Dynamics of a supercritical composite shaft mounted on viscoelastic supports

The damping in a carbon fiber reinforced plastic (CFRP) laminate is greater than that which occurs in most metallic materials. In the supercritical regime, the damping can trigger unstable whirl oscillations, which can have catastrophic effects. The vibrations occurring in a supercritical composite drive shaft are investigated here in order to predict instabilities of this kind. A simply supported carbon/epoxy composite tube mounted on viscoelastic supports is studied, using an approximation of the Rayleigh–Timoshenko equation. The damping process is assumed to be hysteretic. The composite behavior is described in terms of modulus and loss factor, taking homogenized values. The critical speeds are obtained in several analytical forms in order to determine the effects of factors such as the rotatory inertia, the gyroscopic forces, the transverse shear and the supports stiffness. Assuming that the hysteretic damping can be expressed in terms of the equivalent viscous model, the threshold speed is obtained in the form of an analytical criterion. The influence of the various factors involved is quantified at the first critical speed of a subcritical composite shaft previously described in the literature. The influence of the coupling mechanisms on the unsymmetrical composite laminate and the end fittings is also investigated using a finite element model. None of these parameters were found to have a decisive influence in this case. Those having the greatest effects were the transverse shear and the supports stiffness. The effects of the composite stacking sequence, the shaft length and the supports stiffness on the threshold speed were then investigated. In particular, drive shafts consisting only of ±45° or ±30° plies can be said to be generally unstable in the supercritical regime due to their very high loss factors.     

The influence of lateral interactions in the occurrence of ensemble effects in chemisorption and catalysis

Monte Carlo methods have been used to examine the influence of lateral interactions between adspecies at a metal surface on the poisoning of surface reactions. A simple model is employed in which the nearest neighbour interaction energy (B) between the poison species is allowed to vary between −5 and 10 kJ mol⁻¹. The variation in the maximum extent of chemisorption is evaluated for differing values of B and poison coverage. It is demonstrated that the common procedure used to determine critical ensemble sizes produces misleading results which are seriously in error when lateral forces of interaction are considered and the catalytic significance of the results is discussed.     

Optical edge modes in photonic liquid crystals

An analytic theory of localized edge modes in chiral liquid crystals (CLCs) is developed. Equations determining the edge-mode frequencies are found and analytically solved in the case of low decaying modes and are solved numerically for the problem parameter values typical for the experiment. The discrete edge-mode frequencies specified by the integer numbers n are located close to the stop-band edge frequencies outside the band. The expressions for the spatial distribution of the n’s mode field in a CLC layer and for its temporal decay are presented. The possibilities of a reduction of the lasing threshold due to the anomalously strong absorption effect are theoretically investigated for a distributed feedback lasing in CLCs. It is shown that a minimum of the threshold pumping wave intensity may be reached, generally, for the pumping wave propagating at an angle to the helical axis. However, for lucky values of the related parameters, it may be reached for the pumping wave propagating along the helical axis. The lowest threshold pumping wave intensity occurs for the lasing at the first low-frequency band-edge lasing mode and the pumping wave propagating at an angle to the spiral axis corresponding to the first angular absorption maximum of the anomalously strong absorption effect at the high-frequency edge of the stop band. The study is performed in the case of the average dielectric constant of the liquid crystal coinciding with the dielectric constant of the ambient material. Numerical calculations of the distributed feedback lasing threshold at the edge-mode frequencies are performed for typical values of the relevant parameters.     

