Stability analyses of a vertical axis automatic washing machine without balancer

This paper analyzes the nonlinear vibration characteristics associated with the spin drying process of a vertical axis automatic washing machine without any balancer. At first, damping properties born with the machine's suspension system are discussed and a mathematical model involving tangential damping forces is built. Based on a rotating coordinate transformation, this model is then converted to an autonomous form for stability analyses. The continuation and bifurcation software AUTO [1] is applied and a Hopf bifurcation phenomenon is observed from a one-parameter bifurcation diagram. Based on several two-parameter bifurcation diagrams, several parameters affecting the Hopf bifurcation are then discussed. At last, bifurcation results are validated by time responses of the autonomous system. For a further view of the spin drying process, simulations of the non-autonomous system are also provided. This paper provides a new insight into the spin drying process of the vertical axis automatic washing machine.     

HIGHER VIBRATION MODES IN RAILWAY TRACKS AT THEIR CUT-OFF FREQUENCIES

Forced vibrations of a railway track excited at the cut-off frequency of one of its wave modes are examined theoretically, numerically and experimentally in the frequency range from 5 to 50 kHz. The background of this paper is the new idea of using the local vibration zone of the rail close to the excitation to detect passing train wheels. An important parameter which influences this local vibration zone is system damping. The determination of a new quality factor to characterize damping of a system which both resonates and interacts with travelling waves is first studied in the case of a beam on a viscoelastic foundation. Some key differences compared with a single-degree-of-freedom (s.d.o.f.) mechanical oscillator are pointed out and an adopted damping measurement method is suggested. The phenomenological behavior of higher vibration modes is then investigated using a model of several elastically connected beams referred to as the multiple-mode model. Modal damping is introduced and the model is studied both in a continuous and in a discretely supported configuration. Both localized and non-localized modes are observed in the latter case. The cut-off frequencies and mode shapes are also determined experimentally at a real test track using a scanning laser interferometer and show good agreement with numerical calculations. The spatial behavior of the measured system response at the test track corresponds well to the effects predicted by the multiple-mode model. Damping measurements are performed and the quality factors of several modes are determined and discussed.     

Semirealistic models of the cochlea

The aim of this paper is the introduction and comparison of consistent albeit passive mechanical models for the whole cochlea. A widely used transmission line filterbank, which hydrodynamically speaking is a long wave approximation (L model), suffers from a well-known inconsistency: its main modeling assumption is not valid within the resonance region, where most of the overall excitation takes place. In the present paper two approaches to overcome this inconsistency are discussed. One model is the average pressure (AP) model by Duifhuis, the other is obtained by a combination of a long and a short wave approximation (LS model). Considerable differences between the L and the LS model are observed. All models are compared by inserting them into the full integral equation obtained from the hydrodynamic equations and the boundary conditions. Here the LS model fares better than the AP model for small damping, whereas the opposite is true for higher damping. As expected, the L model fails badly in the resonance region.     

Dynamics modelling of a flexible hub-beam system with a tip mass

This paper presents a finite-element model for a flexible hub-beam system with a tip mass. Both viscous damping and air drag force are introduced into this model. The complete coupling between the system rigid and flexible degrees of freedom is allowed since the start of the formulation and developing the system kinematic variables. Based on deformation theory and geometric constraints, a second order approximation for the displacement field is proposed and the dynamic stiffening is accounted for. Hamilton's principle is utilized in deriving the equations of motion. The corresponding dynamics models of the tip mass and damping forces are developed in a consistent manner through formulating their energy expressions and applying Hamilton's principle. The finite element method is employed for spatial discretization due to its versatility, high accuracy and convergence. Numerical simulations show that the second order term in deformation field can have significant effect on dynamics behavior of flexible multibody systems. It is also shown that the traditional linear model cannot account for dynamic stiffening and may lead to erroneous result in some high-speed systems because the deformation field commonly used in structural dynamics is straight employed in this model. In contrast, the developed model (CCM) based on the second order deformation field can predict valid results. The effects of tip mass and damping on dynamics behavior of the hub-beam system are also discussed.     

