用强迫对抗自由振动:第二部分——阻尼振动和衰减强迫

IF 12.2 1区 工程技术 Q1 MECHANICS
L. Campos, Manuel J. S. Silva
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引用次数: 0

摘要

本论文分两部分讨论了最简单阻尼连续系统的主动振动抑制,即弹性弦的横向振动,具有恒定的张力和单位长度的质量密度,摩擦力与速度成正比,由电报或波扩散方程描述,在两个互补部分。最初的第一部分考虑了非共振和共振力,通过集中的点力或独立于时间的连续力分布,在没有阻尼的情况下,在强迫和自由振荡之间存在相移,在这种情况下,强迫电报方程简化为强迫经典波动方程。当前和最后的第二部分使用强迫波扩散方程来模拟阻尼的影响,作为振幅衰减和时间相移,对于单点力的非谐振和谐振强迫,以恒定的幅度或以任意速率指数衰减。假设有一个两端固定的有限弹性弦,自由振荡在时空上是(i)正弦模式,由于阻尼的作用,时间上呈指数衰减。施加频率与固有频率不同的非共振强迫振荡在时空中也是正弦的,具有恒定的振幅和相移,使得施加的力的功平衡了耗散。对于施加频率等于固有频率的共振强迫,时空中的正弦振荡具有(iii)恒定的振幅和π/2的相移。在这两种情况下,(ii)非共振或(iii)共振强迫在一段时间后主导了衰减的自由振荡。即使通过优化强迫以最小化振荡的总能量,它仍然低于自由振荡的能量,但只是在很短的时间内-通常是周期的一小部分。一种更有效的对抗阻尼自由振荡的方法是使用振幅随时间呈指数衰减的强迫;通过适当选择相对于自由阻尼的强迫衰减,可以将振荡总能量在所有时间内降低到不超过自由振荡能量的1/16。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the Countering of Free Vibrations by Forcing: Part II—Damped Oscillations and Decaying Forcing
The present two-part paper concerns the active vibration suppression for the simplest damped continuous system, namely the transverse oscillations of an elastic string, with constant tension and mass density per unit length and friction force proportional to the velocity, described by the telegraph or wave-diffusion equation, in two complementary parts. The initial part I considers non-resonant and resonant forcing, by concentrated point forces or continuous force distributions independent of time, with phase shift between the forced and free oscillations, in the absence of damping, in which case the forced telegraph equation reduces to the forced classical wave equation. The present and final part II uses the forced wave-diffusion equation to model the effect of damping, both as amplitude decay and phase shift in time, for non-resonant and resonant forcing by a single point force, with constant magnitude or magnitude decaying exponentially in time at an arbitrary rate. Assuming a finite elastic string fixed at both ends, the free oscillations are (i) sinusoidal modes in space-time with exponential decay in time due to damping. The non-resonant forced oscillations at an applied frequency distinct from a natural frequency are also (ii) sinusoidal in space-time, with constant amplitude and a phase shift such that the work of the applied force balances the dissipation. For resonant forcing at an applied frequency equal to a natural frequency, the sinusoidal oscillations in space-time have (iii) a constant amplitude and a phase shift of π/2. In both cases, the (ii) non-resonant or (iii) resonant forcing dominates the decaying free oscillations after some time. Even by optimizing the forcing to minimize the total energy of oscillation, it remains below the energy of the free oscillation alone, but only for a short time—generally a fraction of the period. A more effective method of countering the damped free oscillations is to use forcing with amplitude decaying exponentially in time; by suitable choice of the forcing decay relative to the free damping, the total energy of oscillation over all time can be reduced to no more than 1/16th of the energy of the free oscillation.
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来源期刊
CiteScore
28.20
自引率
0.70%
发文量
13
审稿时长
>12 weeks
期刊介绍: Applied Mechanics Reviews (AMR) is an international review journal that serves as a premier venue for dissemination of material across all subdisciplines of applied mechanics and engineering science, including fluid and solid mechanics, heat transfer, dynamics and vibration, and applications.AMR provides an archival repository for state-of-the-art and retrospective survey articles and reviews of research areas and curricular developments. The journal invites commentary on research and education policy in different countries. The journal also invites original tutorial and educational material in applied mechanics targeting non-specialist audiences, including undergraduate and K-12 students.
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