The horizontal apparent mass of the standing human body

The driving-point dynamic responses of standing people (e.g. their mechanical impedance or apparent mass) influence their dynamic interactions with structures on which they are supported. The apparent mass of the standing body has been reported previously for vertical excitation but not for lateral or fore-and-aft excitation. Twelve standing male subjects were exposed to fore-and-aft and lateral random vibration over the frequency range 0.1-5.0 Hz for 180 s at four vibration magnitudes: 0.016, 0.0315, 0.063, and 0.125 m s⁻² rms. With lateral excitation at 0.063 m s⁻² rms, subjects also stood with three separations of the feet. The dynamic forces measured at the driving-point in each of the three translational axes (i.e. fore-and-aft, lateral and vertical) showed components not linearly related to the input vibration, and not seen in previous studies with standing subjects exposed to vertical vibration or seated subjects exposed to vertical or horizontal vibration. A principal peak in the lateral apparent mass around 0.5 Hz tended to decrease in both frequency and magnitude with increasing magnitude of vibration and increase with increasing separation of the feet. The fore-and-aft apparent mass appeared to peak at a frequency lower than the lowest frequency used in the study.     

Magnitude-dependence of equivalent comfort contours for fore-and-aft, lateral and vertical whole-body vibration

It is currently assumed that the same frequency weightings, derived from studies of vibration discomfort, can be used to evaluate the severity of vibration at all vibration magnitudes from the threshold of vibration perception to the vibration magnitudes associated with risks to health. This experimental study determined equivalent comfort contours for the whole-body vibration of seated subjects over the frequency range 2-315 Hz in each of the three orthogonal axes (fore-and-aft, lateral and vertical). The contours were determined at vibration magnitudes from the threshold of perception to levels associated with severe discomfort and risks to health.At frequencies greater than 10 Hz, thresholds for the perception of vertical vibration were lower than thresholds for fore-and-aft and lateral vibration. At frequencies less than 4 Hz, thresholds for vertical vibration were higher than thresholds for fore-and-aft and lateral vibration. The rate of growth of sensation with increasing vibration magnitude was highly dependent on the frequency and axis of vibration. Consequently, the shapes of the equivalent comfort contours depended on vibration magnitude. At medium and high vibration magnitudes, the equivalent comfort contours were reasonably consistent with the frequency weightings for vibration discomfort in current standards (i.e. W_b and W_d). At low vibration magnitudes, the contours indicate that relative to lower frequencies the standards underestimate sensitivity at frequencies greater than about 30 Hz. The results imply that no single linear frequency weighting can provide accurate predictions of discomfort caused by a wide range of magnitudes of whole-body vibration.     

Lateral magnetic stiffness under different parameters in a high-temperature superconductor levitation system

Magnetic stiffness determines the stability of a high-temperature superconductor(HTS) magnetic levitation system.The quantitative properties of the physical and geometrical parameters that affect the stiffness of HTS levitation systems should be identified for improving the stiffness by some effective methods. The magnetic stiffness is directly related to the first-order derivative of the magnetic force with respect to the corresponding displacement, which indicates that the effects of the parameters on the stiffness should be different from the relationships between the forces and the same parameters.In this paper, we study the influences of some physical and geometrical parameters, including the strength of the external magnetic field(B0) produced by a rectangular permanent magnet(PM), critical current density(Jc), the PM-to-HTS area ratio(α), and thickness ratio(β), on the lateral stiffness by using a numerical approach under zero-field cooling(ZFC)and field cooling(FC) conditions. In the first and second passes of the PM, the lateral stiffness at most of lateral positions essentially increases with B0 increasing and decreases with β increasing in ZFC and FC. The largest lateral stiffness at every lateral position is almost produced by the minimum value of Jc, which is obviously different from the lateral force–Jc relation. The α-dependent lateral stiffness changes with some parameters, which include the cooling conditions of the bulk HTS, lateral displacement, and movement history of the PM. These findings can provide some suggestions for improving the lateral stiffness of the HTS levitation system.     

