Gulay Altay Askar
Dept. of Civil Eng., Bogazici Univ., Bebek, 80815 Istanbul, Turkey
M. C. Dokmeci
Istanbul Tech. Univ., P.K. 9, Taksim, 80191 Istanbul
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.