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通过引入一维线性阻尼振子基本积分来构造其他第一积分, 包括不含时的积分. 将这种方法推广到多维情形, 构造二维和n维线性阻尼振子不同形式的第一积分; 证明不同类型的二维线性阻尼振子都存在三个独立的不含时的第一积分, n维线性阻尼振子存在2n-1个独立的不含时的第一积分. 利用变量变换将线性阻尼振子的第一积分变换成简谐振子形式的第一积分.
关键词:
线性阻尼振子
第一积分
基本积分
简谐振子 相似文献
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本文讨论了有质量弹簧的弹簧振子的动力学,运用哈密顿函数解出了振子的运动方程,并推导出振动周期与弹簧质量和阻尼的关系. 相似文献
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运用跃变旋转矢量法,即通过旋转矢量的起点、长度和相位的变化规律对受到空气弱阻尼作用和滑动摩擦力作用的弹簧振子的振动进行了研究.讨论了在滑动摩擦力作用下空气阻尼为临界阻尼和欠阻尼情况下的弹簧振子的运动,根据阻尼和初值情况得出不同的振动曲线.并对弹簧振子4种相图和相图旋转矢量进行了比较. 相似文献
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利用一种直接方法将阻尼谐振动微分方程变换成等价的自伴随形式,并构造出阻尼振子的两个拉格朗日函数和哈密顿函数,导出了阻尼谐振子的Noether守恒量. 相似文献
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阻尼振幅究竟如何衰减 总被引:1,自引:0,他引:1
弹簧振子的阻尼振动是一种重要的振动模型。如果阻尼系数为v,振子速度为v,则在阻尼力(-vv)作用下,振子的位移x随时间t的变化为其中阻尼振动的圆频率。 低于 无阻尼时的圆频率ω0.阻尼因子是振子质量),它满足低阻尼条件初位相,众所周知,阻尼振动不是严格意义上的周期性运动,不过我们仍把振子所能达到的最大距离称作振幅,只是能量的消耗使之衰减.然而几乎所有的教科书都认为(1)式中的A0是阻尼振幅衰减的起始值,并认为阻尼振幅按A0e-BT方式衰减①。按此意画成的与(1)式对应的位移-时间曲线就如(图一),其中虚线为A。e-’‘,表示振… 相似文献
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F. Badrakhan 《Journal of sound and vibration》1985,100(2):243-255
The effects of combined viscous with Coulomb damping, Reid damping and bilinear hysteretic damping on the free motion of an oscillator are studied directly by integration of the differential equations of motion and by the use of first integrals for the first time. The amplitude decay during the free motion is considered in order to separate and determine the various types of damping. 相似文献
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M. Gitterman 《Journal of statistical physics》2012,146(1):239-243
We consider an oscillator with a random mass for which the particles of the surrounding medium adhere to the oscillator for
some random time after the collision (Brownian motion with adhesion for a harmonically bound particle). This is another form
of a stochastic oscillator, different from oscillator usually studied that is subject to a random force or having random frequency
or random damping. Calculation of the first two stationary moments shows that for white multiplicative noise of week strength
the second moment coincides with that of usual Brownian motion, but for symmetric dichotomous noise, the second moment may
appear the same type of the “energetic” instability, which exists for white noise random frequency or damping coefficient. 相似文献
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The Brownian motion of the Duffing oscillator is analyzed in the case when the oscillator damping is small compared with its frequency, whereas the nonlinearity may be arbitrary. The expressions for the time-correlation functions of coordinates are obtained in an explicit form. If the nonlinearity is small, the dynamics of the system is shown to be determined by a relation between the frequency straggling due to fluctuations of the amplitude and damping. At large nonlinearity the correlators do not depend on the damping. The frequency dependences of the spectral representations of the correlators of coordinates are investigated for various ratios between the oscillator parameters. 相似文献
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It is well known that the power absorbed by a linear oscillator when excited by white noise base acceleration depends only on the mass of the oscillator and the spectral density of the base motion. This places an upper bound on the energy that can be harvested from a linear oscillator under broadband excitation, regardless of the stiffness of the system or the damping factor. It is shown here that the same result applies to any multi-degree-of-freedom nonlinear system that is subjected to white noise base acceleration: for a given spectral density of base motion the total power absorbed is proportional to the total mass of the system. The only restriction to this result is that the internal forces are assumed to be a function of the instantaneous value of the state vector. The result is derived analytically by several different approaches, and numerical results are presented for an example two-degree-of-freedom-system with various combinations of linear and nonlinear damping and stiffness. 相似文献
