Standing and propagating waves in cubically nonlinear media
2006 (English)In: Mathematical Modeling of Wave Phenomena / [ed] Nilsson, B; Fishman, L, MELVILLE, NY: AMER INST PHYSICS , 2006, Vol. 834, 187-195 p.Conference paper (Refereed)
The paper has three parts. In the first part a cubically nonlinear equation is derived for a transverse finite-amplitude wave in an isotropic solid. The cubic nonlinearity is expressed in terms of elastic constants. In the second part a simplified approach for a resonator filled by a cubically nonlinear medium results in functional equations. The frequency response shows the dependence of the amplitude of the resonance on the difference between one of the resonator's eigenfrequencies and the driving frequency. The frequency response curves are plotted for different values of the dissipation and differ very much for quadratic and cubic nonlinearities. In the third part a propagating N-wave is studied, which fulfils a modified Burgers' equation with a cubic nonlinearity. Approximate solutions to this equation are found for new parts of the wave profile.
Place, publisher, year, edition, pages
MELVILLE, NY: AMER INST PHYSICS , 2006. Vol. 834, 187-195 p.
, AIP CONFERENCE PROCEEDINGS, ISSN 0094-243X ; 834
cubic nonlinear media, nonlinear acoustic resonator, cubic resonator, N-wave propagation
IdentifiersURN: urn:nbn:se:kth:diva-41955DOI: 10.1063/1.2205802ISI: 000237610000019ScopusID: 2-s2.0-33845586974ISBN: 0-7354-0325-2OAI: oai:DiVA.org:kth-41955DiVA: diva2:445773
2nd Conference on Mathematical Modeling of Wave Phenomena. Vaxjo, SWEDEN. AUG 14-19, 2005
QC 201110052011-10-052011-10-042011-10-05Bibliographically approved