The vibration discomfort of standing persons: 0.5-16-Hz fore-and-aft, lateral, and vertical vibration

To minimise the discomfort of standing people caused by vibration of a floor, it is necessary to know how their sensitivity to vibration depends on the frequency of the vibration. This study was designed to determine how the discomfort of standing people exposed to horizontal and vertical vibration depends on vibration frequency over the range 0.5-16 Hz. Using the method of magnitude estimation, sixteen subjects judged the discomfort caused by fore-and-aft, lateral, and vertical sinusoidal vibration at each of the sixteen preferred one-third octave centre frequencies from 0.5 to 16 Hz at each of nine magnitudes. Subjects also reported the main cause of their discomfort. Equivalent comfort contours were constructed, reflecting the effect of frequency on subject sensitivity to vibration acceleration. With horizontal vibration, at frequencies between 0.5 and 3.15 Hz the discomfort was similar when the vibration velocity was similar, whereas at frequencies between 3.15 and 16 Hz the discomfort was similar when the vibration acceleration was similar. At frequencies less than 3.15 Hz, the subjects experienced problems with their stability, whereas at higher frequencies vibration discomfort was mostly experienced from sensations in the legs and feet. With vertical vibration, discomfort was felt in the lower-body and upper-body at all frequencies. The frequency weightings in current standards for predicting the vibration discomfort of standing persons have been greatly influenced by the findings of studies with seated subjects: the weightings are consistent with the experimentally determined frequency-dependence of discomfort caused by vertical vibration but inconsistent with the experimentally determined frequency-dependence of discomfort caused by horizontal vibration. The results suggest that the responses of seated and standing people are similar for vertical vibration, but differ for horizontal vibration, partly due to greater instability in standing persons.     

基于超导块材磁刚度特性的永磁轨道优化设计

目前高温超导磁悬浮实验车使用的是单极永磁轨道(PMG).为了提高磁悬浮车的运行稳定性,人们做出了大量的研究.磁悬浮刚度是设计优化高温超导磁悬浮车的一项很重要的参数.文中研究了七块YBCO块材阵列在两种结构不同的永磁轨道上方的竖直方向刚度和横向力刚度的特性.通过比较测试结果,得出七块YBCO阵列与双极型永磁轨道组成的磁悬...     

A distributed-mass approach for dynamic analysis of Bernoulli-Euler plane frames

The exact dynamic analysis of plane frames should consider the effect of mass distribution in beam elements, which can be achieved by using the dynamic stiffness method. Solving for the natural frequencies and mode shapes from the dynamic stiffness matrix is a nonlinear eigenproblem. The Wittrick-Williams algorithm is a reliable tool to identify the natural frequencies. A deflated matrix method to determine the mode shapes is presented. The dynamic stiffness matrix may create some null modes in which the joints of beam elements have null deformation. Adding an interior node at the middle of beam elements can eliminate the null modes of flexural vibration, but does not eliminate the null modes of axial vibration. A force equilibrium approach to solve for the null modes of axial vibration is presented. Orthogonal conditions of vibration modes in the Bernoulli-Euler plane frames, which are required in solving the transient response, are theoretically derived. The decoupling process for the vibration modes of the same natural frequency is also presented.     

Magnitude-dependence of equivalent comfort contours for fore-and-aft, lateral, and vertical vibration at the foot for seated persons

Vibration at the feet can contribute to discomfort in many forms of transport and in some buildings. Knowledge of the frequency-dependence of discomfort caused by foot vibration, and how this varies with vibration magnitude, will assist the prediction of discomfort caused by vibration. With groups of 12 seated subjects, this experimental study determined absolute thresholds for the perception of foot vibration and quantified the discomfort caused by vibration at the foot. The study investigated a wide range of magnitudes (from the threshold of perception to levels associated with severe discomfort) over a wide range of frequencies (from 8 to 315 Hz in one-third octave steps) in each of the three orthogonal translational axes (fore-and-aft, lateral, and vertical). The effects of gender and shoes on absolute thresholds for the perception of vertical vibration at the foot were also investigated. Within each of the three axes, the vibration acceleration corresponding to the absolute thresholds for the perception of vibration, and also all contours showing conditions producing equivalent discomfort, were highly frequency-dependent at frequencies greater than about 40 Hz. The acceleration threshold contours were U-shaped at frequencies greater than 80 Hz in all three axes of excitation, suggesting the involvement of the Pacinian channel in vibration perception. At supra-threshold levels, the frequency-dependence of the equivalent comfort contours in each of the three axes was highly dependent on vibration magnitude. With increasing vibration magnitude, the conditions causing similar discomfort across the frequency range approximated towards constant velocity. Thresholds were not greatly affected by wearing shoes or subject gender. The derived frequency weightings imply that no single linear frequency weighting can provide accurate predictions of discomfort caused by a wide range of magnitudes of foot vibration.     

