Forced wave motion with internal and boundary damping

Tobias Louw; Scott Whitney; Anu Subramanian; Hendrik Viljoen

doi:10.1063/1.3674316

Forced wave motion with internal and boundary damping

Tobias Louw, Scott Whitney, Anu Subramanian, Hendrik Viljoen

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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 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 language	English (US)
Article number	014702
Journal	Journal of Applied Physics
Volume	111
Issue number	1
DOIs	https://doi.org/10.1063/1.3674316
State	Published - Jan 1 2012

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.1063/1.3674316

Cite this

@article{dab43d7a2a2c4755a69a939a95fef076,

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 δw/δz + {\~α}δw/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.",

author = "Tobias Louw and Scott Whitney and Anu Subramanian and Hendrik Viljoen",

note = "Funding Information: This work was supported, in part, by the American Recovery and Reinvestment Act of 2009 research grant 1R21RR024437-01A1 from the Department of Health and Human Services.",

year = "2012",

month = jan,

day = "1",

doi = "10.1063/1.3674316",

language = "English (US)",

volume = "111",

journal = "Journal of Applied Physics",

issn = "0021-8979",

publisher = "American Institute of Physics",

number = "1",

}

TY - JOUR

T1 - Forced wave motion with internal and boundary damping

AU - Louw, Tobias

AU - Whitney, Scott

AU - Subramanian, Anu

AU - Viljoen, Hendrik

N1 - Funding Information: This work was supported, in part, by the American Recovery and Reinvestment Act of 2009 research grant 1R21RR024437-01A1 from the Department of Health and Human Services.

PY - 2012/1/1

Y1 - 2012/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84855937991&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84855937991&partnerID=8YFLogxK

U2 - 10.1063/1.3674316

DO - 10.1063/1.3674316

M3 - Article

C2 - 22271934

AN - SCOPUS:84855937991

SN - 0021-8979

VL - 111

JO - Journal of Applied Physics

JF - Journal of Applied Physics

IS - 1

M1 - 014702

ER -

Forced wave motion with internal and boundary damping

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this