Five-parameter fractional derivative model for polymeric damping materials

Fractional derivative models offer a powerful tool to describe the dynamic behaviour of real viscoelastic materials. A version of the fractional derivative models characterized by five parameters is presented and investigated in this paper in order to describe asymmetrical loss factor peak and the high-frequency behaviour of polymeric damping materials. The speculative derivation of the model constitutive equation containing time derivatives of stress and strain of different orders is given. The model behaviour is investigated in the frequency domain, the physical meaning of the model parameters is defined and constraints on the parameter values are made. It is shown that the asymmetry of loss peak and the high-frequency behaviour of the model are governed by the difference between the order of time derivatives of stress and strain. Moreover, it is shown that this difference is related to the high-frequency limit value of the loss factor. The model is fitted to experimental data on some polymeric damping materials to verify its behaviour.     

Transient analysis of nonlinear Euler–Bernoulli micro-beam with thermoelastic damping,via nonlinear normal modes

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.     

MODELLING AND VIBRATION CONTROL OF BEAMS WITH PARTIALLY DEBONDED ACTIVE CONSTRAINED LAYER DAMPING PATCH

A detailed model for the beams with partially debonded active constraining damping (ACLD) treatment is presented. In this model, the transverse displacement of the constraining layer is considered to be non-identical to that of the host structure. In the perfect bonding region, the viscoelastic core is modelled to carry both peel and shear stresses, while in the debonding area, it is assumed that no peel and shear stresses be transferred between the host beam and the constraining layer. The adhesive layer between the piezoelectric sensor and the host beam is also considered in this model. In active control, the positive position feedback control is employed to control the first mode of the beam. Based on this model, the incompatibility of the transverse displacements of the active constraining layer and the host beam is investigated. The passive and active damping behaviors of the ACLD patch with different thicknesses, locations and lengths are examined. Moreover, the effects of debonding of the damping layer on both passive and active control are examined via a simulation example. The results show that the incompatibility of the transverse displacements is remarkable in the regions near the ends of the ACLD patch especially for the high order vibration modes. It is found that a thinner damping layer may lead to larger shear strain and consequently results in a larger passive and active damping. In addition to the thickness of the damping layer, its length and location are also key factors to the hybrid control. The numerical results unveil that edge debonding can lead to a reduction of both passive and active damping, and the hybrid damping may be more sensitive to the debonding of the damping layer than the passive damping.     

Effect of magnon-phonon interaction on phonon damping of two-dimensional Heisenberg ferromagnetic system at finite temperature

A magnon-phonon interaction model is developed on the basis of a two-dimensional square Heisenberg ferromagnetic system. By using Matsubara Green function theory we studied the transverse and longitudinal acoustic phonon dampings and calculated the transverse and longitudinal acoustic phonon damping curves on the main symmetric point and line in the first Brillouin zone. It is found that on the line Δ there is no damping for transverse acoustic phonon and on the line Z there is no damping for longitudinal acoustic phonon. In the first Brillouin zone the damping of transverse acoustic phonons is at least one order larger than that of longitudinal acoustic phonons. The influences of various parameters on transverse and longitudinal acoustic phonon dampings are discussed and the lifetime and the density of state of transverse and longitudinal acoustic phonons are explored as well according to the relation of the phonon damping and its lifetime and the relation of the phonon damping and its density of state.     

Parameter sensitivity of a T-junction sea model; the importance of the internal damping loss factors

For a typical building acoustics configuration, a T-junction of plates formed by a light weight wall placed on a heavy floor, a statistical energy analysis (SEA) model is presented. Only structural systems (i.e., no acoustic wavefields) are considered. Besides bending waves also in-plane waves, quasi-longitudinal and plane transverse waves, in particular, are included in the calculation. A parametric survey is conducted on the T-junction model—for one frequency (1000 Hz) only—in order to find the sensitivity of the SEA model to the inaccuracies of its parameters. It is shown that, when using reverberation time measurements of the plates to determine the internal damping loss factors, the worst case variations of the internal damping loss factors cause variations in the junction dampings of bending waves of about one order higher than any of the other parameters. Therefore, the conclusion is that in cases where the internal damping loss factors are large with respect to the coupling loss factors, it is necessary to obtain more accurate estimates for the internal damping loss factors than are found with simple reverberation time measurements of plates.     

