Optimum design of a Lanchester damper for a viscously damped single degree of freedom system subjected to inertial excitation

The problem of designing an optimum Lanchester damper for a viscously damped single degree of freedom system subjected to inertial harmonic excitation is investigated. Two criteria are used for optimizing the performance of the damper: (i) minimum motion transmissibility; (ii) minimum force transmissibility. Explicit expressions are developed for determining the absorber parameters.     

Effective mass overshoot in single degree of freedom mechanical systems with a particle damper

We study the response of a single degree of freedom mechanical system composed of a primary mass, M, a linear spring, a viscous damper and a particle damper. The particle damper consists in a prismatic enclosure of variable height that contains spherical grains (total mass m_p). Contrary to what it has been discussed in previous experimental and simulation studies, we show that, for small containers, the system does not approach the fully detuned mass limit in a monotonous way. Rather, the system increases its effective mass up and above M+m_p before reaching this expected limiting value (which is associated with the immobilization of the particles due to a very restrictive container). Moreover, we show that a similar effect appears in the tall container limit where the system reaches effective masses below the expected asymptotic value M. We present a discussion on the origin of these overshoot responses and the consequences for industrial applications.     

The effect of a viscously damped dynamic absorber on a linear multi-degree-of-freedom system

The effect of a viscously damped dynamic absorber on the dynamic behaviour of a linear vibration system with many degrees of freedom is investigated. The dynamic absorber is connected to the roof of the primary system. In the sequence, optimal values for the parameters describing the behaviour of the dynamic absorber are determined, in order that the transmissibility of the composite system be minimized over the whole frequency range. As an application, respective types of anti-vibration mountings are proposed.     

Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads

Optimum design of dynamic vibration absorbers (DVAs) installed on linear damped systems that are subjected to random loads is studied and closed-form design formulas are provided. Three cases are considered in the optimization process: Minimizing the variance of the displacement, velocity and acceleration of the main mass. Exact optimum design parameters for the velocity case, which to the best knowledge of the author do not exist in the literature, are derived for the first time. Exact solutions are found to be directly applicable for practical use with no simplification needed. For displacement and acceleration cases, a solution for the optimum absorber frequency ratio is obtained as a function of optimum absorber damping ratio. Numerical simulations indicate that optimum absorber damping ratio is not significantly related to the structural damping, especially when the displacement variance is minimized. Therefore, optimum damping ratio derived for undamped systems is proposed for damped systems for the displacement case. When acceleration variance is minimized, however, the optimum damping ratio derived for undamped systems is found not as accurate for damped systems. Therefore, a more accurate approximate expression is derived. Numerical comparisons with published approximate expressions at the same level of complexity indicated that proposed design formula yield more accurate estimates. Another important finding of the paper is that for specific applications where all of the response parameters are desired to be minimized simultaneously, DVAs designed per velocity criteria provide the best overall performance with the least complexity in the design equations.     

Accuracy and robustness of four basic single degree of freedom methods for determining the modal parameters of non-lightly damped systems

An adequate measurement strategy (the combination of measurement method, response parameter, and where applicable, damping estimator) should be used for accurate determination of the natural frequency and damping of non-lightly damped single degree of freedom (SDOF) systems, otherwise, significant measurement bias errors can exist. The accuracy of four commonly used methods is studied and the measurement strategies that are exact are identified. This can depend on the damping mechanism, which if not known can be gleaned from patterns of bias errors between frequency estimations from different strategies. Since in practice a SDOF system rarely exists, or as SDOF techniques are knowingly applied to multiple degree of freedom (MDOF) systems, the robustness of the strategies in the presence of a secondary mode is studied, and the more robust (and therefore preferable) strategies are identified. The measurement method based on the real spectral part is advantageous as it evaluates the damping exactly and is independent of the damping mechanism, in addition the natural frequency obtained is independent of the response parameter. However, this method is not a relatively robust one, and is also sensitive to phase changes accrued during measurements.     

Effect of an impact damper on a multi-degree of freedom system

Theoretical analysis of the steady state vibrational motion of a multi-degree of freedom system equipped with an impact damper is presented. The analysis is based on the assumption that two generally distributed impacts occur in each cycle. The theory is applied to the special case of a single degree of freedom main system and the effects of various parameters are investigated. The theoretically possible modes of steady state motion with two impacts/cycle and with no impacts are predicted. The non-linear behaviour of the damper is manifested by the existence of as many as three modes of steady state motion for a given exciting frequency. The conditions leading to more or less than two impacts/cycle are predicted although the system response under such conditions is not studied. Experimental results are presented and compared with theoretical predictions.     

Resonance bands in a two degree of freedom Hamiltonian system

In perturbations of integrable two degree of freedom Hamiltonian systems, the invariant (KAM) tori are typically separated by zones of instability or resonance bands inhabited by elliptic and hyperbolic periodic orbits and homoclinic orbits. We indicate how the Melnikov method or the method of averaging can asymptotically predict the widths of these bands in specific cases and we compare these predictions with numerical computations for a pair of linearly coupled simple pendula. We conclude that, even for low order resonances, the first order asymptotic results are generally useful only for very small coupling (ε10^-4).     

