Non-linear normal forms of forced oscillations of piecewise linear systems at super-harmonic resonances

Uspenskiy, B.; Аврамов, К. В.; Nikonov, O. V.

doi:10.15407/pmach2017.04.024

Cited by 1 publication

(2 citation statements)

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“…The solution of the nonlinear system of differential equations (4) will be sought using the method of normal oscillations [23][24][25][26][27][28]. According to its main idea, the unknown functions ϕ(t) and z(t) must be connected by the relation z(t) = λϕ(t).…”

Section: Investigation Resultsmentioning

confidence: 99%

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Method of normal oscillations and substantiation of the choice of parameters for certain nonlinear systems with two degrees of freedom

Sokil,

Senyk,

Sokil

et al. 2023

Math. Model. Comput.

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On the example of the plane model of wheeled vehicle oscillations with adaptive power characteristic of the suspension system, the methodology for selecting its main parameters that would maximize the movement smoothness is developed. To solve this problem, the mathematical model of relative oscillations of the sprung part is constructed, provided that they are carried out in the vertical plane. The latter represents the system of two nonlinear differential equations describing the relative displacement of the center of mass of the sprung part and the angle of rotation of the latter around the transverse axis passing through the center of mass of the specified part. To construct the approximate analytical solution of this equations system, and thus to describe the main parameters that determine the relative position of the sprung part under reasonable assumptions, the method of normal oscillations of nonlinear systems with concentrated masses is used. This made it possible to obtain the system of ordinary differential equations of the first order that describe the amplitude–frequency characteristics of the sprung part vibrations. Due to the analysis of the latter it is determined that at a certain ratio between the parameters describing the power characteristics of the suspension system, it can perform isochronous vertical and longitudinal–angular oscillations, and thus it is possible to achieve maximum comfort in transporting passengers or dangerous cargo over rough terrain. The main obtained results can be used to create the software product for adaptive suspension, and their validity is confirmed by: a) in passing to the limit, obtaining results known from literary sources; b) generalization, based on the use of periodic Ateb-functions, of widely tested analytical methods for constructing solutions of differential equations with strong nonlinearity.

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Section: Investigation Resultsmentioning

confidence: 99%

“…The structure of these equations is the same. In addition, from the methodologies for obtaining them and the condition of normal sprung part oscillations, their solutions are expressed [26] through periodic Ateb functions [29,30] by the following dependence…”

Section: Investigation Resultsmentioning

confidence: 99%