Asymptotics and spectral properties of the acoustic vibrations of a body perforated by narrow channels. (English) Zbl 0616.76094

Fleury, Françoise; Sanchez-Palencia, Enrique

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.

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