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.     

Electron current drive by fusion-product-excited lower hybrid drift instability

We present first principles simulations of the direct collisionless coupling of the free energy of fusion-born ions into electron current in a magnetically confined fusion plasma. These simulations demonstrate, for the first time, a key building block of some "alpha channeling" scenarios for tokamak experiments. Spontaneously excited obliquely propagating waves in the lower hybrid frequency range undergo Landau damping on resonant electrons, drawing out an asymmetric tail in the electron parallel velocity distribution, which carries a current.     

Line shape distortion in a nonlinear auto-oscillator near generation threshold: application to spin-torque nano-oscillators

The power spectrum of an auto-oscillator with a large frequency nonlinearity in a noisy environment is calculated. The power spectrum becomes strongly non-Lorentzian, broadened, and asymmetric near the generation threshold. A Lorentzian spectrum is recovered far below and far above the threshold, which suggests that line shape distortions provide a signature of the threshold. We show that the developed theory adequately describes the observed behavior of a strongly nonlinear spin-torque nano-oscillator.     

Practical industrial method of increasing structural damping in machinery,I: Squeeze-film damping with air

There is frequently a need to reduce sound radiation due to resonant flexural motion of stiff machinery panels. This can be achieved by applying squeeze-film damping to the vibrating panel by attaching an auxiliary plate parallel to the surface, thereby trapping a thin layer of air. Relative vibration of the plates pumps this air at high velocities, resulting in energy loss due to the air viscosity. In this study the damping below the critical frequency of the “thick plate” with an “attached plate” and air layer has been investigated by using an impedance approach. This model is incorporated into a two element Statistical Energy Analysis (SEA) model to predict the damping well above the critical frequency of the thick plate. The agreement between the predicted and measured results is remarkably good. Below the critical frequency the damping is pumping controlled, while above critical the plate couplings are the controlling factor.     

Biomechanically inspired modelling of pedestrian-induced forces on laterally oscillating structures

Despite considerable interest among engineers and scientists, bi-directional interaction between walking pedestrians and lively bridges has still not been well understood. In an attempt to bridge this gap a biomechanically inspired model of the human response to lateral bridge motion is presented and explored. The simple inverted pendulum model captures the key features of pedestrian lateral balance and the resulting forces on the structure. The forces include self-excited components that can be effectively modelled as frequency-dependent added damping and mass to the structure. The results of numerical simulations are in reasonable agreement with recent experimental measurements of humans walking on a laterally oscillating treadmill, and in very good agreement with measurements on full-scale bridges. In contrast to many other models of lateral pedestrian loading, synchronisation with the bridge motion is not involved. A parametric study of the model is conducted, revealing that as pedestrians slow down as a crowd becomes more dense, their resulting lower pacing rates generate larger self-excited forces. For typical pedestrian parameters, the potential to generate negative damping arises for any lateral bridge vibration frequency above 0.43 Hz, depending on the walking frequency. Stability boundaries of the combined pedestrian–structure system are presented in terms of the structural damping ratio and pedestrian-to-bridge mass ratio, revealing complex relations between damping demand and bridge and pedestrian frequencies, due to the added mass effect. Finally it is demonstrated that the model can produce simultaneous self-excited forces on multiple structural modes, and a realistic full simulation of a large number of pedestrians, walking randomly and interacting with a bridge, produces structural behaviour in very good agreement with site observations.     

Damping mechanism in dynamic force microscopy

A general theory is presented which describes the damping in dynamic force microscopy due to the proximity of the surface, consistently with resonant frequency shift effects. Orders of magnitude for the experimentally measured "dissipation" and image corrugation are reproduced. It is suggested that the damping does not mainly result from energy dissipation, but arises because not all solutions of the microlever equation of motion are accessible. The damping is related to the multivalued nature of the analytical resonance curve, which appears at some critical tip-surface separation.     

A far-infrared bolometric observation of the pinned charge-density wave in TTF-TCNQ

The polarized bolometric signal between 5 and 50 cm^?1 from a TTF-TCNQ single crystal near 10 K has been successfully fitted to a Lorentzian oscillator of natural frequency 3.4 ± 0.6 cm^?1 and a damping of 0.05 ± 0.03 cm^?1. This is presumably the phase mode of the pinned charge-density wave, with interchain Coulomb interaction probably being responsible for the pinning. The low damping is thought to be due to two-phonon “difference” processes, which are also thought to be responsible for a temperature-dependent feature at 25 cm^?1. No dependence of the pinned-mode frequency on electric field could be detected.     