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In this paper an Euler–Bernoulli model has been used for vibration analysis of micro-beams with large transverse deflection. Thermoelastic damping is considered to be the dominant damping mechanism and introduced as imaginary stiffness into the equation of motion by evaluating temperature profile as a function of lateral displacement. The obtained equation of motion is analyzed in the case of pure single mode motion by two methods; nonlinear normal mode theory and the Galerkin procedure. In contrast with the Galerkin procedure, nonlinear normal mode analysis introduces a nonconventional nonlinear damping term in modal oscillator which results in strong damping in case of large amplitude vibrations. Evaluated modal oscillators are solved using harmonic balance method and tackling damping terms introduced as an imaginary stiffness is discussed. It has been shown also that nonlinear modal analysis of micro-beam with thermoelastic damping predicts parameters such as inverse quality factor, and frequency shift, to have an extrema point at certain amplitude during transient response due to the mentioned nonlinear damping term; and the effect of system?s characteristics on this critical amplitude has also been discussed. 相似文献
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Using the Langevin equations, we calculated the stationary second-order moment (mean-square displacement) of a stochastic harmonic oscillator subject to an additive random force (Brownian motion in a parabolic potential) and to different types of multiplicative noise (random frequency or random damping or random mass). The latter case describes Brownian motion with adhesion, where the particles of the surrounding medium may adhere to the oscillator for some random time after the collision. Since the mass of the Brownian particle is positive, one has to use quadratic (positive) noise. For all types of multiplicative noise considered, replacing linear noise by quadratic noise leads to an increase in stability. 相似文献
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In addition to the case usually considered of a stochastic harmonic oscillator subject to an external random force (Brownian motion in a parabolic potential) or to a random frequency and random damping, we consider an oscillator with random mass subject to an external periodic force, where the molecules of a surrounding medium, which collide with a Brownian particle are able to adhere to the oscillator for a random time, changing thereby the oscillator mass. The fluctuations of mass are modelled as trichotomous noise. Using the Shapiro–Loginov procedure for splitting the correlators, we found the first two moments. It turns out that the second moment is a non-monotonic function of the characteristics of noise and periodic signal, and for some values of these parameters, the oscillator becomes unstable. 相似文献
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研究了有界噪声与谐和激励作用下的Duffing-Rayleigh振子的动力学行为.首先运用随机Melnikov过程方法得到系统出现混沌的条件,结果表明随着非线性阻尼参数的增加系统会从混沌运动到周期运动,随着Wiener过程强度参数的增加,系统由混沌进入周期的临界幅值会先递增后不变.最后,用两类数值方法即最大Lyapunov指数与Poincare截面验证了上述结果.
关键词:
有界噪声
随机Melnikov过程
混沌运动
周期运动 相似文献
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针对黏性介质引起的Brown粒子质量存在随机涨落以及阻尼力对历史速度具有记忆性等问题, 本文首次提出分数阶质量涨落谐振子模型, 以考察黏性介质中Brown粒子的动力学特性. 首先, 将Shapiro-Loginov 公式分数阶化, 使之适用于对含指数关联随机系数的分数阶随机微分方程的求解. 然后, 利用随机平均法和分数阶Shapiro-Loginov公式推导系统稳态响应振幅的解析表达式, 并据此研究系统的共振行为; 最后, 通过仿真实验验证理论结果的可靠性. 研究表明: 1)质量涨落噪声可诱导系统产生随机共振行为; 2)记忆性阻尼力可诱导系统产生参数诱导共振行为; 3)不同参数条件下, 系统表现出单峰共振、双峰共振等多样化的共振形式.
关键词:
黏性介质
质量涨落
阻尼记忆性
分数阶谐振子 相似文献
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从理论和实例上对线性振子过阻尼和临界阻尼特性曲线进行分析对比,发现在某特定条件下过阻尼能较快地恢复到平衡位置,还发现从平衡位置开始的线性振子,过阻尼状态时峰值较小,恢复时间较长;而临界阻尼状态下恢复时间较短,峰值较大. 相似文献