Flexural vibration of axially loaded beams with linear or parabolic taper

Curves are presented which enable the first five natural frequencies to be found for axially loaded tapered members with an important family of cross sections. Previous curves have only included axial forces in a very limited number of cases, whereas here axial forces within the range of greatest practical importance can always be allowed for. The present curves cover 11 combinations of end conditions, three types of taper, all taper ratios between 0·2 and 1, and all axial forces between ?P_c and 0·6P_c where P_c is the critical buckling load for pure compression and can be found from curves provided (a list of principal nomenclature is given in Appendix 2). The cross sections covered include thin circular ones of constant thickness and thin-walled cross sections consisting of constant thickness flat plates which all have their breadths tapering in the same way. Truncated wedges of varying depth and constant width are also covered. The taper is linear between the ends, or linear between a maximum value at the centre and equal values at the ends, or parabolic with a maximum value at the centre. Simple examples show how the curves can be used to obtain natural frequencies or buckling loads to an accuracy which is almost always about 1%. The curves also illustrate how natural frequencies and buckling loads of thin-walled members are altered by changing the amount and type of a member's taper while keeping its wall thickness and mass constant. Finally, it is shown that, for the ranges covered by the curves, frequencies which separate the first five natural frequencies can be found a priori. The theory used to obtain the curves was simply to divide the tapered member into sufficient uniform members to ensure convergence to the tapered result to better than plotting accuracy. Exact Bernoulli-Euler dynamic stiffnesses, which allowed for axial force effects, were used for these uniform components. In Appendix 1 the effects of using exact Timoshenko stiffnesses instead of the Bernoulli-Euler ones are illustrated.     

A criterion for the use of linear regression analysis in the determination of low values of absorption coefficient using the impedance tube method

This article describes a quick and convenient method for estimating the percentage error associated with any measurement of absorption coefficient using the impedance tube method. A parameter Z is calculated, using constants appropriate to the tube and the decibel difference between a pressure maximum and minimum. The value of this parameter can be used as a criterion as to whether a more accurate determination, using linear regression, should be employed. The technique is valuable as an aid when low values of absorption coefficient, particularly at low frequencies, are to be measured.     

The influence of crack breathing and imbalance orientation angle on the characteristics of the critical speed of a cracked rotor

By analyzing the limitations of weight dominance and by taking the complicated whirl of the rotor into account, general equations of motion have been developed in case of a Jeffcott rotor with a transverse crack. The angle between the crack direction and the shaft deformation direction is used to determine the closing and opening of the crack, allowing one to study the dynamic response without assuming weight dominance. Using the new equations, the dynamic response of a cracked rotor near its critical speed has been computed via a numerical method to investigate the influence of nonlinear breathing of the crack and that of the imbalance orientation angle β on the stability, critical speed and peak response of the rotor. The results show that nonlinear breathing can improve the stability of a rotor in contrast to a rotor with an open crack, and, with a reversed imbalance (70°<β<270°), that it can reduce the vibration response in contrast to an uncracked rotor. The basic characteristics of a cracked rotor near its critical speed are similar to those of an uncracked rotor. The critical speed can be determined by measuring the rotation of the center of gravity. The critical speed of a cracked rotor is located between the natural frequencies of the fully open crack and those of the fully closed crack and depends on the imbalance orientation angle. Its value is lowest at β≈90° and highest at β≈270°. The peak in the response at the critical speed is mainly determined by the imbalance orientation angle. At β≈0° and 180°, the peak corresponds to the maximum and minimum response, respectively.     

舰船螺旋桨轴频估计中线谱要素提取算法

舰船辐射噪声DEMON谱(调制解调谱)线谱要素提取是舰船螺旋桨轴频估计中的关键步骤。现有的线谱提取技术主要用于功率谱线谱检测,侧重于线谱频率的确定,不能满足舰船螺旋桨轴频估计需求。本文根据DEMON谱线谱的特点及人工提取线谱的过程,设计了一种新的线谱要素提取算法,改进了谱峰筛选技术,将多时刻的DEMON线谱基于最大似然估计和谱峰序列相似度加以融合决策,最终确定了线谱频率和幅值(峰值)及边界。通过实际数据验证,此线谱要素提取算法更适用于螺旋桨轴频估计,可提高轴频估计的准确率。     

Functional derivative δTcδα2F(ω) for weak-coupling superconductors with paramagnetic impurities

We have calculated analytically the functional derivative $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{F(ω)}$ for weak-coupling superconductors with paramagnetic impurities using a simple “square-well model” for the electron-phonon interaction. The formulas obtained are sufficiently simple that we can obtain results as close to the critical concentration as we wish. It is found that the position of the maximum of the functional derivative continues to shift towards small frequencies with increasing concentration and that the height at maximum increases indefinitely.     

