Nonlinear standing waves in a closed tub
Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering2002 (English)Conference paper (Refereed) PublishedAlternative title
Olinjärå stående vågor i en sluten tub (Swedish)
Simplified nonlinear evolution equations describing nonsteady-state forced vibrations in an acoustic resonator having one closed end and the other end periodically oscillating are derived. An approach is used based on a nonlinear functional equation. This approach is shown to be equivalent to the version of the successive approximation method developed in 1964 by Chester. It is explained how the acoustic field in the cavity is described as a sum of counterpropagating waves with no cross-interaction. The nonlinear Q-factor and the nonlinear frequency response of the resonator are calculated for steady-state oscillations of both inviscid and dissipative media. The general expression for the mean intensity of the acoustic wave in terms of the characteristic value of a Mathieu function is derived. Some results from a perturbation calculation of the wave profile are given.
Place, publisher, year, edition, pages
nonlinear standing waves, acoustic resonator, nonlinear Q-factor
IdentifiersURN: urn:nbn:se:bth-9278Local ID: oai:bth.se:forskinfo37044192C3152928C12572990050579BOAI: oai:DiVA.org:bth-9278DiVA: diva2:837072
International Conference Mathematical Modelling of Wave Phenomena 3-8 November