Duration of whole-body vibration exposure its effect on comfort

Most human response to vibration standards imply that low vibration levels are acceptable for longer periods than higher levels. In such standards it is usually assumed that the relationship between exposure duration and vibration level is of a similar form for a wide range of different types of motion. The experiment described in this paper was conducted to determine whether the relative discomfort produced by 4 Hz and 16 Hz sinusoidal whole-body vertical (a_z) vibration was dependent on the duration of the vibration exposure.Each of eight seated subjects was exposed to two 36-minute vibration sessions. Both sessions consisted of ten-second periods of 4 Hz and 16 Hz vibration alternating continuously. In one session the 4 Hz motion was set at the “standard” level of 0·75 m/s² r.m.s. while the level of the 46 Hz “test” motion could be adjusted by the subjects. In the other session the 16 Hz motion was the standard at 0·75 m/sl r.m.s. and the level of the 4 Hz motion could be adjusted. The subjects were required to control the intensity of the test motion to compensate for periodic changes in its intensity made by the experimenter and so to maintain it at a level which produced similar discomfort to that caused by the standard motion.It was found that the relationship between the average levels of the two motions when adjusted to produce similar discomfort was independent of the vibration duration. The findings are discussed in relation to other laboratory research and the need for a better understanding of the effects of the duration of a vibration on its acceptability.     

Dynamic and subjective responses of seated subjects exposed to simultaneous vertical and fore-and-aft whole-body vibration: The effect of the phase between the two single-axis components

Subjective and dynamic responses of seated subjects exposed to simultaneous vertical and fore-and-aft sinusoidal whole-body vibration were investigated. The effect of the phase difference between the vertical and the fore-and-aft vibration on the responses was of a particular interest in this study. Fifteen subjects were exposed to dual-axis vibrations at six frequencies (2.5-8 Hz) and at eight phases between the two single-axis components (0-315°). The magnitude of vibration in each axis was constant at 0.7 m s⁻² rms. Discomfort caused by vibration was measured by the method of magnitude estimation. The motion of the body were measured at the head and three locations along the spine with accelerometers attached to the body surface. The most significant effect of the phase between the two single-axis components on the discomfort was observed at 5 Hz: about 40% difference in the median discomfort estimate caused by changing the phase. The transmissibilities from vertical seat vibration to vertical motions of the spine varied from 0.5 to 2.0 by changing the phase between the two single-axis components at frequencies from 2.5 to 5 Hz. The effect of the phase observed in the dynamic response was not predicted by the superposition of the responses to each single-axis vibration. The discomfort caused by the dual-axis vibration tended to be correlated better with the combinations of the dynamic responses measured in the two axes than with the dynamic responses in a single axis.     

Comparison of the apparent masses and cross-axis apparent masses of seated humans exposed to single- and dual-axis whole-body vibration

Humans are exposed to whole-body vibration in many types of environment. In almost all cases, the vibration to which the human is exposed comprises multi-axis vibration, such that vibration occurs in all directions simultaneously. Despite the complex nature of vibration to which humans are exposed in the workplace, almost all laboratory studies investigating the biomechanical response of the person have been completed using single-axis simulators. This paper presents a study whereby 15 male subjects were exposed to single-axis whole-body vibration in the x-, y- and z-directions and dual-axis vibration in the xy-, xz-, and yz-directions using a 6 degree-of-freedom vibration simulator. All vibration magnitudes were 0.4 ms⁻² rms in each axis. Acceleration and force was measured in the x-, y-, and z-direction during all trials. Subjects sat in two postures (‘back-on’ and ‘back-off’) on a flat rigid seat. Apparent masses measured using single-axis and dual-axis vibration stimuli showed comparable results; similarly, cross-axis apparent masses (i.e. the ratio of the force in one direction to the acceleration in another direction) were almost identical for the single- and dual-axis vibration stimuli. All results were in agreement with data previously published using single-axis vibration. In most cases, the peaks in the apparent mass and the cross-axis apparent mass occurred at a slightly lower frequency for the dual-axis vibration than for the single-axis vibration. It is hypothesised that this change is due to a nonlinear effect, analogous to that which occurs with increasing vibration magnitude for single-axis vibration.     

Analyses of biodynamic responses of seated occupants to uncorrelated fore-aft and vertical whole-body vibration