Solution of the Master Equation in the Amplitude Damping Model Under the Action of Linear Resonance Force

The amplitude damping model master equations of density operators under the action of linear resonance force can be concisely solved by virtue of thermo entangled state representation and the technique of integration within an ordered product of operators. We obtain the infinitive operator-sum representation of density operators. This approach may also be effective to treat other master equations. Further, the evolution of the coherent state in this model is discussed. The results show that the coherent state maintains its original coherence character in the amplitude damping model under the action of linear resonance force.     

Slow relaxation,confinement, and solitons

Millisecond crystal relaxation has been used to explain anomalous decay in doped alkali halides. We attribute this slowness to Fermi-Pasta-Ulam solitons. Our model exhibits confinement of mechanical energy released by excitation. Extending the model to long times is justified by its relation to solitons, excitations previously proposed to occur in alkali halides. Soliton damping and observation are also discussed.     

Microscopic damping mechanism of micro-porous metal films

Metal thin films are used widely to solve the vibration problem. However, damping mechanism is still not clear, which limits the further improvement of the damping properties for film and the development of multi-functional damping coating. In this paper, Damping microscopic mechanism of porous metal films was investigated at both macroscopically and microscopically mixed levels. Molecular dynamics simulation method was used to model and simulate the loading-unloading numerical experiment on the micro-pore and vacancy model to get the stress-strain curve and the microstructure diagram of different defects. And damping factor was calculated by the stress-strain curve. The results show that dislocations and new vacancies appear in the micro-pores when metal film is stretched. The energetic consumption from the motion of dislocation is the main reason for the damping properties of materials. Micro-mechanism of damping properties is discussed with the results of in-situ experiment.     

Calculation of the Storage Time of the Ions Confined in a Paul Trap

A Brownian motion model for the energy of the ions trapped in the pseudopotential well of a Paul trap is proposed and the exact solutions of the storage time in terms of the mean first passage time (MFPT) in the cases of white noises and colored noises are theoretically calculated. The relationships with the damping coefficient, noise parameters and the energy distribution of the ions are also discussed.     

颗粒离散元模拟中的阻尼系数标定

离散元模型中所采用的阻尼系数是不确定的,经常凭主观经验设定.为了使得物理模型与现实中的颗粒动力学属性符合更好,通过采用声频采样技术对物理模型中的阻尼系数进行标定,得出与实验符合的阻尼系数应为0.5左右.利用标定后的阻尼系数模拟了一元颗粒在圆柱形容器里的随机堆积过程,得到最终的堆积密度为0.625,与经典的实验结果一致.研究证明,在得到模型阻尼系数的同时,也确认了数值模型的正确性和用声频采样技术进行高精度碰撞时间检测的可行性. 关键词： 颗粒堆积 阻尼系数标定 声频采样 离散元法     

Quantum tunneling: A general study in multi-dimensional potential barriers with and without dissipative coupling

Quantum tunneling is formulated in terms of the time evolution of a localized state and thus shown to be dependent upon the eigenspectrum of the system Hamiltonian. A number of exactly solvable models with local and non-local double-well potentials are discussed, and it is shown how, for local potentials, other solvable models can be generated by using Gelfand-Levitan and Darboux transformations. Tunneling in multi-dimensional potential barriers is investigated under semi-classical approximation by developing the method of asymptotic expansion of the wave function for large quantum numbers and the WKB approximation for separable systems. General expressions for the imaginary-time tunneling trajectory are obtained in both methods and specific applications are discussed. Approximation schemes for non-separable systems are also presented. A general study of dissipative multi-dimensional tunneling is carried out by using the Gisin equation, the Schrödinger-Langevin equation and the complex potential model. It is shown that, in general, different models of dissipation are not equivalent in the tunneling context. Using these models one can show (a) the existence of critical damping beyond which no tunneling can occur, (b) that tunneling trajectories are dependent on the damping constant and (c) that dissipation may stabilize the excited state rather than the ground state. Finally the tunneling time delay in one-dimensional systems for undamped and for dissipative systems is formulated in terms of the phase shift, and this has been used to show that the effect of damping on the time delay is ignorable.     

