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In the article solves particular problems of the impact of non-stationary external loads on plane structural elements interacting with a deformable medium.The oscillation frequencies and their influence on the dynamic behavior of a plane element under normal load are investigated, as well as the effect of a moving load on the values of transverse displacement. When solving applied problems of oscillations of rectangular plane elements interacting with the environment, a wide class of boundary value problems of oscillations associated with various boundary conditions at the edges of a plane element arises. When taking into account non-stationary external influences, the main of the main parameters is the frequency of natural oscillations of the plane element, taking into account the deformable base, temperature, pre-tension, anisotropy and other factors.

This work proposes an effective algorithm for description of nonlinear deformation of hereditary materials based on Rabotnov’s method of isochronous creep curves. The notions have been introduced for experimental and model rheological parameters and similarity coefficients of isochronous curves. It has been shown how using them, one can find instantaneous strains at various stress levels for description of nonlinear deformation of hereditary materials at creep. Relevant equations have been determined from the nonlinear integral equation of Yu. N. Rabotnov for the application cases of Rabotnov’s fractional exponential kernel and Abel’s kernel for nonlinear deformation of hereditary materials at creep. The improved methods have been given for determination of creep parameters α, ε0, δ, β, and λ. By processing and using test results for material Nylon 6 and glass-reinforced plastic TC 8/3-250, the process has been shown for sequential implementation of the developed methods for description of linear and nonlinear deformation of these materials at creep. From the results of the experimental investigation performed by the authors of this paper, it has been determined that fine-grained, dense asphalt concrete at the temperature of 20 ± 2 °C and stresses up to 0.183 MPa at direct tension is deformed considerably in a nonlinear way. It has been shown in an illustrative way by construction of isochronous creep curves at various load durations and curves of experimental rheological parameter at various stresses. Nonlinear deformation of asphalt concrete at creep is adequately described by the proposed methods.