title: Forced wave motion with internal and boundary damping.
abstract: 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.
authors.forename: Tobias
authors.initials: T
authors.lastname: Louw
authors.forename: Scott
authors.initials: S
authors.lastname: Whitney
authors.forename: Anu
authors.initials: A
authors.lastname: Subramanian
authors.forename: Hendrik
authors.initials: H
authors.lastname: Viljoen