Angular dependence of vertical force and torque when magnetic dipole moves vertically above flat high-temperature superconductor

The interaction between a permanent magnet (PM) assumed as a magnetic dipole and a flat high-temperature superconductor (HTS) is calculated by the advanced frozen-image model. When the dipole vertically moves above the semi-infinite HTS, the general analytical expression of vertical force and that of torque are obtained for an arbitrary angle between the magnetization direction of the PM and the c axis of the HTS. The variations of the force and torque are analyzed for angle and vertical movements in both zero-field cooling (ZFC) condition and field cooling (FC) condition. It is found that the maximum vertical repulsive or attractive force has the positive or negative cosine relation with the angle. However, the maximum torque has the positive or negative sine relation. From the viewpoint of the rotational equilibrium, the orientation of the magnetic dipole with zero angle is deemed to be an unstable equilibrium point in ZFC, but the same orientation is considered as a stable equilibrium point in FC. In addition, both of the variation cycles of the maximum force and torque with the angle are π.     

环形ZnO薄膜谐振器的横模抑制与测试分析

采用Tiersten方程研究了环形ZnO薄膜谐振器中横模寄生问题, 获得了环(圆)形薄膜谐振器的横模振动方程, 求得横模位移场解和频率色散方程; 然后采用电磁学模式合成理论进行分析, 发现环形薄膜谐振器横模频率与环形电极的内外径之比a/b有关, 振动模式可由圆形薄膜谐振器横模模式合成得到, 通过控制a/b能够抑制横模模式数和调控基膜频率. 采用外差激光干涉仪和网络矢量分析仪测量并比较了同批次的圆形和环形薄膜谐振器的上电极横模振动图样和电阻抗曲线. 振动图样显示环形薄膜谐振器振动模式可由半径为a和半径为b的圆形薄膜谐振器振动模式合成, 仅存在节圆数大于0的横模振动, 等于0的横模模式被抑制; 电阻抗曲线显示当a/b为0.436时, 环形薄膜谐振器的基频(约1217 MHz)和圆形的(0, 1)模式频率相等. 测量数据验证了模式合成理论的分析结果正确性, 为薄膜谐振器的横模抑制研究提供了理论基础和新方法.     

Influences of cooling height and lateral moving speed on the levitation characteristics of YBaCuO bulks

Using an updated high-temperature superconductor (HTS) maglev measurement system, electromagnetic forces between a YBaCuO bulk superconductor and a permanent magnet (PM) have been measured under different cooling height (CH) and different lateral moving speed of the PM. It is found that the influence of the moving speed on both the levitation and lateral force is substantial and as such the results shown in this work are a benefit to the understanding of levitation systems.     

Influence of experimental methods on crossing in magnetic force–gap hysteresis curve of HTS maglev system

The crossing in magnetic levitation force–gap hysteresis curve of melt high-temperature superconductor (HTS) vs. NdFeB permanent magnet (PM) was experimentally studied. One HTS bulk and PM was used in the experiments. Four experimental methods were employed combining of high/low speed of movement of PM with/without heat insulation materials (HIM) enclosed respectively. Experimental results show that crossing of the levitation force–gap curve is related to experimental methods. A crossing occurs in the magnetic force–gap curve while the PM moves approaching to and departing from the sample with high or low speed of movement without HIM enclosed. When the PM is enclosed with HIM during the measurement procedures, there is no crossing in the force–gap curve no matter high speed or low speed of movement of the PM. It was found experimentally that, with the increase of the moving speed of the PM, the maximum magnitude of levitation force of the HTS increases also. The results are interpreted based on Maxwell theories and flux flow-creep models of HTS.     

