BFGM plate: vibration analysis, Young’s modulus and density 2D identification

The problem of steady-state in-plane vibrations of an elastic isotropic rectangular plate made of bidirectional FGM is considered. For generality of consideration, the problem statement is given in the dimensionless form. Young’s modulus, density and Poisson’s ratio are variable in two coordinates. Determination of the displacement field in the general case is carried out numerically using FEM. A detailed accuracy analysis is performed on the basis of the problem on plate’s free vibration as an example. The effect of each material parameter on the amplitude-frequency characteristic is studied. A general statement of the inverse problem on the identification of the variation in material properties based on the displacement measurements in the area of load application for a given frequency range is formulated. Three particular 2D problems on separate and joint reconstruction of Young’s modulus and density are considered. Taking into account the revealed features, the solution of these problems is constructed using the projection iterative process. The equation for finding unknown corrections is formulated for each problem. Examples of reconstruction are presented, the results obtained are discussed.