On the Linear Intrinsic Dynamics of Thin Shells

Equations for the linear intrinsic dynamics of shells are presented and discussed. The variables in the proposed method are the six strain measures (½ × incremental metric and incremental curvature tensors of the reference surface). Two versions are presented. In the “compatibility version”, the field equations are: (a) expressions for the three extensional strain-accelerations in terms of the stress resultants and loads, and (b) the three incremental Gauss and Codazá-Mainardi compatibility equations of the reference surface. Constitutive relations are appended to complete the formulation. In the “rate version”, the field equations are expressions for the six strain-accelerations (extensional and bending) in terms of the stress-resultants and loads. Equivalence to the “compatibility version” is shown, provided that the initial conditions are satisfied. Two examples are given. In the first, specialization is made to the case of circular cylindrical shells. In the second, an inplane vibration problem of a rectangular plate is studied.