Nonlinear Standing Waves in a Layer Excited by the Periodic Motion of its Boundary
Blekinge Institute of Technology, Department of Mechanical Engineering2002 (English)Conference paper (Refereed) PublishedAlternative title
Ickelinjära stånde vågor i ett skikt med periodisk rörelse av dess vägg (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. The process of development of a standing wave is described analytically for three different types of periodic motion of the wall: harmonic excitation, sawtooth-shaped motion and "inverse saw motion".
Place, publisher, year, edition, pages
Moscow, Russia, 2002.
acoustic resonator, nonlinear standing waves, resonator shock waves, nonlinear Q-factor, acoustic sawtooth waves
IdentifiersURN: urn:nbn:se:bth-9854Local ID: oai:bth.se:forskinfo802346F87BFB8E19C1256C2A004CBC0EOAI: oai:DiVA.org:bth-9854DiVA: diva2:837820
Proceedings of 16th International Symposium of Nonlinear Acoustics, August 19-23, 2002, Moscow