Fleury, Françoise; Sanchez-Palencia, Enrique Asymptotics and spectral properties of the acoustic vibrations of a body perforated by narrow channels. (English) Zbl 0616.76094 Bull. Sci. Math., II. Sér. 110, 149-176 (1986). Using homogenization asymptotic techniques, we study the acoustic vibrations of a gas contained in narrow channels hollowed in a solid body (and maybe some outer region surrounding the body). Only solutions depending on time by the factor exp(-i\(\omega\) t) are considered. The homogenized equations describing the asymptotics of the phenomena are not elliptic, as only derivatives in the direction of the channels appear. In the non-dissipative case, the associated operator is self-adjoint; according to the geometric configuration, it may exhibit eigenvalues with finite or infinite multiplicity or a continuous spectrum. The boundary conditions and the corresponding boundary layers between the body and the outer fluid are studied. Cited in 10 Documents MSC: 76Q05 Hydro- and aero-acoustics 76N99 Compressible fluids and gas dynamics Keywords:homogenization asymptotic techniques; acoustic vibrations; narrow channels; solid body; homogenized equations; eigenvalues; multiplicity; continuous spectrum; boundary conditions; boundary layers PDF BibTeX XML Cite \textit{F. Fleury} and \textit{E. Sanchez-Palencia}, Bull. Sci. Math., II. Sér. 110, 149--176 (1986; Zbl 0616.76094) OpenURL