Vol'nikov Mikhail Ivanovich, Candidate of engineering sciences, associate professor, sub-department of automation and control, Penza State Technological University (1a/11 Baydukova lane/Gagarina street, Penza, Russia), E-mail: firstname.lastname@example.org
Smogunov Vladimir Vasil'evich, Doctor of engineering sciences, professor, sub-department of theoretical and applied mechanics and graphics, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: email@example.com
Background. The lack of an unified theory for describing dynamic processes with friction in heterogeneous structures requires the creation of nonlinear mathematical models that take into account various factors affecting the dynamics of heterostructures. Obtaining adequate models of the dynamics of heterostructures with friction is an important task for modeling the dissipative properties of structures under vibro-shock effects. The aim of the work is to study mathematical models of the dynamics of heterostructures with friction to obtain an adequate description of the models and their further use in research, to identify the dependences of internal friction in heterostructures on external factors.
Materials and methods. It is proposed to use the hypothesis of complex stiffness and internal friction to obtain a mathematical description of the dynamics of heterostructures with friction, taking into account the influence of external factors on the change in the stiffness of structures. Methods of mathematical modeling were used to prove the adequacy of the models.
Results. Mathematical models of dynamic processes in heterogeneous structures are developed. The hypotheses of complex stiffness and internal friction are used. Presented the results of mathematical modeling. Recommendations on the use of mathematical models in modeling depending on external disturbances are presented.
Conclusion. In a wide range of frequencies, it is advisable to use the model of complex stiffness, as the most adequate. It is necessary to take into account the influence of external factors on the coefficient of friction, such as temperature, frequency, strain amplitudes and stresses, etc.
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