The apparent mass and seat-to-head-transmissibility response functions of the seated human body were investigated under exposures to fore-aft (x), vertical (z), and combined fore-aft and vertical (x and z) axis whole-body vibration. The coupling effects of dual-axis vibration were investigated using two different frequency response function estimators based upon the cross- and auto-spectral densities of the response and excitation signals, denoted as H₁ and H_v estimators, respectively. The experiments were performed to measure the biodynamic responses to single and uncorrelated dual-axis vibration, and to study the effects of hands support, back support and vibration magnitude on the body interactions with the seatpan and the backrest, characterized in terms of apparent masses and the vibration transmitted to the head. The data were acquired with 9 subjects exposed to two different magnitudes of vibration applied along the individual x- and z-axis (0.25 and 0.4 m/s² rms), and along both the axis (0.28 and 0.4 m/s² rms along each axis) in the 0.5-20 Hz frequency range. The two methods resulted in identical single-axis responses but considerably different dual-axis responses. The dual-axis responses derived from the H_v estimator revealed notable effects of dual-axis vibration, as they comprised both the direct and cross-axis responses observed under single axis vibration. Such effect, termed as the coupling effect, was not evident in the dual-axis responses derived using the commonly used H₁ estimator. The results also revealed significant effects of hands and back support conditions on the coupling effects and the measured responses. The back support constrained the upper body movements and thus showed relatively weaker coupling compared to that observed in the responses without the back support. The effect of hand support was also pronounced under the fore-aft vibration. The results suggest that a better understanding of the seated human body responses to uncorrelated multi-axis whole-body vibration could be developed using the power-spectral-density based H_v estimator.     

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.     

CHAOTIC AND NON-LINEAR DYNAMIC ANALYSIS OF A TWO-AXIS RATE GYRO WITH FEEDBACK CONTROL MOUNTED ON A SPACE VEHICLE

An analysis is presented in this paper for a two-axis rate gyro subjected to linear feedback control mounted on a space vehicle, which is spinning with uncertain angular velocity ω_z(t) about its spin of the gyro. For the autonomous case in which ω_z(t) is steady, the stability analysis of the system is studied by Routh-Hurwitz theory. For the non-autonomous case in which ω_z(t) is sinusoidal function, this system is a strongly non-linear damped system subjected to parametric excitation. By varying the amplitude of sinusoidal motion, periodic and chaotic responses of this parametrically excited non-linear system are investigated using the numerical simulation. Some observations on symmetry-breaking bifurcations, period-doubling bifurcations, and chaotic behavior of the system are investigated by various numerical techniques such as phase portraits, Poincaré maps, average power spectra, and Lyapunov exponents. In addition, some discussions about chaotic motions of this system can be suppressed and changed into regular motions by a suitable constant motor torque are included.     

The nature of anharmonicity and anomalous piezoelectric properties of ferroelectric SbSBr crystal

The contribution of soft mode at Sb atom's sites, to the temperature dependences of Sb atom's equilibrium position's difference Δz(T) has been studied theoretically, when SbSBr crystal is deformed along a(x), b(y) and c(z)-axis in paraelectric phase and is deformed along c(z)-axis in ferroelectric phase. The largest change of Δz₃₃(T) occurs in the ferroelectric phase near the phase transition temperature in the range from 16 K to 21 K. The temperature dependence of Sb atom's equilibrium position's displacements Δz₃₃ is very similar to the temperature dependence of experimental piezoelectric modulus, when SbSBr crystal is deformed in the direction of c(z)-axis in ferroelectric phase.     

Development of noise and vibration ride comfort criteria.

A laboratory investigation was directed at the development of criteria for the prediction of ride quality in a noise-vibration environment. The stimuli for the study consisted of octave bands of noise centered at 500 and 2000 Hz and vertical floor vibrations composed of either 5 Hz sinusoidal vibration, or random vibrations centered at 5 Hz and with a 5 Hz bandwidth. The noise stimuli were presented at A-weighted sound pressure levels ranging from ambient to 95 dB and the vibration and acceleration levels ranging from 0.02--0.13 grms. Results indicated that the total subjective discomfort response could be divided into two subjective components. One component consisted of subjective discomfort to vibration and was found to be a linear function of vibration acceleration level. The other component consisted of discomfort due to noise which varied logarithmically with noise level (power relationship). However, the magnitude of the noise discomfort component was dependent upon the level of vibration present in the combined environment. Based on the experimental results, a model of subjective discomfort that accounted for the interdependence of noise and vibration was developed. The model was then used to develop a set of criteria (constant discomfort) curves that illustrate the basic design tradeoffs available between noise and vibration.     

Anomalous thermoelastic behaviour of cubic potassium cyanide

The temperature dependence of all elastic constants of cubic potassium cyanide has been measured by ultrasonic methods in the range from -105.4 to 181°C. Until about 180°C all elastic wave velocities increase with higher temperatures. The behaviour of the shear constant c₄₄ is given by c₄₄ = a · logT/T₀ with a = 0.219 · 10¹¹dyn.cm^?2 and T₀ = 153.7°K with a good approximation. These unusual effects are assigned to the librational vibrations and orientational jumping processes of the CN-ions. The phase transition at -105.5°C is a consequence of the low c₄₄ value.     

