Numerical Analysis of an Inverse Elastodynamic Problem in a Functionally Graded Multiferroic Composite Thin Plate by Method of Characteristics

Abstract

This study deals with an inverse elastodynamic problem in a functionally graded thin plate composed of piezoelectric and magnetostrictive materials. All response quantities are considered to be initially zero. It is assumed that the top surface of the thin plate is fixed to a flat rigid body and the bottom surface is subjected to an unknown impact pressure and that an induced voltage between the top and bottom surfaces is known. The material properties are assumed to vary in the thickness direction according to a power low distribution. This elastodynamic problem is solved numerically by employing the method of charateristics and then the particle velocity and stress are obtained for the case where the materials at the top and bottom surfaces of the thin plate are taken to be CoFe₂O₃ and BaTiO₃ , respectively. Finally, time histories of the impact pressure and dynamic stress are presented graphically.