Dislocation damping in alkali halides

In the amplitude independent region the dislocation damping is attributed to either phonon-drag (Granato-Lücke theory) or to the compensating charge-cloud surrounding electrically charged dislocations (Robinson-Birnbaum theory). The experimental results for the dependence of the damping on temperature, frequency and dislocation charge are compared with the two theories. Since it is found that in some cases it is necessary to include both forms of damping, a more complete theory is developed which includes both terms.

In the amplitude dependent region the dislocation damping was thought to be due to the dislocations breaking away from pinning points or breaking through the compensating charge-cloud. Using the piezoelectric defect results for electrically charged dislocation in KCl the force-displacement hysteresis loop for the moving dislocations is determined together with the force-displacement curves for dislocations assuming phonon and charge-cloud damping. These results are found to be inconsistent with the “break away” models for amplitude dependence but instead to be consistent with the restoring force due to an elliptical compensation charge cloud, with a size proportional to the square root of the dislocation charge.     

Time correlation functions and spectral distributions of the duffing oscillator in a random force field

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.     

Light-driven oscillations of entangled nematic colloidal chains

Laser tweezers have been used to drive the oscillations of a chain of entangled colloidal particles in the nematic liquid crystal 5CB. The amplitude and phase of light-driven oscillations have been determined for the motion of individual colloidal particles. The collective motion of 4.8μm silica particles is highly damped for a driving frequency above 0.5Hz. The results were compared to an effective bead-spring model, where the motion of elastically coupled particles is hindered by viscous damping and hydrodynamic coupling. Qualitative agreement between theory and experiment was obtained.     

Raman scattering from sodium and silver in β-alumina

Raman scattering is observed from the vibrations of the mobile sodium and silver ions in β-alumina between 4.2 and 900°K. The frequency response is Lorentzian at all temperatures above 300°K with little change in frequencies and damping rates. It is concluded that diffusive conduction with a well-defined attempt frequency predominates up to 900°K.     

A translational heat-bath model for foreign gas broadening of spectral lines—II. The T approximation

The theory of foreign-gas broadening is developed for a central potential by using the T approximation, in a Green's functions formalism. The translational degrees of freedom of the absorbing and foreign gases are separated from the internal degrees of freedom by a translational heat bath model. The line profile is expressed by a Lorentzian in which the half width and shift are functions of frequency. A general method is developed for calculating the half width as a function of frequency. The Lorentzian line profile obtained for a hard-core potential is compared with the explicit line profile obtained for weak potentials by the Born approximation. The results of the present paper are compared with those of other theoretical studies.     

Lebensdauermessung am Ionenstrahl bei kollinearer Laseranregung

Determination of Life Times in Ionic Beams by Collinear Laser Excitation Collinear laser spectroscopy of ionic beams provides a mean of determining life times of ionic states in almost ideal circumstances. Perturbing influences of the environment (collisions) are almost absent and due to the velocity bunching effect the luminosity of the method is rather high. The method itself consists in measuring the fluorescence while changing alternately the polarization of the exciting laser beam from perpendicular to parallel to the detector. The difference of the respective counting rates is recorded as a function of a magnetic field applied parallel to the laser beam (zero field level-crossing). The underlying shape of the recordings is not a Lorentzian but a product of such a function and two Doppler distributions. The width of the Doppler distributions exceeds the one of the Lorentzian by only an order of magnitude in the cases considered. Both the distributions are centered around zero magnetic field strength unless the laser frequency is slightly off line. In the latter case asymmetric curves result which are difficult to evaluate. Moreover, optical pumping may cause saddles in the curve center with narrow oscillations superposed on them. This could be reproduced by writing down the equations of motion of the statistical tensors solving them afterwards on a computer. The alignment shows striking similarity to the recorded curves when plotted versus the magnetic field. The life times of two excited levels of Ar⁺ investigated in that way could be ascertained. They are in the range of a few nanoseconds.     

