一类二自由度非线性系统的正振方法及参数选择的证明

B. Sokil, A. Senyk, M. Sokil, A. Y. Lisnichuk
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引用次数: 0

摘要

以具有自适应动力特性的轮式车辆振动平面模型为例,提出了使悬架系统运动平顺性最大化的主要参数选择方法。为了解决这一问题,建立了弹簧部件在垂直平面上进行相对振动的数学模型。后者表示两个非线性微分方程的系统,描述了弹簧部件的质量中心的相对位移和弹簧部件绕横轴经过指定部件的质量中心的旋转角度。为了构造该方程组的近似解析解,从而描述在合理的假设条件下决定簧载部件相对位置的主要参数,采用了集中质量非线性系统的正振法。这样就有可能得到描述簧载部件振动幅频特性的一阶常微分方程组。由于对后者的分析,确定了在描述悬架系统功率特性的参数之间的一定比例下,它可以进行等时的垂直和纵向角振荡,从而可以在崎岖地形上运输乘客或危险货物时实现最大的舒适性。获得的主要结果可用于创建自适应悬浮软件产品,其有效性通过以下方式得到确认:a)通过极限,获得文献资料中已知的结果;b)基于周期ateb函数的应用,推广了构造强非线性微分方程解的广泛检验的解析方法。
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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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来源期刊
Mathematical Modeling and Computing
Mathematical Modeling and Computing Computer Science-Computational Theory and Mathematics
CiteScore
1.60
自引率
0.00%
发文量
54
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