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Acoustic Field

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Numerical Simulation of Mechatronic Sensors and Actuators

Abstract

Acoustic waves can propagate in non-viscous media just in the form of longitudinal waves.

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Notes

  1. 1.

    We have: \(d\rho ^{-1} = - (1/\rho ^2) d\rho \).

  2. 2.

    Same formulation holds for the acoustic velocity potential \(\psi \).

References

  1. A.D. Pierce, Acoustics—An Introduction to its Physical Principles and Applications (Acoustical Society of America, Woodbury, 1991)

    Google Scholar 

  2. E. Zwicker, H. Fastl, Psychoacoustics (Springer, Berlin, 1999)

    Book  Google Scholar 

  3. V.P. Kuznetsov, Equations of nonlinear acoustics. Sov. Phys. Acoust. 16(4), 467–470 (1971)

    Google Scholar 

  4. M.F. Hamilton, D.T. Blackstock, Nonlinear Acoustics (Academic Press, San Diego, 1998)

    Google Scholar 

  5. S.I. Aanonsen, T. Barkvek, J.N. Tjotta, S. Tjotta, Distortion and harmonic generation in the near field of a finite amplitude sound beam. J. Acoust. Soc. Am. 75, 749–768 (1984)

    Article  MATH  Google Scholar 

  6. F. Brezzi, M. Fortin, Mixed and Hybrid Finite Element Methods (Springer, New York, 1991)

    Book  MATH  Google Scholar 

  7. P.A. Raviart, J.M. Thomas, A mixed finite element method for 2nd order elliptic problems, in Mathematical Aspects of the Finite Element Method. Lecture Notes in Mathematics, pp. 292–315 (1977)

    Google Scholar 

  8. G.C. Cohen, Higher-Order Numerical Methods for Transient Wave Equations (Springer, Berlin, 2002)

    Book  MATH  Google Scholar 

  9. G. Cohen, S. Fauqueux, Mixed finite elements with mass-lumping for the transient wave equation. J. Comput. Acoust. 8, 171–188 (2000)

    Article  MathSciNet  Google Scholar 

  10. D.N. Arnold, D. Boffi, R.S. Falk, Quadrilateral H(div) finite elements. SIAM J. Numer. Anal. 42, 2429–2451 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  11. A. Hüppe, Spectral Finite Elements for Acoustic Field Computation. Ph.D. thesis, Alpen-Adria-Universität, Klagenfurt, (2013)

    Google Scholar 

  12. B. Flemisch, M. Kaltenbacher, S. Triebenbacher, B. Wohlmuth, Non-matching grids for a flexible discretization in computational acoustics. Commun. Comput. Phys. 11(2), 472–488 (2012)

    MathSciNet  Google Scholar 

  13. F. Ihlenburg, I. Babuska, Finite element solution of the Helmholtz equation with high wave number part I: the h version of the finite element method. Comput. Math. Appl. 30, 9–37 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  14. M. Ainsworth, Discrete dispersion relation for hp-version finite element approximation at high wave number. SIAM J. Numer. Anal. 42(2), 553–575 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  15. L. Olson, K. Bathe, An infinite element for analysis of transient fluid-structure interactions. Eng. Comput. 2, 319–329 (1985)

    Article  Google Scholar 

  16. D. Dreyer, O. von Estorff, Improved conditioning of infinite elements for exterior acoustics. Int. J. Numer. Methods Eng. 58, 933–953 (2003)

    Article  MATH  Google Scholar 

  17. R. Clayton, B. Engquist, Absorbing boundary conditions for acoustic and elastic wave equations. Bull. Seismol. Soc. Am. 67, 1529–1540 (1977)

    Google Scholar 

  18. B. Engquist, A. Majda, Absorbing boundary conditions for the numerical simulation of waves. Math. Comput. 31, 629–651 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  19. M. Hofer, Finite-Elemente-Berechnung von periodischen Oberflächenwellen-Strukturen. Ph.D. thesis, University of Erlangen-Nuremberg, (2003)

    Google Scholar 

  20. J.P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114, 185 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  21. F. Collino, P. Monk, The perfectly matched layer in curvilinear coordinates. SIAM J. Sci. Comput. 19, 2061–2090 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  22. I. Harari, M. Slavutin, E. Turkel, Analytical and numerical studies of a finite element PML for the Helmholtz equation. J. Comput. Acoust. 8, 121–127 (2000)

    Article  MathSciNet  Google Scholar 

  23. Fang Q. Hu, Absorbing boundary conditions. Int. J. Comput. Fluid Dyn. 18, 513–522 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  24. I. Singer, E. Turkel, A perfectly matched layer for Helmholtz equation in a semi-infinite strip. J. Comput. Phys. 201, 439–465 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  25. F.L. Teixeira, W.C. Chew, Complex space approach to perfectly layers: a review and some developments. Int. J. Numer. Model. 13, 441–455 (2000)

    Article  MATH  Google Scholar 

  26. A. Bermúdez, L. Hervella-Nieto, A. Prieto, R. Rodríguez, An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems. J. Comput. Phys. 223(2), 469–488 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  27. E. Becache, S. Fauqueux, P. Joly, Stability of matched layers, group velocities and anisotropic waves. J. Comput. Phys. 188, 399–433 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  28. J.H. Bramble, J.E. Pasciak, Analysis of a finite PML approximation for the three dimensional time-harmonic Maxwell and acoustic scattering problems. Math. Comput. (2006)

    Google Scholar 

  29. T. Rylander, J.M. Jin, Perfectly matched layer for the time domain finite element method. J. Comput. Phys. 238–250 (2004)

    Google Scholar 

  30. Björn Sjögreen and, N. Anders Petersson, Perfectly matched layers for Maxwell’s equations in second order formulation. J. Comput. Phys. 209(1), 19–46 (2005)

    Article  MathSciNet  Google Scholar 

  31. Daniel Appelö, Gunilla Kreiss, Application of a perfectly matched layer to the nonlinear wave equation. Wave Motion 44(7–8), 531–548 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  32. B. Kaltenbacher, M. Kaltenbacher, I. Sim, A modified and stable version of a perfectly matched layer technique for the 3-d second order wave equation in time domain with an application to aeroacoustics. J. Comput. Phys. 235, 407–422 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  33. A. Hüppe, M. Kaltenbacher, Stable matched layer for the acoustic conservation equations in the time domain. J. Comput. Acoust. 20(1), 17 (2012)

    Article  Google Scholar 

  34. A. Hüppe, M. Kaltenbacher, Finite element solution of the Helmholtz equation with high wave number part II: the h-p version of the FEM. SIAM J. Numer. Anal. 34(1), 315–358 (1997)

    Article  MathSciNet  Google Scholar 

  35. D.T. Blackstock, Connection between the Fay and Fubini solutions for plane sound waves of finite amplitude. J. Acoust. Soc. Am. 39(6), 1019–1026 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  36. J. Hoffelner, Simulation, Erzeugung und Anwendung von hochintensivem Ultraschall. Ph.D. thesis, University of Erlangen-Nuremberg, (2003)

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mechanics and Mechatronics, Vienna University of Technology, Vienna, Austria

    Manfred Kaltenbacher

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  1. Manfred Kaltenbacher
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Correspondence to Manfred Kaltenbacher .

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Kaltenbacher, M. (2015). Acoustic Field. In: Numerical Simulation of Mechatronic Sensors and Actuators. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40170-1_5

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  • DOI: https://doi.org/10.1007/978-3-642-40170-1_5

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