Ruchhardt Oscillator Decay- Thermodynamic basis for Hysteretic Damping
Randall D. Peters
使用热力学参数的基础上的理想气体定律，它表明，滞后（也称为结构）阻尼是这个经典的振荡器，用于测量气体的热容量的比率的能量耗散的自然形式。
Using thermodynamic arguments based on the ideal gas law, it is shown that hysteretic (also called structural) damping is the natural form of energy dissipation for this classic oscillator that is used to measure the ratio of heat capacities for a gas.
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Asymptotic Behavior of an Unforced Duhem-Type Hysteretic Oscillator
研究未受迫振子的渐近行为，分析其粘弹性塑性滞回元件的解的全局存在性、唯一性和收敛性。
The behavior of a new Hysteretic Nonlinear Energy Sink (HNES) coupled to a linear primary oscillator is investigated in shock mitigation. Apart from a small mass and a nonlinear elastic spring of the Duffing oscillator, the HNES is also comprised of a purely hysteretic and a linear elastic spring of potentially negative stiffness, connected in parallel. The Bouc-Wen model is used to describe the force produced by both the purely hysteretic and linear elastic springs. Coupling the primary oscillator with the HNES three nonlinear equations of motion are derived, in terms of the two displacements…
Beyond the Linear Damping Model for Mechanical Harmonic Oscillators
折叠摆的稳态运动已被研究使用的驱动频率，主要是低于仪器的自然（共振）频率。虽然该机械振荡器的自由衰减呈现教科书指数，但是用于亚共振驱动的仪器的稳态行为可能非常复杂。虽然线性阻尼模型不能解释的响应，一般特征可以理解与非线性，修改库仑阻尼模型的作者开发。
Harmonic Oscillator Potential to describe Internal Dissipation
假设一个恒定的势能函数对耗散谐振子有意义，那么一个重要的问题是转折点的时间依赖性。转向点研究表明，外部（粘性）阻尼的共同模型不能正确地描述那些许多系统中，结构（内部摩擦）阻尼是最重要的耗散源。对于内摩擦阻尼，势能的较好模型是函数不稳定的模型。
Oscillator damping with more than one mechanism of internal friction dissipation
作者的修正库仑阻尼模型已被推广，以适应内部摩擦，来自几个耗散机制同时作用。由于其基本的非线性性质，内摩擦阻尼导致自由衰减中的振荡器的品质因数Q随时间变化。给出的例子表明理论与实验之间存在合理的一致性。
This paper addresses the total mechanical energy of a single degree of freedom fractional oscillator. Based on the energy storage and dissipation properties of the Caputo fractional derivatives, the expression for total mechanical energy in the single degree of freedom fractional oscillator is firstly presented. The energy regeneration due to the external exciting force and the energy loss due to the fractional damping force during the vibratory motion are analyzed. Furthermore, based on the mean energy dissipation of the fractional damping element in steady-state vibration, a new concept of m…
Nonlinear Damping of the LC Circuit using Anti-parallel Diodes
我们研究了一个简单的变化的串联RLC电路中，反并联二极管取代电阻。这导致具有非线性阻尼项的阻尼谐振子，该非线性阻尼项在零电流处最大，并且对于远离零的电流以逆电流关系减小。一组非线性微分方程的振荡器电路推导和集成电路测量比较数值。该协议是非常好的瞬态和稳态响应。与标准RLC电路不同，该电路的行为是幅度相关的。特别地，对于瞬态响应，振荡器从欠阻尼行为过渡到过阻尼行为，并且对于被驱动振荡器，随着驱动源幅度增加，谐振响应变得更尖锐和更强。该设备价格便宜，并且在高级物理实验室中很常见。
Creep and Mechanical Oscillator Damping
虽然“摩擦”包括在许多模型的振荡器阻尼，包括粘性的应用到钟摆，他们“错过了标记”方面的概念理解的机制负责能量损失。本文的理论纠正了这些误解，考虑内部摩擦的影响，这是来自振荡器的结构构件，通过二次而不是主要的蠕变。该简单模型能较好地描述Q值随频率的变化。
An approximate solution is presented for simple harmonic motion in the presence of damping by a force which is a general power-law function of the velocity. The approximation is shown to be quite robust, allowing for a simple way to investigate amplitude decay in the presence of general types of weak, nonlinear damping.