Transitions in convection driven by a horizontal temperature gradient

We report the first detailed experimental study of transitions in the convection of a low Prandtl number fluid driven by a horizontal temperature gradient. The observed states, from time independent to one frequency with noise, to pure noise, to two frequencies with noise, can be related to the two secondary flows predicted for a cavity with large lateral extent, transverse stationary and longitudinal oscillatory rolls. Measured wavelengths and frequencies for the longitudinal rolls are in agreement with theoretical values, while the critical Grashof number is much higher than expected. Our results call for a new theoretical approach which takes both instability mechanisms into account.     

Modal coupling effects in the free vibration of elastically interconnected beams

The problem of free vibration of a uniform beam elastically interconnected to a cantilevered beam, representing an idealized launch vehicle aeroelastic model in a wind tunnel, is studied. With elementary beam theory modelling, numerical results are obtained for the frequencies, mode shapes and the generalized modal mass of this elastically coupled system, for a range of values of the spring constants and cantilevered beam stiffness and inertia values. The study shows that when the linear springs are supported at the nodal points corresponding to the first free-free beam mode, the modal interaction comes primarily from the rotational spring stiffness. The effect of the linear spring stiffness on the higher model modes is also found to be marginal. However, the rotational stiffness has a significant effect on all the predominantly model modes as it couples the model deformations and the support rod deformations. The study also shows that through the variations in the stiffness or the inertia values of the cantilever beam affect only the predominantly cantilever modes, these variations become important because of the fact that the cantilevered support rod frequencies may come close to, or even cross over, the predominantly model mode frequencies. The results also bring out the fact that shifting of the support points away from the first mode nodal points has a maximum effect only on the first model mode.     

扫描相机标定脉冲信号位置的确定及噪声处理

 扫描相机标定数据处理中的一个关键问题是如何准确确定脉冲信号的位置,实验数据的信噪比和脉冲信号位置的定义方法都会对标定结果的准确性产生影响。采用了取半高宽的方法来确定扫描相机标定脉冲信号的位置,在信噪比比较高 （大于100） 的情况下,该方法确定标定信号的位置可以达到亚像素水平。对于信噪比比较低 (小于10) 的实验数据,先采用快速傅里叶变换方法对其进行滤波,通过滤波可以极大地抑制噪声信号的影响,然后采用“半高宽法”确定脉冲信号的位置,最后得出可信的标定结果。当扫描相机定在0.3 ns的扫描档时,通过该方法得到的扫描速度为0.214 ps/pixel,扫描不确定度为0.002 9 ps/pixel,拟合线性相关系数为0.999 7。     

Image enhancement by the modified high-pass filtering approach

We demonstrate a brand-new method for image enhancement by using a modified high-pass filtering approach. Some specific spatial frequencies are selectively magnified by exaggerating the local visibility of an image. Then a high-pass filter is employed to adjust those critical frequencies. The enhanced final image has well-sharpened fine characteristics.     

FREE VIBRATIONS OF SELF-STRAINED ASSEMBLIES OF BEAMS

This paper examines the natural frequencies and modes of transverse vibration of two simple redundant systems comprising straight uniform Euler-Bernoulli beams in which there are internal self-balancing axial loads (e.g., loads due to non-uniform thermal strains). The simplest system consists of two parallel beams joined at their ends and the other is a 6-beam rectangular plane frame. Symmetric mode vibration normal to the plane of the frame is studied. Transcendental frequency equations are established for the different systems. Computed frequencies and modes are presented which show the effect of (1) varying the axial loads over a wide range, up to and beyond the values which cause individual members to buckle (2) pinning or fixing the beam joints (3) varying the relative flexural stiffness of the component beams. When the internal axial loads first cause any one of the component beams to buckle, the fundamental frequency of the whole system vanishes. The critical axial loads required for this are determined. A simple criterion has been identified to predict whether a small increase from zero in the axial compressive load in any one member causes the natural frequencies of the whole system to rise or fall. It is shown that this depends on the relative flexural stiffnesses and buckling loads of the different members. Computed modes of vibration show that when the axial modes reach their critical values, the buckled beam(s) distort with large amplitudes while the unbuckled beam(s) move either as rigid bodies or with bending which decays rapidly from the ends to a near-rigid-body movement over the central part of the beam. The modes of the systems with fixed joints change very little (if at all) with changing axial load, except when the load is close to the value which maximizes or minimizes the frequency. In a narrow range around this load the mode changes rapidly. The results provide an explanation for some computed results (as yet unpublished) for the flexural modes and frequencies of flat plates with non-uniform thermal stress distributions.     