Flexural wave suppression by an acoustic metamaterial plate

A new acoustic metamaterial plate is presented for the purpose of suppressing flexural wave propagation. The metamaterial unit cell is made of a plate with a lateral local resonance (LLR) substructure which consists of a four-link mechanism, two lateral resonators and a vertical spring. The substructure presents negative Young’s modulus property in certain frequency range. We show theoretically and numerically that two large low-frequency band gaps are obtained with different formation mechanisms. The first band gap is due to the elastic connection with the foundation while the second is induced by the lateral resonances. Besides, four-link mechanisms can transform the flexural wave into the longitudinal vibration which stimulates the lateral resonators to vibrate and to generate inertial forces for absorbing the energy and thus preventing the wave propagation. Frequency response function shows that damping from the vertical spring has little influence on the band gaps, although the damping can smooth the variation of frequency response (see the dotted line in Figs. 10 and 11). Increasing the damping of the lateral resonators may broaden the second band gap but deactivate its effect. This study provides guidance for flexibly tailoring the band characteristics of the metamaterial plate in noise and vibration controls.     

Holding characteristics of planar objects suspended by near-field acoustic levitation

The authors have found the acoustic levitation phenomenon where planar objects of 10 kg weight can be levitated near a vibration surface. This phenomenon has been studied for non-contact transportation. A circular planar object can be suspended without contacting a circular vibration plate. We have studied the holding force which acts horizontally on the levitated objects. The horizontal position of the object is stabilized by this force. In this paper, we discuss the effect of the radius of a levitated object, levitation distance, displacement amplitude of the vibration plate and the vibration mode on the suspending force.     

Non-linear dual-axis biodynamic response to vertical whole-body vibration

Seated human subjects have been exposed to vertical whole-body vibration so as to investigate the non-linearity in their biodynamic responses and quantify the response in directions other than the direction of excitation. Twelve males were exposed to random vertical vibration in the frequency range 0.25-25 Hz at four vibration magnitudes (0.125, 0.25, 0.625, and 1.25 m s⁻² r.m.s.). The subjects sat in four sitting postures having varying foot heights so as to produce differing thigh contact with the seat (feet hanging, feet supported with maximum thigh contact, feet supported with average thigh contact, and feet supported with minimum thigh contact). Forces were measured in the vertical, fore-and-aft, and lateral directions on the seat and in the vertical direction at the footrest.The characteristic non-linear response of the human body with reducing resonance frequency at increasing vibration magnitudes was seen in all postures, but to a lesser extent with minimum thigh contact. Appreciable forces in the fore-and-aft direction also showed non-linearity, while forces in the lateral direction were low and showed no consistent trend. Forces at the feet were non-linear with a multi-resonant behaviour and were affected by the position of the legs.The decreased non-linearity with the minimum thigh contact posture suggests the tissues of the buttocks affect the non-linearity of the body more than the tissues of the thighs. The forces in the fore-and-aft direction are consistent with the body moving in two directions when exposed to vertical vibration. The non-linear behaviour of the body, and the considerable forces in the fore-aft direction should be taken into account when optimizing vibration isolation devices.     

Levitation force relaxation under reloading in a HTS Maglev system

The loading capacity of the high-temperature superconducting (HTS) Maglev vehicle is an important parameter in the practical application. It is closely related to the levitation force of the HTS bulk. Many papers reported that the levitation force showed the relaxation characteristic. Because different loads cause different levitation gaps and different applied magnetic fields, the levitation force relaxations under the different loads are not the same. In terms of cylindrical YBCO bulk levitated over the permanent magnetic guideway, the relationship between the levitation force relaxation and the reloading is investigated experimentally in this paper. The decrement, the decrement rate and the relaxation rate of the levitation force are calculated, respectively. This work might be helpful for studying the loading capacity of the HTS Maglev vehicle.     

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.     

