Active cancellation of unsteady stress oscillation in a functionally graded piezoelectric thin plate subjected to impact loading

When a functionally graded material plate is subjected to impact pressure, an unsteady oscillation of dynamic stress with tensile stress is induced and thus may cause serious damage to the plate. In this paper, active cancellation of the unsteady stress oscillation through piezoelectric actuation is investigated. First, a one-dimensional electro-elastodynamic problem in a functionally graded piezoelectric thin plate subjected to impact pressure is mathematically analyzed under the assumption that material properties vary exponentially in the thickness direction. The analytical results lead to the oscillation cancelling condition that the dynamic component disappears from the mathematical expression of stress. Secondly, employing the method of characteristics, a similar electro-elastodynamic problem is numerically analyzed when material properties are assumed to vary in the thickness direction according to a power low distribution. The actuation voltages which cancel the unsteady stress oscillations for various values of the volume fraction exponent are found to be obtained by utilizing the oscillation cancelling condition derived from the mathematical analysis of the first problem. Applying the obtained results, active cancellation of the unsteady stress oscillation may be possible even in the case of another functionally graded piezoelectric thin plate.