### ASA 127th Meeting M.I.T. 1994 June 6-10

## 5pSA6. A theory for vibrations of poroelastic shells.

**Gulay Altay Askar
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*Dept. of Civil Eng., Bogazici Univ., Bebek, 80815 Istanbul, Turkey
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**M. C. Dokmeci
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*Istanbul Tech. Univ., P.K. 9, Taksim, 80191 Istanbul
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Only a few investigations concerning the analysis of poroelastic
structures are directed toward solutions of specific problems [e.g., L. A.
Taber, Int. J. Solids Structures 29, 3125--3143 (1992), and references
therein]. This paper addresses the derivation of a linear theory for vibrations
of poroelastic shells. The three-dimensional fundamental equations of
poroelastic media are expressed in variational form [cf. L. Dormieux and C.
Stolz, C. R. Acad. Sci. 315(II), 407--412 (1992)]. The variational fundamental
equations are obtained from the principle of virtual work through Friedrich's
transformation [M. C. Dokmeci, IEEE Trans. Ultrason. Ferroelec. Freq. Control
UFFC-35, 775--787 (1988) and 37, 369--385 (1990)]. The two-dimensional theory
of poroelastic shells is deduced from the variational equations using Mindlin's
method of reduction for the case when the fluid--solid coupling is included
through Biot's consolidation theory and the field quantities are taken to vary
linearly across the shell thickness. The shear deformable linear theory
accommodates the extensional, thickness, flexural, and coupled vibrations of
poroelastic shells. Specialization in geometry, material properties, and
vibrations is considered, the uniqueness of solutions is examined, and also, a
numerical algorithm that is based on the method of moments is described for the
vibrations of poroelastic shells.