Long-time translation and rotational Brownian motion in two dimensions

The long-time translational and rotational motion of a Brownian particle in two dimensions is studied on the basis of the fluctuation-dissipation theorem and linearized hydrodynamics. The long-time motion follows from the low frequency behavior of the mobility matrix. The coefficient of the long-time tail for the translational motion turns out to be independent of shape and size of the body, in agreement with mode-coupling theory. For rotational Brownian motion the coefficient of the long-time tail is found to depend on the shape of the body. This result is in conflict with a recent prediction from mode-coupling theory, and indicates that the mode-coupling calculation should be revised.This article is dedicated in friendship to Prof. Matthieu Ernst on the occasion of his 60th birthday.     

Landau damping in a bounded magnetized plasma column

The damping decrement of Landau damping and the effect of thermal velocity on the frequency spectrum of a propagating wave in a bounded plasma column are investigated.The magnetized plasma column partially filling a cylindrical metallic tube is considered to be collisionless and non-degenerate.The Landau damping is due to the thermal motion of charge carriers and appears whenever the phase velocity of the plasma waves exceeds the thermal velocity of carriers.The analysis is based on a self-consistent kinetic theory and the solutions of the wave equation in a cylindrical plasma waveguide are presented using Vlasov and Maxwell equations.The hybrid mode dispersion equation for the cylindrical plasma waveguide is obtained through the application of appropriate boundary conditions to the plasma-vacuum interface.The dependence of Landau damping on plasma parameters and the effects of the metallic tube boundary on the dispersion characteristics of plasma and waveguide modes are investigated in detail through numerical calculations.     

A theory of the bion in the one-dimensional sine-Gordon system: I. Quantum statistical mechanics

Introducing an appropriate renormalization to the phase space of the bion, we study the quantum statistical mechanics of the bion in the one-dimensional sine-Gordon system. A bion representation is found for the partition function of the system in the limit of weak coupling, i.e., the free field. From the partition function, the bion distribution is calculated and an approximate analytic formula is obtained both at low and intermediate temperatures. The obtained bion distribution is neither the Bose distribution nor the Fermi distribution, nor the Boltzmann distribution at low temperatures. The self-energy of the bion at finite temperature is also discussed.     

The theory of the sound attenuation in one-dimensional metals

The elasticity theory equations are obtained for a 1d conductor. The frequency dependence of the sound attenuation is analysed, the spatial dispersion being strong or weak. The effect of oscillations of the attenuation is predicted which is due to a jumping nature of electronic motion in a non-uniform field of the sound wave, with a fixed jumping length. That is why the oscillations are of the geometric resonance type. Because of absence of Landau's damping, the frequency dependence of attenuation in a region of strong spatial dispersion is quadratic rather than linear one, as in 3d metals. This dependence is determined by a quantum nature of electronic scattering on separate impurities which move with an oscillating lattice.     

Magnetic hyperfine field for zinc in nickel

Electron mobility in the narrow band solid with a cellular disorder is investigated by methods of the coherent potential theory. Numerical results for the tight-binding model with the Lorentzian distribution of site potentials are presented. The motion of the electron in the region of extended states is neither a well defined coherent band motion nor a simple Brownian diffusion. The statistical electron-hole correlation proves to be important and increases fast with the potential distribution width to band width ratio. The correlation also increases when approaching the mobility edges.     

非Maxwell电子速度分布对受激散射的影响

从考虑动理学效应的受激散射不稳定性的线性理论出发,对于n=2的Maxwell分布函数直到n=5的饱和情况的超高斯分布函数,计算了电子等离子体波和离子声波的频率和阻尼率。对受激喇曼散射和受激布里渊散射进行分析,结果表明,在激光高Z等离子体中,或者在具有激光热斑的中等Z等离子体中,电子等离子体波的阻尼率降低很多,离子声波的频率比Maxwell分布情况升高约15%。这些结果可和实验进行比较。     

Polarization echo in type-II superconductor powders

A theory of polarization echo in powdered type-II superocnductors is presented, which takes into consideration mechanisms of nonlinear excitation, nonlinear damping, and nonlinear dispersion in interaction of radio frequency pulses with twinning boundary dislocations. It is shown that the motion of defects and magnetization jumps associated with it take place with retention of phase information, which is the basis of the long-lived echo. The short-lived dynamic echo and the long-lived static echo are explained and their properties are investigated. The connection of polarization echo with other phenomena due to the defect structure of the material is established.Kazan Physicotechnical Institute, KNTs RAN. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 20–48, July, 1993.