Phonon Excitation and Energy Redistribution in Phonon Space for Energy Dissipation and Transport in Lattice Structure with Nonlinear Dispersion

We first propose fundamental solutions of wave propagation in dispersive chain subject to a localized initial perturbation in the displacement. Analytical solutions are obtained for both second order nonlinear dispersive chain and homogenous harmonic chain using stationary phase approximation. Solution is also compared with numerical results from molecular dynamics(MD) simulations. Locally dominant phonon modes(k-space) are introduced based on these solutions. These locally defined spatially and temporally varying phonon modes k(x, t) are critical to the concept of the local thermodynamic equilibrium(LTE). Wave propagation accompanying with the nonequilibrium dynamics leads to the excitation of these locally defined phonon modes. It is found that the system energy is gradually redistributed among these excited phonons modes(k-space). This redistribution process is only possible with nonlinear dispersion and requires a finite amount of time to achieve a steady state distribution. This time scale is dependent on the spatial distribution(or frequency content) of the initial perturbation and the dispersion relation. Sharper and more concentrated perturbation leads to a faster energy redistribution and dissipation. This energy redistribution generates localized phonons with various frequencies that can be important for phonon-phonon interaction and energy dissipation in nonlinear systems.Depending on the initial perturbation and temperature, the time scale associated with this energy distribution can be critical for energy dissipation compared to the Umklapp scattering process. Ballistic type of heat transport along the harmonic chain reveals that at any given position, the lowest mode(k = 0) is excited first and gradually expanding to the highest mode(kmax(x, t)), where kmax(x, t) can only asymptotically approach the maximum mode kBof the first Brillouin zone(kmax(x, t) → kB). No energy distributed into modes with kmax(x, t) k kBdemonstrates that the local thermodynamic equilibrium cannot be established in harmonic chain. Energy is shown to be uniformly distributed in all available phonon modes k ≤ kmax(x, t) at any position with heat transfer along the harmonic chain. The energy flux along the chain is shown to be a constant with time and proportional to the sound speed(ballistic transport).Comparison with the Fourier's law leads to a time-dependent thermal conductivity that diverges with time.     

The equation of state of quarks and mesons in a renormalization group flow picture

Non-perturbative flow equations within an effective linear sigma model coupled to constituent quarks for two quark flavours are derived and solved. A heat kernel regularization is employed for a renormalization group improved effective potential. We determine the initial values of the coupling constants in the effective potential at zero temperature. Solving the evolution equations with the same initial values at finite temperature in the chiral limit, we find a second-order phase transition at T_c≈150 MeV. Due to the smooth decoupling of massive modes, we can directly link the low-temperature four-dimensional theory to the three-dimensional high-temperature theory. We calculate the equation of state in the chiral limit and for finite pion masses and determine universal critical exponents.     

Filter switching device for dual-wavelength videoimaging

An inexpensive, dual-wavelength, videoimaging system that can be used for parallel observation of two fluorescent dyes is described. All four filters, two for excitation and two for emission, are placed on the same oscillating holder. Filters are coupled with a single dichroic mirror having two spectral windows. A coil driven by an electronic circuit connected to photosensors, which determine the position of the holder, moves the magnet that shifts the position of the filters. Since the filter holder is placed between two springs, it oscillates with the frequency of mechanical resonance. As a result the filter switching did not require much power and did not produce significant vibrations of the base. Switching frequencies up to 4.5 s^–1 were reached with the first experimental device. System performance was tested using phospholipid vesicles loaded with water-soluble and membrane dyes. It has been demonstrated that the device can be used successfully in experiments on membrane fusion with rhodamine- and calcein-labeled liposomes.     

