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Resonant properties of a nonlinear dissipative layer excited by a vibrating boundary: Q-factor and frequency response
KTH, School of Engineering Sciences (SCI), Mechanics.
2005 (English)In: Journal of the Acoustical Society of America, ISSN 0001-4966, E-ISSN 1520-8524, Vol. 117, no 2, 601-612 p.Article in journal (Refereed) Published
Abstract [en]

Simplified nonlinear evolution equations describing non-steady-state forced vibrations in an acoustic resonator having one closed end and the other end periodically oscillating are derived. An approach based on a nonlinear functional equation is used. 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 on the base of exact nonlinear solutions for different laws of periodic motion of the wall. For harmonic excitation the wave profiles are described by Mathieu functions, and their mean energy characteristics by the corresponding eigenvalues. The sawtooth-shaped motion of the boundary leads to a similar process of evolution of the profile, but the solution has a very simple form. Some possibilities to enhance the Q-factor of a nonlinear system by suppression of nonlinear energy losses are discussed.

Place, publisher, year, edition, pages
2005. Vol. 117, no 2, 601-612 p.
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-37911DOI: 10.1121/1.1828548ISI: 000226986900014Scopus ID: 2-s2.0-13544260589OAI: oai:DiVA.org:kth-37911DiVA: diva2:435604
Note
QC 20110819Available from: 2011-08-19 Created: 2011-08-19 Last updated: 2017-12-08Bibliographically approved

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