On the solution and Lagrangian representation of Duffing oscillator with damping
本文在弱阻尼极限下通过去除阻尼项得到阻尼Duffing方程的解析解，分析阻尼对相路径的畸变影响，并构造无阻尼与阻尼情形的Lagrangian表示，为系统量子化提供基础。
The amplitude decay of a harmonic oscillator damped simultaneously by weak linear and nonlinear damping forces
本文基于能量耗散率与阻尼力功率关系，推导恒幅、线性和二次速度阻尼共同作用下弱阻尼谐振子的振幅衰减近似解，并经数值解验证其在实验相关参数范围内准确可靠。
Damped harmonic oscillator revisited: a new approach to energy decay in the case of Coulomb, Stokes, and Newton damping
本文提出了一种新方法，用于描述Coulomb、Stokes和Newton阻尼机制下谐振子的能量衰减，通过直接分析框架和精确解推导，为物理教学提供理论支持。
New approach to approximate analytical solutions of a harmonic oscillator with weak to moderate nonlinear damping: Part I
本文提出了一种新方法，用于求解具有弱至中等非线性阻尼的调和振子的近似解析解，并验证了其在不同阻尼情况下的有效性。
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless. Afterwards, approximated expressions that relate the two equations parameters for the case that the fractional order is close to an integer number are presented. Following, a numerical regression is made using power series expansion, and, also from fractional calculus, the fact that both equations cannot be equivalent is concluded. In the end, from the numerical re…
Model of Internal Friction Damping in Solids
基于长周期摆的考虑，建立了一个由固体内摩擦引起的谐振子阻尼模型。假设一个复杂的弹性模量来描述应力-应变滞后的支持结构的钟摆产生一个表达式的品质因数Q，同意许多实验涉及材料阻尼。因此，这种线性模型的近似值与一般理论相反。
Normal Mode Expansion of Damped Coupled Oscillators in 3 dimensions
本文主要研究在没有阻尼的情况下，一维以上振子系统的自由振动。基本的方法在于解耦在各个垂直方向上的运动。一旦方程解耦，现有的技术的正常模式展开的一维振荡器被用来解决的运动方程。我还研究了驱动系统的振荡器在更高的维度中的速度依赖阻尼力的存在下的运动。
The force of dry friction is studied extensively in introductory physics but its effect on oscillations is hardly ever mentioned. Instead, to provide a mathematically tractable introduction to damping, virtually all authors adopt a viscous resistive force. While exposure to linear damping is of paramount importance to the student of physics, the omission of Coulomb damping might have a negative impact on the way the students conceive of the subject. In the paper, we propose to approximate the action of Coulomb friction on a harmonic oscillator by a sinusoidal resistive force whose amplitude is…
In this paper the Bagley-Torvik Equation is considered with the order of the damping term allowed to range between one and two. The solution is found to be representable as a convolution of trigonometric and exponential functions with the driving force. The properties of the effective decay rate and the oscillation frequency with respect to the order of the fractional damping are also studied. It is found that the effective decay rate and oscillation frequency have a complex dependency on the order of the derivative of the damping term and exhibit properties one might expect of a thermodynamic…
Addendum: Modeling the amplitude and energy decay of a weakly damped harmonic oscillator using the energy dissipation rate and a simple trick (2025 Eur. J. Phys. 46(1) 015004)
本研究调整粘性阻尼的已有方法，推导滑动摩擦、空气阻力两种阻尼下弱阻尼谐振子的近似振幅衰减，得到对应一阶微分方程与时变振幅，适合大一本科生理解掌握。
An analytical solution to the nonlinear differential equation describing the equation of motion of a particle moving in an unforced physical system with linear damping, governed by a cubic potential well, is presented in terms of the Jacobi elliptic functions. In the attractive region of the potential the system becomes an anharmonic damped oscillator, however with asymmetric displacement. An expression for the period of oscillation is derived, which for a nonlinear damped system is time dependent, and in particular it contains a quartic root of an exponentially decaying term in the denominato…
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