Based on the laws of classical mechanics, in particular, the law of conservation of momentum, the paper describes the developed mathematical model of signal propagation during vibration diagnostics. At the beginning, the problem of signal propagation was investigated, which was reduced to solving the problem of wave propagation. According to the analysis of experimental results investigated, that the attenuated nature of the signals must be taken into account. For this purpose, a mathematical model has been developed, which allows to solve the problem of the propagation of damped signals. Comparative analysis allows to conclude that the constructed model is adequate.
Using the basic relationships of the hereditary theory of viscoelasticity and asymptotic methods, the problem of natural oscillations of structural-inhomogeneous, multiply connected, axisymmetric shell structures is reduced to an effectively solvable mathematical problem of complex eigenvalues, in which approximate engineering methods are proposed.
The methods for solving the problems of natural vibrations of structurally inhomogeneous, multi-connected, axisymmetric shell structures based on the hereditary theory of viscoelasticity are given in the paper. Using the basic relations of the hereditary theory of viscoelasticity and asymptotic methods, the problem of natural vibrations of structurally inhomogeneous, multi-connected, axisymmetric shell structures is reduced to the effectively solvable mathematical problem of complex eigenvalues, in which approximate engineering methods are proposed.
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