Modeling of nonsymmetrical damage in plate-like structures

A two-dimensional model for in-plane vibrations of a damped linear elastic Hookean partially clamped plate-like structure with a nonsymmetrical damage is proposed. The model includes both active and passive contributions of piezoelectric ceramic patches bonded to the surface of the structure. Both strong and weak formulations of the equations of motion are presented. The problem is then formulated as a second-order equation in time. The existence, uniqueness of the solutions, and continuity with respect to the data are discussed.