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首页> 外文会议>ASME international mechanical engineering congress and exposition >A NEW INCREMENTAL HARMONIC BALANCE METHOD WITH TWO TIME SCALES FOR QUASI-PERIODIC MOTIONS OF AN AXIALLY MOVING BEAM WITH INTERNAL RESONANCE UNDER SINGLE-TONE EXTERNAL EXCITATION
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A NEW INCREMENTAL HARMONIC BALANCE METHOD WITH TWO TIME SCALES FOR QUASI-PERIODIC MOTIONS OF AN AXIALLY MOVING BEAM WITH INTERNAL RESONANCE UNDER SINGLE-TONE EXTERNAL EXCITATION

机译：单轴外部激励下具有内部共振的轴运动梁准周期运动的两个时间尺度增量调和新方法

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摘要

In this work, a new incremental harmonic balance (IHB) method with two time scales, where one is a fundamental frequency, and the other is an interval distance of two adjacent frequencies, is proposed for quasi-periodic motions of an axially moving beam with three-to-one internal resonance under single-tone external excitation. It is found that the interval frequency of every two adjacent frequencies, located around the fundamental frequency or one of its integer multiples, is fixed due to nonlinear coupling among resonant vibration modes. Consequently, only two time scales are used in the IHB method to obtain all incommensurable frequencies of quasi-periodic motions of the axially moving beam. The present IHB method can accurately trace from periodic responses of the beam to its quasi-periodic motions. For periodic responses of the axially moving beam, the single fundamental frequency is used in the IHB method to obtain solutions. For quasi-periodic motions of the beam, the present IHB method with two time scales is used, along with an amplitude increment approach that includes a large number of harmonics, to determine all the frequency components. All the frequency components and their corresponding amplitudes, obtained from the present IHB method, are in excellent agreement with those from numerical integration using the fourth-order Runge-Kutta method.
机译：在这项工作中，提出了一种新的具有两个时标的增量谐波平衡（IHB）方法，其中一个是基频，另一个是两个相邻频率的间隔距离，用于轴向运动梁的准周期运动。单音外部激励下的三对一内部共振。发现由于共振振动模式之间的非线性耦合，位于基频或其整数倍之一附近的每两个相邻频率的间隔频率是固定的。因此，在IHB方法中仅使用两个时标来获得轴向移动梁的所有准周期运动的不可估量的频率。本发明的IHB方法可以准确地跟踪光束从其周期性响应到准周期运动的过程。对于轴向移动梁的周期性响应，在IHB方法中使用单个基频来获得解。对于光束的准周期性运动，使用具有两个时标的当前IHB方法以及包括大量谐波的幅度增量方法来确定所有频率分量。从当前的IHB方法获得的所有频率分量及其相应的幅度与使用四阶Runge-Kutta方法进行数值积分获得的频率分量及其相应的幅度非常一致。

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