General models describing the interactions between one or a pair of piezoceramic patches and elastic substructures consisting of a cylindrical shell, plate, or beam are presented. In each case, the contributions to the internal moments and forces due to the presence of the patches are carefully discussed. In addition to these material contributions, the input of voltage to the patches produces mechanical strains that lead to external moments and forces. These external loads depend on the

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... l properties of the patch, the geometry of patch placement, and the voltage. The internal and external moments and forces due to the patches are then incorporated into the equations of motion, which yields models describing the dynamics of the combined structure. These models are sufficiently general to allow for potentially different patch voltages, which implies that they can be suitably employed when using piezoceramic patches for controlling system dynamics when both extensional and bending vibrations are present.