Coarsening dynamics of striped patterns in thin granular layers under vertical vibration

The process of pattern formation in granular layers was experimentally studied. Ten layers of granular materials inside a vacuum container were placed under a vertical vibration of A sin2pi f t. Control parameters were the dimensionless acceleration Gamma = A(2pi f)(2)/g and vibration frequency f. When the system was quenched from a flat pattern state to a striped pattern state by instantly increasing Gamma, there were more than 10(4) periods before a full steady striped pattern appeared. This nonequilibrium and nonsteady process showed dynamic scaling behavior. The growth exponent of the characteristic length scale of the ordered domain was 0.25, which agrees with that of the Swift-Hohenberg system.     

Predicting the effects of vertical vibration frequency,combinations of frequencies and viewing distance on the reading of numeric displays

This paper describes a series of experiments to determine the effects of vibration frequency, viewing distance and multiple frequency motions on the reading of numeric characters. Contours of vertical (z-axis) whole-body vibration levels resulting in equal degradation of the reading task were determined over the frequency range 2·8 Hz to 63 Hz. With the seating condition employed, the task was found to be most sensitive to vibration acceleration at a frequency of 11·2 Hz. A marked correlation was observed between reading error and reading speed. The effects of vibration on reading performance were found to be dependent on viewing distance for distance of less than 1·5 m, with the effect increasing as the viewing distance was decreased. The effect of 3·15 Hz vibration was found to increase more rapidly with reductions in viewing distance than that of 16 Hz vibration. The effects of 3·15 and 16 Hz vibration were independent of viewing distance greater than 1·5 m, indicating that the effects of rotational eye motion are dominant at these distances. Four methods were compared for predicting the effects of multiple frequency motion on reading performance given a knowledge of the effect of each component alone. The best predictions of reading error were obtained from the most severe weighted spectral component alone. Inspection of individual subject's data suggests that in many cases the effect of multiple frequency vibration on reading is even less than the effect of the largest sinusoidal component alone.     

Whirling motion of a shallow cable with viscous dampers

The paper deals with the non-linear dynamic analysis of cables with a pair of viscous dampers close to one support. Such cables are characterized by a sag-to-chord-length ratio below 0.02, for which natural frequencies for the vertical and the horizontal vibrations are pair-wise close. Under resonance the non-linear coupling of pairs of modes may cause whirling harmonic motions around the chord line. Whirling motion may occur after bifurcation from single-mode response for harmonic loads in either vertical or horizontal direction. The non-linear features are included in the two coupled modes, while all other modes are treated as linear. The motion is discretized by expansion in terms of the damped complex eigenfunctions. The applied base functions fulfil the transition condition at the damper, leading to fast convergence of the expansion. It is demonstrated that the behaviour of the whirling motion is controlled primarily by the damper acting in the direction of the unloaded mode, whereas the magnitude of the damper in the loaded mode is less important. If the dampers in the vertical and horizontal direction are close to the optimal value of the corresponding taut cable case, substantial reduction of the vibration level of the whirling mode as well as the frequency interval of its occurrence is attained.     

Hot-film anemometry for measuring lateral line stimuli

A hot-film anemometer system has been calibrated and evaluated for the measurement of sinusoidal water motions used in stimulating the mechanosensory lateral line system of a teleost fish. The response of the anemometer system to water motions created by a vibrating sphere was measured over a wide range of frequencies, intensities, and distances from the sphere. The amplitude response of the system to signals along the axis of sphere vibration was found to be linear over a 50-dB range for frequencies from 10-200 Hz, with the lowest end of the dynamic range (between 10(-8) and 10(-9) m) corresponding to physiological measures of best sensitivity in the lateral line system of the mottled sculpin, Cottus bairdi. The measured attenuation of the signal with distance was also linear over this frequency range out to distances of six times the radius ( = 3 mm) of the sphere and followed the predicted falloff rate for a dipolar source. The linear response of the anemometer system over a wide dynamic range encompassing the detection range of the lateral line system, and the match between predicted and measured motions at varying distances from a dipolar source, indicates that hot-film anemometry is a useful technique for measuring low-level, low-frequency signals likely to stimulate the lateral line system and other hydrodynamic detectors.