Acta Scientiarum Polonorum

Abstract: The work deals with the problem of dynamics of bodies made of smart materials in which a characteristic, deterministic and microstructural construction has an influence on the macroscopic properties of the entire system. In particular, the subject of the analysis is the annular plate made of a material with functionally graded properties (FGM). On the microstructural level the structure is constructed from two materials. In the circular direction the structure is periodic. In the radial direction the averaged properties of the structure are functionally variable. The study examined the issue of forced damped vibration. The starting point of discussion is the equation of motion of a thin plate based on Kirchhoff theory. Recently, the outcome of the modeling has been obtained as a partial differential equation for the unknown slowly varying function w⁰. This equation, as opposed to output equations of motion with discontinuous and highly oscillating coefficients, has smooth slowly varying coefficients. Hence, they can be solved easily by numerical methods because of its slowly varying coefficient. Moreover, the study shows the exemplary solutions of model equations for the asymptotic model. There is determined the form of the first symmetrical mode shapes for a sample set task parameters and selected the initial-boundary conditions.