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This paper is concerned with mathematical aspects of modelling vibration of a plate with piezoelectric actuators. Particularly, a thin Kirchho Love plate with arbitrary shaped actuators (e.g. triangles, parallelograms, discs) is considered. The moments that act upon a structure and are induced by piezoelectric actuators, are described by the generalized tensor product of a distribution and distribution-valued function. Finally, the formula for the solution of the Cauchy problem in the class of absolutely continuous tempered distribution-valued functions is derived.

Analytical Solution of the Problem of Vibration of Plates with Piezoelectric Actuators with Arbitrary Shape in Distribution Formulation