A standing acoustic wave with shocks in a cubically nonlinear medium
2008 (English)In: NONLINEAR ACOUSTICS FUNDAMENTALS AND APPLICATIONS / [ed] Enflo, BO; Hedberg, CM; Kari, L, 2008, Vol. 1022, 263-266 p.Conference paper (Refereed)
It is well known that transversal elastic waves in homogeneous solids satisfy a wave equation with a cubic nonlinearity. This equation with resonator boundary conditions can be transformed into a functional equation, which can be reduced to a second order partial differential equation with a cubic nonlinearity. From this equation, by specializing to steady state and integrating one step, we obtain a first order ordinary differential equation with three terms in addition to the derivative: a cubic and a linear term in the dependent variable and a known term (sinus). The coefficient of the derivative is proportional to the dissipation and assumed to be small. Among several cases the most complicated case, the coefficient of the linear term lying between zero and (0.5) (2/3) = 0.63, is treated in this paper. In each period the solution has two shocks. At one side of each shock it is necessary to introduce an intermediate boundary layer between the outer region and the inner region next to the shock. The intermediate solution is matched both outwards and inwards. The actual first order ordinary differential equation is also solved numerically both in the outer region and in the neighborhood of the shocks.
Place, publisher, year, edition, pages
2008. Vol. 1022, 263-266 p.
, AIP CONFERENCE PROCEEDINGS, ISSN 0094-243X ; 1022
cubic nonlinear media, nonlinear acoustic resonator, shocks
Fluid Mechanics and Acoustics
IdentifiersURN: urn:nbn:se:kth:diva-38618DOI: 10.1063/1.2956203ISI: 000257236700061ScopusID: 2-s2.0-49149091800ISBN: 978-0-7354-0544-8OAI: oai:DiVA.org:kth-38618DiVA: diva2:450960
18th International Symposium on Nonlinear Acoustics, Stockholm, SWEDEN, JUL 07-10, 2008
QC 201110242011-10-242011-08-312011-10-24Bibliographically approved