Nonlinear Standing Waves in a Layer Excited by the Periodic Motion of its Boundary

Document type: Conference Papers
Peer reviewed: Yes
Full text:
Author(s): Bengt Enflo, Oleg Rudenko, Claes Hedberg
Title: Nonlinear Standing Waves in a Layer Excited by the Periodic Motion of its Boundary
Translated title: Ickelinjära stånde vågor i ett skikt med periodisk rörelse av dess vägg
Conference name: Proceedings of 16th International Symposium of Nonlinear Acoustics, August 19-23, 2002, Moscow
Year: 2002
City: Moscow, Russia
Organization: Blekinge Institute of Technology
Department: Dept. of Mechanical Engineering (Institutionen för maskinteknik)
Dept. of Mechanical Engineering S-371 79 Karlskrona
+46 455 38 50 00
Authors e-mail:
Language: English
Abstract: 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".
Subject: Mechanical Engineering\Structural Dynamics
Mechanical Engineering\General
Keywords: acoustic resonator, nonlinear standing waves, resonator shock waves, nonlinear Q-factor, acoustic sawtooth waves