Solving a coupled field problem by eigenmode expansion and finite element method

Bernd Baumann, Marcus Wolff, Bernd Kost, Hinrich Groninga


The propagation of sound in fluids is governed by a set of coupled partial differential equations supplemented by an appropriate equation of state. In many cases of practical importance one restricts attention to the case of ideal fluids with vanishing transport coefficients. Then, the differential equations decouple and sound propagation can be described by the wave equation. However, when loss mechanisms are important, this is in general not possible and the full set of equations has to be considered. For photoacoustic cells, an alternative procedure has been used for the calculation of the photoacoustic signal of cylinder shaped cells. The method is based on an expansion of the sound pressure in terms of eigenmodes and the incorporation of loss through quality factors of various physical origins. In this paper, we demonstrate that the method can successfully be applied to photoacoustic cells of unconventional geometry using finite element analysis.

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Michaelian, K. H., Photoacoustic Infrared Spectroscopy, Wiley-Interscience, Hoboken, 2003.

Kreuzer, L. B., The Physics of Signal Generation and Detection, in: Pao, Y.-H., ed., Optoacoustic

Spectroscopy and Detection, Academic Press, New York 1977, 1–25.

Hess, ed., Photoacoustic, Photothermal and Photochemical Processes in Gases, Springer-Verlag, Berlin,

Rey, J. M., Marinov, D., Vogler, D. E. and Sigrist, M. W., Investigation and optimisation of a multipass resonant photoacoustic cell at high absorption levels, Applied Physics B: Lasers and Optics, 2005, 80, 2, 261–266.

Mesquita, R. C., Mansanares, A. M., da Silva, E. C., Barja, P. R., Miranda, L. C. M., Vargas, H., Open Photoacoustic Cell: Applications in Plant Photosynthesis Studies, Instrumentation Science & Technology, 2006, Vol. 34, Issue 1 & 2, 33–38.

Levesque, D., Rousset, G., Bertrand, L., Finite-element Simulation of the Photoacoustic-Thermal Signal Generation, Canadian Journal of Physics, 1986, Vol. 64, 1030–1036.

Kasai, M., Fukushima, S., Gohshi, Y., Sawada, T., Ishioka, M., Kaihara, M., A basic analysis of pulsed photoacoustic signals using the finite elements method, Journal of Applied Physics, 1988, Vol. 64, Issue 3, 972–976.

Nakayuki, T., Takahashi, K., Computer Simulation of Laser-Generated Ultrasonic Wave by Finite Element Method: Photoacoustic Effect and Spectroscopy, Japanese Journal of Applied Physics, Supplement, 1991, Vol. 30, No. 1, 265–267.

Baumann, B., Kost, B., Groninga, H. G., Wolff, M., Eigenmode analysis of photoacoustic sensors via finite element method, Review of Scientific Instruments, 2006, 77, 044901.

Baumann, B., Wolff, M., Kost, B., Groninga, H. G., Finite Element Calculation of Photoacoustic Signals, Applied Optics, 2007, Vol. 46, No.7, 1120–1125.

Morse, P. M., Ingard, K. U., Theoretical Acoustics, McGraw-Hill, New York, 1968.

Temkin, S., Elements of Acoustics, John Wiley & Sons, New York, 1981.


VDI-Wärmeatlas, 9. Auflage, Springer Verlag, Berlin, 2002.


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