence matrix solution for the dynamic response of elastic aircraft. J Aeronaut Sci 17:540–550

    Article  MathSciNet  Google Scholar 

  7. Carrer JAM, Mansur WJ, Vanzuit RJ (2009) Scalar wave equation by the boundary element method: a D-BEM approach with non-homogeneous initial conditions. Comput Mech 44:31–44

    Article  MathSciNet  Google Scholar 

  8. Carrer JAM, Oliveira MF, Vanzuit RJ, Mansur WJ (2012) Transient heat conduction by the boundary element method: D-BEM approaches. Int J Numer Methods Eng 89:897–913

    Article  MathSciNet  Google Scholar 

  9. Santiago JAF, Telles JCF, Valentim VA (1999) An optimized block matrix manipulation for boundary elements with subregions. Adv Eng Softw 30:701–713

    Article  Google Scholar 

  10. Atalaya MA, Dilara ED, Aydin M (2004) Multi-region heat conduction problems by boundary element method. Int J Heat Mass Transf 47:1549–1553

    Article  Google Scholar 

  11. Lei W, Liu C, Li H, Qin X, Chen R (2017) Iterative coupling of precise integration FEM and TD-BEM for elastodynamic analysis. IN: The 2017 World Congress on Advances in Structural Engineering and Mechanics (ASEM17), Ilsan (Seoul), Korea

  12. Ghavanloo E, Fazelzadeh SA (2019) Wave propagation in one-dimensional infinite acoustic metamaterials with long-range interactions. Acta Mech 230:4453–4461

    Article  MathSciNet  Google Scholar 

  13. Kolman R, Cho SS, Gonzalez JG, Park KC, Berezovski A (2017) An explicit time scheme with local time stepping for one-dimensional wave propagation in a biomaterial bar. In: 23rd international conference engineering mechanics, Svratka, Czech Republic, pp 474–477

  14. Graff KF (1991) Wave motion in elastic solids. Dover Publications, Inc., New York

    MATH  Google Scholar 

  15. Greenberg MD (1971) Application of Green’s Functions in Engineering and Sciences. Prentice-Hall Inc., Eaglewood Cliffs

    Google Scholar 

  16. Mei CC (1995) Mathematical analysis in engineering. Cambridge University Press, Cambridge

    Book  Google Scholar 

  17. Demirel V, Wang S (1987) Efficient boundary element method for two-dimensional transient wave propagation problems. Appl Math Model 11:411–416

    Article  MathSciNet  Google Scholar 

  18. Mansur WJ, de Lima-Silva W (1992) Efficient time truncation in two-dimensional BEM analysis of transient wave propagation problems. Earthq Eng Struct Dyn 21:51–63

    Article  Google Scholar 

  19. Soares D Jr, Mansur WJ (2004) Compression of time generated matrices in two-dimensional time-domain elastodynamic BEM analysis. Int J Numer Methods Eng 61:1209–1218

    Article  Google Scholar 

  20. Carrer JAM, Mansur WJ (2006) Solution of the two-dimensional scalar wave equation by the time-domain boundary element method: Lagrange truncation strategy in time integration. Struct Eng Mech 23:263–278

    Article  Google Scholar 

  21. Carrer JAM, Mansur WJ (2007) A step-by-step approach in the time-domain BEM formulation for the scalar wave equation. Eng Mech 27:683–696

    Google Scholar 

  22. Vladimirov VS (1979) Generalized functions in mathematical physics. Nauka Publishers, Moscow

    MATH  Google Scholar 

  23. Rao SS (1995) Mechanical vibrations, 3rd edn. Addison-Wesley Publishing Company Inc, Reading

    Google Scholar 

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Acknowledgements

The first author would like to thank the support from the Brazilian Council for Scientific and Technological Development (CNPq), under the process number 201451/2018-2/PDE.

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Authors and Affiliations

  1. PPGMNE: Programa de Pós-Graduação em Métodos Numéricos em Engenharia, Universidade Federal do Paraná, Caixa Postal 19011, Curitiba, PR, CEP 81531-990, Brazil

    J. A. M. Carrer

  2. Programa de Engenharia Civil, COPPE/UFRJ, Universidade Federal do Rio de Janeiro, Caixa Postal 68506, Rio de Janeiro, CEP 21945-970, Brazil

    W. J. Mansur

Authors
  1. J. A. M. Carrer
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  2. W. J. Mansur
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Correspondence to J. A. M. Carrer.

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Technical Editor: José Roberto de França Arruda.

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Carrer, J.A.M., Mansur, W.J. One-dimensional scalar wave propagation in multi-region domains by the boundary element method. J Braz. Soc. Mech. Sci. Eng. 42, 134 (2020). https://doi.org/10.1007/s40430-020-2226-5

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