Vibration and buckling of flat free-free plates under non-uniform in-plane thermal stresses

Detailed consideration is given to the modes and frequencies of a free rectangular Kirchoff plate subjected to in-plane stresses generated by prescribed non-uniform surface temperature distributions which are doubly symmetrical about the plate central axes. Physical understanding is sought of phenomena observed by previous investigators. Stress distributions corresponding to three different temperature distributions have first been studied and incorporated in a Rayleigh Ritz analysis to find natural frequencies and modes. All frequencies change as the temperature changes, some much more than others. All eventually vanish, one after the other, as the temperature reaches certain critical positive and negative values at which the plate goes into statically unstable buckling modes. Whether the frequencies rise or fall with rising temperature at the plate centre depends on the relative magnitudes of pairs of positive and negative critical temperatures. The modes of buckling at each pair of critical temperatures may differ greatly from one another and also from the vibration modes at zero temperature. The relationship between the square of the frequency and the temperature is then no longer approximately linear, although it is exactly so for certain simple in-plane stress distributions. Conditions have nevertheless been identified under which it is a very good approximation to the actual frequencies of the heated plate over wide temperature ranges.     

The effects of air temperature and humidity on the acoustic design of voice alarm systems on underground stations

Sound attenuation of air due to climatic conditions is often assumed to be constant and/or negligible in the electro acoustic design of voice alarm (VA) systems. However, air attenuation variations can be significant in large underground spaces and particularly as the frequency increases to the mid to high frequencies which are the most relevant to speech intelligibility. This investigation evaluates and quantifies the impact of the variability of the most influential climatic parameters, air temperature and relative humidity, on the performance of VA systems in underground stations. Computer simulations were employed to predict the effect of varying these climatic parameters on key performance metrics. Results demonstrated a significant increase in the values of reverberation time parameters with both temperature and humidity, at frequencies critical for speech intelligibility. Consequently the values of speech intelligibility related metrics decreased with rising temperatures and humidity. Hence, the study shows how ignoring temperature and humidity effects can lead to calculation errors in the design of VA systems. These errors could cause over-specification of the absorption required of surface materials, and the inaccurate prediction of acoustic and speech intelligibility related parameters.     

结构微裂纹混频非线性超声检测方法研究

给出了一种基于混频效应的非线性超声微裂纹检测方法。首先,对结构损伤混频检测机理及信号特征提取方法进行了理论分析,之后,根据试件中差频分量及和频分量幅值分布随激励信号频率变化关系,优化确定出混频检测参数。最后,进行了异侧混频激励下无损检测试验研究,并分析了激励信号频率变化对混频检测效果的影响。结果表明,异侧激励混频检测模式不仅可以实现结构中疲劳微裂纹检测,而且可以实现缺陷的定位。且检测信号频率选择对混频检测信噪比有一定的影响。当检测信号中的混频分量幅值最大时,混频检测效果最佳。因此,在优化检测参数基础上,异侧混频激励检测模式可以很好实现结构微裂纹的检测与定位。      

Wideband modulation instability at combination frequencies in wave beams

We study theoretically wideband modulation instability at combination frequencies in media having cubic nonlinearity of self-focusing type along with the higher-order defocusing nonlinearity. It is assumed that in a medium with a purely cubic nonlinearity, the medium dispersion does not permit modulation instability. In this case, a collapse of the wave field exists if the beam power is higher than the critical power of self-focusing. The higher-order nonlinearity limits the field at the nonlinear focus, and the instability at combination frequencies becomes possible. It turns out that the field at the nonlinear focus increases with increasing excess of the beam power over the critical power of self-focusing. The obtained values of the nonlinear dielectric permittivity are used for determination of the growth rates of instability at combination frequencies. These growth rates ensure an increase in the combination fields from noise levels up to values comparable with the field of the high-power beam. Such an increase takes place if the beam power is severalfold higher than the critical one. The developed theory can be used for explanation of spectrum superbroadening during self-focusing of sufficiently short laser pulses and high-harmonic generation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 6, pp. 522–532, June 2007.