| Popis: |
The inverse problem of determining the piezoelectric characteristics of a functional gradient piezoceramic cylinder based on acoustic analysis of steady-state oscillations caused by a mechanical load is considered. The problem consisted in identification of unknown functions of the piezoelectric characteristics with nonuniform polarization of the cylinder in the case when the elastic moduli of unpolarized ceramics are known. As additional information, the values of the displacement function at some point of the surface of the cylinder in a given frequency range were used. To solve the inverse problem, a special approach based on projection schemes and the method of algebraization is proposed. This approach makes it possible to determine the unknown function-characteristics in the form of expansions with respect to systems of independent functions. The required coefficients of the expansions were determined from the corresponding systems of linear and nonlinear equations obtained using the weak formulation of the problem. The results of solving the inverse problem are illustrated by computational experiments. Keywords: electroelasticity, piezoceramics, functionally graded piezoelectric material, inhomogeneous cylinder, inverse problems, method of algebraization. |
