A theory for vibrations of poroelastic shells

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...