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

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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Mathematical Modeling and Computing, Vol. 10, No. 3, pp. 927–934 (2023)