On diagnostics of the properties of functional-gradient composites considering rheology

The solution of inverse problems on determining the variable rheological properties of functional-gradient beams using additional information about the angle of rotation of the end section is presented within the framework of the most used models: Euler–Bernoulli and Timoshenko. Within the framework of the concept of complex modules, nonlinear operator equations are obtained that connect the given and sought functions (instantaneous and long-term module, relaxation time). The solution is based on the linearization method and the formulation of an iterative process, at each step of which it is necessary to solve complex-valued boundary value problems and invert completely continuous operators with complex-valued kernels. Functions reflecting the laws of change in long-term and instantaneous modules have been restored. The results of computational experiments in some special cases are presented.