Standing and propagating waves in cubically nonlinear media
Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering2006 (English)In: Proceedings of the International Conference Mathematical Modelling / [ed] Nilsson, Börje, American Institute of Physics , 2006, 187-195 p.Chapter in book (Other academic)Alternative title
Stående och fortplantande vågor i ett kubiskt olinjärt medium (Swedish)
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
American Institute of Physics , 2006. 187-195 p.
IdentifiersURN: urn:nbn:se:bth-9285Local ID: oai:bth.se:forskinfo1A64513BC479B615C1257292003FBC68OAI: oai:DiVA.org:bth-9285DiVA: diva2:837079