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 [Formula: see text] 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.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3262849 | PMC |
| http://dx.doi.org/10.1063/1.3674316 | DOI Listing |
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