单自由度非线性保守系统作大振幅振动时周期的计算方法

简要介绍了单自由度非线性保守系统作大振幅振动时周期的计算方法,并给出了几个常见典型振动问题的周期公式．     

The duality of a single particle with an n-dimensional internal degree of freedom

The wave-particle duality of a single particle with an n-dimensional internal degree of freedom is re-examined theo- retically in a Mach-Zehnder interferometer. The famous duality relation D2 ＋ V2 〈 1 is always valid in this situation, where D is the distinguishability and V is the visibility. However, the sum of the particle information and the wave information, D2 V2, can be smaller than one for the input of a pure state if this initial pure state includes the internal degree of freedom of the particle, while the quantity D2~ V2 is always equal to one when the internal degree of freedom of the particle is excluded.     

Dynamic condensation in a damped system through rational selection of primary degrees of freedom

Various system reduction methods have been proposed to calculate eigenvalues and eigenvectors with computational efficiency. In the case of system condensation, the method of selecting proper primary degrees of freedom (PDOFs) is crucial because they are closely related to the accuracy and reliability of eigensystem prediction in a reduced system. Although reasonable selection methods for PDOFs have been proposed for undamped systems, these methods cannot be directly extended to damped systems. We propose a PDOF selection method for a damped system. The proposed method is based on the ratio of DOF-wise energy distributions. In order to estimate the energy distribution of the structure, Ritz vectors are obtained using a two-sided Lanczos algorithm. Energy distribution matrices are calculated from the obtained Ritz vectors. Then, degrees of freedom (DOFs) corresponding to the lowest Rayleigh quotients are selected as the PDOFs. The efficiency and reliability of the proposed method are demonstrated using numerical examples.     

On the nonlinear dynamics of a single degree of freedom oscillator with a time-varying mass

In this paper the forced vibrations of an undamped single degree of freedom oscillator with a time varying mass will be studied. An initial value problem for an oscillator equation with a Rayleigh type of nonlinearity will be formulated, and by applying a straight-forward perturbation method the problem will be solved approximately. The approximations of the solutions will be used to construct a map. By using this map the stability properties of the solutions can be determined. The stability properties of the nonlinear problem will be compared to those for the linear problem, which have been studied earlier in the literature. The instability regions in the parameter space and some phase-space figures for the nonlinear problem will be computed numerically. It will also be shown how the behaviour of the solutions changes when the instability regions in the parameter space are crossed.     

两自由度并联机器人控制系统设计

针对机电装配、医药包装等行业自动化抓取和放置实际应用的需求,设计了一种采用直线伺服驱动技术的两自由度高速并联机器人。首先进行了机器人的机械结构设计,并且通过运动学分析,结合运用蒙特卡洛法与几何法求解出并联机器人的工作空间;其次采用MCU+CPLD(STM32F103+MaxⅡ)的双控制架构,根据工作空间结构在MCU中设计出高效的运动轨迹生成算法,并在CPLD中运用DDS技术将伺服运动参数转换成脉冲经一级差分后输出到伺服驱动器。在双控制器的通信方面合理利用CPLD中的状态机提出了双级数据缓冲方式,使得MCU写与CPLD读交错进行,可以实现数据的无缝刷新。最后进行了并联机器人系统样机的制作与调试,分析结果表明所研制的机器人控制系统能够使机器人快速抓放金属小球,实现稳定可靠运行。     

A U(1) gauge-Higgs system with a radial degree of freedom

The phase diagram of a lattice U(1) gauge-Higgs model is derived without freezing the Higgs field length. For sufficienly small Higgs self-coupling strength, the “confinement” and “Higgs” phases are separated, in contrast to what is observed in the fixed length model.     

Stability of a system of three degrees of freedom subjected to a circulatory force

The free vibrations of a uniformly accelerating linear elastic, non-dissipative system of three degrees of freedom, carrying a tip mass and subjected to a constant circulatory thrust applied at a free end, are investigated for the purpose of determining the influence of the orientation of the thrust on the system's state of stability. A dimensionless bi-cubic frequency equation whose coefficients depend upon the tip mass parameter, the thrust parameter, and the tangency coefficient, α, is solved and eigencurves are plotted for several values of α. These eigencurves reveal that, for a certain range of small values of α, the system becomes unstable by divergence for any positive thrust, no matter how small. There also exists a range of α for which the system is first unstable by divergence, secondly stable, and finally unstable by flutter as the magnitude of the thrust is increased. For α sufficiently large, the system is stable for a certain range of values of the thrust, but eventually it becomes unstable by flutter as the thrust is increased beyond its critical value.     

Generating “idealised” impulse response functions to improve or repair single degree of freedom system measurements

A single degree of freedom (SDOF) system can be characterised using transient or continuous time signals and both should lead to the same frequency response function. As commonly defined, the equation of the displacement response of a SDOF system to impulse excitation alone is ambiguous leading to two possible interpretations: the impulse response (IR) and one corresponding to solely the free oscillation of the system (FR). These are analysed in detail for idealised and practical cases and it is found that the IR and FR yield two distinct acceleration spectra, and that only the phase distinguishes the normalised FR between displacement, velocity and acceleration alleviating the need to perform differentiation and integration to generate the response in other parameters. An unambiguous mathematical definition of the IR is suggested for the velocity response. Finally, it is shown that an idealised version of the IR can be artificially generated from the FR. This can be used to repair acceleration signals that have a truncated or distorted impulsive part, alleviate spectral windowing effects and generally allow cleaner response spectra. This is demonstrated experimentally.