Linear Mechanical System Dynamics under the Influence of Additive and Multiplicative Polyharmonic High-Frequency Effects with the Non-Multiple Frequencies

Abstract

The paper assumes that in a general case each element of a system is being excited. It provides solution by the Bogolyubov method in two approximations with a slight modification. Motion is represented as the sum of the "slow" and "fast" components. Problem formalization is proposed making it possible to identify influences in the motion vector equation as the scalar elements with the matrix coefficients of a special form, which fundamentally simplified the analytical transformations. Since external influences appear to be the aperiodic processes, fast harmonics averaging over a period in the second approximation is replaced by the motion segregation, as in the first approximation. The paper shows that low-frequency oscillations could appear in the system at combination frequencies of the external influence harmonics, including the multiple ordinary and parametric resonances, as well as the constant components. The formalization used makes it possible not only to uniformly describe all the possible options in applying the load additive and multiplicative components, but also to obtain a solution to the problem posed structurally in the same form as for the scalar equation. The results are confirmed by an example, where they are compared with the solution obtained by the motion numerical simulation

Please cite this article in English as:

Tushev O.N., Kondratyev E.K. Linear mechanical system dynamics under the influence of additive and multiplicative polyharmonic high-frequency effects with the non-multiple frequencies. Herald of the Bauman Moscow State Technical University, Series Mechanical Engineering, 2024, no. 2 (149), pp. 121--133 (in Russ.). EDN: SZGJSA

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