Wave motion in a medium with a cubic nonlinearity
| Document type: | Conference Papers |
|---|---|
| Peer reviewed: | Yes |
| Full text: | |
| Author(s): | Claes Hedberg, Bengt Enflo, Oleg Rudenko |
| Title: | Wave motion in a medium with a cubic nonlinearity |
| Translated title: | Vågrörelse i ett medium med kubisk olinjaritet |
| Conference name: | 4th Polyakov Readings |
| Year: | 2006 |
| Pagination: | 65-74 |
| City: | S:t Petersburg |
| Organization: | Blekinge Institute of Technology |
| Department: | School of Engineering - Dept. Mathematics and Science (*** Error ***) School of Engineering S- 371 79 Karlskrona +46 455 38 50 00 http://www.tek.bth.se/ |
| Authors e-mail: | claes.hedberg@bth.se |
| Language: | English |
| Abstract: | An example of wave motion in a medium with a cubic nonlinearity is a transverse finite amplitude wave in an isotropic solid. The corresponding cubically nonlinear wave equation is derived with the nonlinearity expressed in terms of elastic constants. This nonlinear wave equation with dissipation is studied for standing and propagating waves. For standing waves in a resonator a simplified approach results in functional equations, from which frequency response curves are derived. These curves show the dependence of the amplitude on the difference between one of the resonator's ekgenfrequencies and the driving frequency. The frequency response curves are plotted for different values of the dissipation and are very different for quadratic and cubic nonlinearities. In the propagating wave case an N-wave evolution is studied, described by a modified Burgers' equation with a cubic nonlinearity. Approximate solutions to this equation are found for parts of the wave profile not studied in detail before. |
| Subject: | Mechanical Engineering\Structural Mechanics Mechanical Engineering\Structural Dynamics |
| Keywords: | cubic nonlinearity, nonlinear acoustic, nonlinear wave propagation |
