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Journal of Applied Physics / Volume 111 / Issue 1 / ARTICLES / Applied Biophysics

J. Appl. Phys. 111, 014702 (2012); http://dx.doi.org/10.1063/1.3674316 (8 pages)

Forced wave motion with internal and boundary damping

Tobias Louw1, Scott Whitney1, Anu Subramanian1, and Hendrik Viljoen1,2

1Department of Chemical and Biomolecular Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, USA
2Department of Internal Medicine, University of Nebraska Medical Center, Omaha, Nebraska 68198, USA

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(Received 2 February 2011; accepted 7 December 2011; published online 6 January 2012)

A d’Alembert-based solution of forced wave motion with internal and boundary damping is presented with the specific intention of investigating the transient response. The dynamic boundary condition is a convenient method to model the absorption and reflection effects of an interface without considering coupled PDE’s. Problems with boundary condition of the form math+mathmath = 0 are not self-adjoint which greatly complicates solution by spectral analysis. However, exact solutions are found with d’Alembert’s method. Solutions are also derived for a time-harmonically forced problem with internal damping and are used to investigate the effect of ultrasound in a bioreactor, particularly the amount of energy delivered to cultured cells. The concise form of the solution simplifies the analysis of acoustic field problems.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. MATHEMATICAL MODEL
    1. Justification of the dynamic boundary condition
    2. D’Alembert solution for an arbitrary forcing function and no internal damping
    3. D’Alembert solution for a time-harmonic forcing function and internal damping
    4. Extension to an arbitrary forcing function and internal damping
  3. RESULTS
    1. Applications
      1. Transient response
      2. Energy and energy dissipation
  4. CONCLUSIONS

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KEYWORDS and PACS

Keywords

absorption coefficients, biological tissues, biomechanics, biomedical ultrasonics, bioreactors, cellular biophysics, damping, reflection, spectral analysis, transient response

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3674316

PUBLICATION DATA

ISSN

0021-8979 (print)  
1089-7550 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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Figures (8) Tables (1)

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