Mindlin plate theory for damage detection: Source solutions

A consideration of the relevant length scales and time scales suggests that Mindlin plate theory provides a judicious model for damage detection. A systematic investigation of this theory is presented that emphasizes its mixed vector-scalar character and analogies with 3D elasticity. These analogies lead to the use of Helmholtz potentials, and to compact statements of the reciprocal theorem and the representation theorem. The plate response for a point moment is derived using a direct source specification, rather than an indirect specification through boundary conditions. Solutions are presented for combinations of such point moments (doublets) that represent, respectively, a center of bending, a center of twist and a center of inplane twist. The flexural response due to finite sources, such as piezoelectric actuators, can be modeled by distributions of centers of bending. Detailed results are presented for a circular, and for a narrow rectangular actuator. The far-field radiation pattern for an array of equally spaced actuators parallel to a straight boundary is derived. The solutions presented for the point moment and the point force constitute the components of a dyadic Green’s function which is required, along with its spatial derivatives, for a representation of plate-wave scattering by flexural inhomogeneities.