铰链处有粘性摩擦的双摆动力学。I. 运动的数学模型和时态图的构建

A. S. Smirnov, I. A. Kravchinskiy
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引用次数: 0

摘要

摘要 本文讨论了具有相同链节参数和末端载荷的双数学摆的动态行为,该摆在其两个铰链处受到粘性摩擦的影响,其耗散系数通常不同。给出了小偏差时系统运动的线性数学模型,并推导出包含两个无量纲耗散参数的特征方程。在低阻尼情况下,推导出近似分析表达式,从而可以评估和比较系统在每种振动模式下运动时的阻尼系数。当无量纲参数平面被判别曲线划分为系统运动性质不同的区域时,就会产生耗散运动状态图。我们注意到,在所考虑的系统中可能会出现耗散内部共振;我们以分析的形式确定了其存在的条件,并展示了这些条件的图解。本出版物是耗散双摆动力学研究的第一部分,其续篇将作为单独出版物 "铰链处有粘性摩擦的双摆动力学 "介绍。II.耗散振动模式和阻尼参数优化"。
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Dynamics of a Double Pendulum with Viscous Friction at the Hinges. I. Mathematical Model of Motion and Construction of the Regime Diagram

Abstract

The paper discusses the dynamic behavior of a double mathematical pendulum with identical parameters of links and end loads, which is under the influence of viscous friction at both of its hinges with generally different dissipative coefficients. A linear mathematical model of system motion for small deviations is given, and a characteristic equation containing two dimensionless dissipative parameters is derived. For the case of low damping, approximate analytical expressions are derived that make it possible to evaluate and compare with each other the damping factors during motion of the system in each of the vibration modes. A diagram of dissipative motion regimes is constructed, which arises when the plane of dimensionless parameters is divided by discriminant curves into regions with a qualitatively different character of system motion. It is noted that a dissipative internal resonance can occur in the system under consideration; the conditions for its existence are established in an analytical form, and a graphic illustration of these conditions are also displayed. This publication is the first part of the study of the dynamics of a dissipative double pendulum, the continuation of which will be presented as a separate publication “Dynamics of a Double Pendulum with Viscous Friction at the Hinges. II. Dissipative Vibration Modes and Optimization of the Damping Parameters.”

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来源期刊
CiteScore
0.70
自引率
50.00%
发文量
44
期刊介绍: Vestnik St. Petersburg University, Mathematics  is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.
期刊最新文献
Solution of the Local-Boundary-Value Problem of Control for a Nonlinear Stationary System Taking into Account Computer System Verification On the Approximation of the Attraction Field of a Rigid Body by the Attraction Field of Four Material Points of the Same Mass Rigid-Body Dynamics from the Euler Equations to the Attitude Control of Spacecraft in the Works of Scientists from St. Petersburg State University. Part 2 Regression Models for Calculating State-to-State Coefficients of the Rate of Vibrational Energy Exchanges Astronomical Research at the Mathematics Faculty of St. Petersburg University, I
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