On the problem of analyzing the linear mechanical system dynamic behavior exposed to the high-frequency action
Authors: Tushev O.N., Kondratyev E.K.
Published in issue: #4(148)/2024
DOI: 10.18698/2308-6033-2024-4-2347
Category: Mechanics | Chapter: Theoretical Mchanics, Machine Dynamics
The paper considers a problem of analyzing the linear multidimensional system dynamics exposed to action of the additive and parametric sinusoidal high-frequency components with the aliquant frequencies. In accordance with the N.N. Bogolyubov method, solution is presented as superposition of the slow and fast components with the external influence frequencies; two approximations are studied. Since external influence is practically aperiodic in general due to the frequencies non-multiplicity, the high-frequency harmonics averaging over a period in the second approximation is replaced by the motion repeated segregation into the slow and fast. It is shown that parametric component causes an increase in the system rigidity, which somewhat transforms the natural frequencies. Due to the aliquant frequencies in the system, low-frequency oscillations arise at the combination frequency equal to the difference in additive and parametric component frequencies. Thus, resonant modes are possible in the system. If the frequencies are equal, a constant component appears in the solution. Solution is obtained in the analytical vector form, which is convenient in the analysis. The results are illustrated with an example.
EDN ZEUNVC
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