考虑外部切向载荷的杆侧摆动数学模型

IF 0.8 Q2 MATHEMATICS
I. V. Kudinov, A. V. Pashin, Yu. A. Kryukov
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引用次数: 0

摘要

摘要 在考虑到内部摩擦和外部切向谐波载荷的情况下,为一端固定的杆的横向振荡建立了数学模型。对数值计算结果的分析表明,当杆件的自然振荡频率与外部载荷频率相吻合时,就会产生共振振荡,同时杆件振荡的振幅会显著增加,但会受到摩擦系数的限制。当载荷频率接近自然振荡频率时,杆件各点的振幅会出现周期性的增大和减小,这就是分叉-扑动振荡(节拍)。当负载振荡的振幅和频率发生变化时,杆振荡以振幅-频率调制的波包形式出现。一般来说,杆振荡的振幅和频率都是无限大的。在靠近固定端的杆段,可以观察到最小振幅下的最大频率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

A Mathematical Model of Rod Lateral Oscillations Considering an External Tangential Load

A Mathematical Model of Rod Lateral Oscillations Considering an External Tangential Load

Abstract

A mathematical model has been developed for lateral oscillations of a rod fixed at one end, taking into account internal friction and external tangential harmonic loading. Analysis of the results of numerical calculations has shown that when the natural oscillation of the rod coincide with the external load frequency, resonant oscillations occur, accompanied by significant increase in the amplitude of rod oscillations, limited by the friction coefficient. At load frequencies approaching to the natural oscillation frequency, the amplitude of oscillations at each point of the rod is accompanied by periodic increase and decrease, qualifying them as bifurcation-flutter oscillations (beats). When the amplitude and frequency of the load oscillation change, the rod oscillations occur in the form of wave packets with amplitude-frequency modulation. In general, rod oscillations occur with an infinitely large number of amplitudes and frequencies. The maximum frequency at minimum amplitude is observed in sections of the rod close to the fixed end.

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来源期刊
CiteScore
1.50
自引率
42.90%
发文量
127
期刊介绍: Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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