Abstract
The problems of determining the variable rheological properties of functionally gradient beams from some additional information about displacements are considered. Vibrations of a cantilevered inhomogeneous viscoelastic beam are studied in the framework of two models - Euler-Bernoulli and Timoshenko. The oscillations are caused by a moment concentrated at the end of the beam, oscillating in time. Within the framework of the concept of complex modules, operator relations linking the given and desired functions are obtained. Functions reflecting the laws of change of long-term and instantaneous modules have been restored. The results of computational experiments on the restoration of functions of various types are presented.
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