Adaptive control of an unsteady stress oscillation in a functionally graded multiferroic composite thin plate

Abstract

An unsteady stress oscillation is known to be caused in a functionally graded material (FGM) thin plate by the action of impact loading. Since the stress then changes alternately and intensively from compression to tension as time advances, it may lead to serious damage to the FGM thin plate. Therefore, the development of an analytical model for control of the dynamic stress adapted to the action of impact loading is required. In this paper, adaptive control of an unsteady stress oscillation is investigated for a functionally graded multiferroic composite (FGMC) thin plate subjected to uniform impact pressure. Material properties of the FGMC thin plate are assumed to vary in the thickness direction according to a power law distribution. This elastodynamic problem is analyzed under the assumption that the volume fraction exponent and uniform impact pressure are unknown, whereas a piezoelectric voltage is measured across the thin plate during the first cycle of the oscillation. The magnitudes of the unknown exponent and pressure as well as an appropriate magnetic potential difference for control of the unsteady stress oscillation are considered to be determined within the period of the second cycle from knowledge on the basis of the measured piezoelectric voltage. Finally, numerical calculations have been carried out for the case where the appropriate magnetic potential difference is applied to the FGMC thin plate from the third cycle. Obtained results demonstrate that the maximum amplitude of the controlled unsteady stress oscillation is successfully reduced by about 46% and the performance of the adaptive control is monitored through the piezoelectric sensing. In consequence, the analytical model for adaptive control and monitoring of the unsteady stress oscillation has been proposed.