Advanced asymptotic approaches and perturbation theory methods in the study of the mathematical model of single-frequency oscillations of a nonlinear elastic body

2020;
: pp. 269–277
https://doi.org/10.23939/mmc2020.02.269
Received: February 25, 2020
Revised: March 11, 2020
Accepted: March 31, 2020
1
Hetman Petro Sahaidachnyi National Army Academy
2
Hetman Petro Sahaidachnyi National Army Academy, Lviv Polytechnic National University
3
Lviv Polytechnic National University
4
Lviv Polytechnic National University

A combination of asymptotic methods in nonlinear mechanics with basic techniques of perturbation theory to study a mathematical model of the nonlinear oscillation system is proposed in the paper.  The system under consideration describes the torsional vibrations of an elastic body, where its elastic properties are under the nonlinear law.  The relationships presented as the ordinary differential equations are obtained due to the proposed procedure.  Therefore, the main parameters of the single-frequency oscillations and the resonance conditions can be determined.  There are proposed applications of the obtained results to the optimization problem concerning the processing equipment.

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Mathematical Modeling and Computing, Vol. 7, No. 2, pp. 269–277 (2020)