Influence of imperfectly bonded micropolar elastic half-space with non-homogeneous viscoelastic layer on propagation behavior of shear wave

A mathematical model is developed in which the effect of imperfect bonding between the constituents of layer and half-space on the phase velocity and damped velocity of SH-wave is discussed. The model consists of a micropolar elastic half-space bonded imperfectly with a heterogeneous viscoelastic layer. The dispersion equation and damping equation of SH-wave propagation in the said model is obtained in the closed form analytically. The effects of imperfect bonding, internal friction, heterogeneity, micropolarity, and complex interface stiffness parameters highlighted through numerical computation and graphical demonstrations. Standard Love-wave equation and dispersion equation as well as damping equation for perfectly bonded micropolar half-space with heterogeneous viscoelastic layer is obtained as a special case of the problem. Through comparative study of homogeneity with heterogeneity in the layer; imperfect bonding of layer and half-space with their welded (perfect) contact; and presence of micropolarity in half-space with its absence in half-space are compared meticulously.     

A first-principles molecular dynamics approach for predicting optical phonon lifetimes and far-infrared reflectance of polar materials

The Lorentz oscillator model is well-known for its effectiveness to describe the far-infrared optical properties of polar materials. The oscillator strength and damping factor in this model are usually obtained by fitting to experimental data. In this work, a method based on first-principles simulations is developed to parameterize the Lorentz oscillator model without any fitting parameters. The high frequency dielectric constant is obtained from density functional perturbation theory, while the optical phonon frequencies and damping factors are calculated using an analysis of ab initio molecular dynamics trajectories. This method is then used to predict the far-infrared properties of GaAs, and the results are in good agreement with experimental data.     

阻尼对水平滚筒内二元颗粒体系径向分离模式形成的影响

采用离散单元数学模型对一充装量为50%的水平薄滚筒内S形二元颗粒体系的分离模式进行了数值模拟试验,研究了不同碰撞阻尼参数下的分离过程,分析了阻尼对分离过程及分离模式的影响.模拟结果表明阻尼对滚筒内颗粒的分离过程及分离模式影响很大,在S形二元颗粒体系水平薄滚筒内,阻尼可控制渗透和离析的协同作用以及自由表面层的流动形式,最终影响分离模式的形成;当阻尼太大时分离模式只能形成月亮模式,阻尼太小时可形成不明显的花瓣模式,只有当阻尼在适当的范围内,自由表面流动层形成雪崩流型式时,分离模式才会呈现规则的花瓣模式,试验结 关键词： 滚筒 模式形成 径向分离 离散单元法     

Theoretical limit of the minimal magnetization switching field and the optimal field pulse for Stoner particles

The theoretical limit of the minimal magnetization switching field and the optimal field pulse design for uniaxial Stoner particles are investigated. Two results are obtained. One is the existence of a theoretical limit of the smallest magnetic field out of all possible designs. It is shown that the limit is proportional to the damping constant in the weak damping regime and approaches the Stoner-Wohlfarth (SW) limit at large damping. For a realistic damping constant, this limit is more than 10 times smaller than that of so-called precessional magnetization reversal under a noncollinear static field. The other is on the optimal field pulse design: if the magnitude of a magnetic field does not change, but its direction can vary during a reversal process, there is an optimal design that gives the shortest switching time. The switching time depends on the field magnitude, damping constant, and magnetic anisotropy.