Forced wave motion with internal and boundary damping

Tobias Louw, Scott Whitney, Anu Subramanian, Hendrik Viljoen

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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 δw/δz + α̃δw/δt = 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.

Original languageEnglish (US)
Article number014702
JournalJournal of Applied Physics
Issue number1
StatePublished - Jan 1 2012

ASJC Scopus subject areas

  • General Physics and Astronomy


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