Mechanical impedances distributed at the fingers and palm of the human hand in three orthogonal directions

The objective of this study is to investigate the basic characteristics of the three axis mechanical impedances distributed at the fingers and palm of the hand subjected to vibrations along three orthogonal directions (x_h, y_h, and z_h). Seven subjects participated in the experiment on a novel three-dimensional (3-D) hand–arm vibration test system equipped with a 3-D instrumented handle. The total impedance of the entire hand–arm system was obtained by performing a sum of the distributed impedances. Two major resonances were observed in the impedance data in each direction. For the hand forces (30 N grip and 50 N push) and body postures applied in this study, the first resonance was in the range of 20–40 Hz, and it was primarily observed in the impedance at the palm. The second resonance was generally observed in the impedance at the fingers, while the resonance frequency varied greatly with the subject and vibration direction, ranging from 100 to 200 Hz in the x_h direction, 60 to 120 Hz in the y_h direction, and 160 to 300 Hz in the z_h direction. The impedance at the palm was greater than that at the fingers below a certain frequency in the range of 50–100 Hz, depending on the vibration direction. At higher frequencies, however, the impedance magnitude at the fingers either approached or exceeded that at the palm. The impedance in the z_h direction was generally higher than those in the other directions, but it became comparable with that in the x_h direction at frequencies above 250 Hz, while the impedance in the y_h direction was the lowest. The frequency dependencies of the vibration power absorptions for the entire hand–arm system in the three directions were different, but their basic trends were similar to that of the frequency weighting defined in the current ISO standard. The implications of the results are discussed.     

Effect of phase on discomfort caused by vertical whole-body vibration and shock--experimental investigation

An experimental study has investigated the effect of "phase" on the subjective responses of human subjects exposed to vertical whole-body vibration and shock. The stimuli were formed from two frequency components: 3 and 9 Hz for continuous vibrations and 3 and 12 Hz for shocks. The two frequency components, each having 1.0 ms(-2) peak acceleration, were combined to form various waveforms. The effects of the vibration magnitude on the discomfort caused by the input stimuli were also investigated with both the continuous vibrations and the shocks. Various objective measurements of acceleration and force at the seat surface, the effects of different frequency weightings and second and fourth power evaluations were compared with judgments of the discomfort of the stimuli. It was found that a 6% to 12% increase in magnitude produced a statistically significant increase in discomfort with both the continuous vibrations and the shocks. Judgments of discomfort caused by changes in vibration magnitude were highly correlated with all of the objective measurements used in the study. The effects on discomfort of the phase between components in the continuous vibrations were not statistically significant, as predicted using evaluation methods with a power of 2. However, small changes in discomfort were correlated with the vibration dose value (VDV) of the Wb frequency-weighted acceleration. The effect of phase between frequency components within the shocks was statistically significant, although no objective measurement method used in the study was correlated with the subjective judgments.     

Crystal structure of 1-amino-2-phenyl benzocycloheptanol hydrobromide monohydrate

Crystals of 1-amino 2-phenyl benzocycloheptanol hydrobromide monohydrate are orthorhombic witha=6·927(17),b=30·947(40),c=30·990(40) Å,z=16 and the space group is Iba2.ρ=1·41 gm/ccρ _cal=1·403 gm/cc,μ for CuK_α=37.06 cm^?1. The structure was solved by heavy atom method using three dimensional x-ray intensity data and refined by block diagonal and full matrix least squares method to anR-index of 0·106. The structure is stabilised by a number of hydrogen bonds of the type N-H…O, O-H…Br, N-H…Br. The heptane rings in this molecule are in chair conformation.     

Inversion-rotation interaction in NH2D: Intensity perturbations in the ν2 band

The parameters of NH₂D in the ground and ν₂ states have been refined by a simultaneous analysis of the microwave, FTIR, and diode laser data. The intensities of 46 NH₂D lines have been measured, and from a least-squares fit of the intensity data the a ← s, s ← a, s ← s, and a ← a transition moments have been derived. The intensities of the lines in the ν₂ band of NH₂D have been calculated taking into account the inversion-rotation interaction. The accuracies of the wavenumbers and intensities calculated with the new parameters are estimated to be better than ±0.0002 cm⁻¹ and ±5%, respectively. The matrix elements for interaction of vibrations through x, y, and z axis couplings are appended.     

A study of electrostatic spring softening for dual-axis micromirror

Electrostatic spring softening is an important characteristic of electrostatically actuated dual-axis micromirror, since it lowers the resonant frequencies. This paper presents an approach based on approximating the electrostatic forces by the first-order Taylor's series expansion to investigate this characteristic. The dual-axis micromirror studied in this paper has three motion modes, two torsional (about x- and y-axis, respectively) and one translational (about z-axis). The stiffnesses of all these modes are softened by a DC bias voltage applied to the mirror plate. The resonant frequencies are lowered with the increment of the bias voltage. The relationship of the bias voltage and the resonant frequencies of all the motion modes is derived. The analytical results show that the resonant frequency curves are affected by the capacitor geometries, i.e. the gap between the mirror plate and the electrodes and the electrodes size. The lowering curves drop slowly when the bias voltage is small. While for large bias voltage, the lowering curves drop rapidly. The experiment results are consistent with those obtained by the analytical approach.     

Dissociative excitation of odd sextet levels of the manganese atom in the e-MnCl2 collisions

The dissociative excitation of odd sextet levels of the manganese atom in collisions between slow electrons and manganese dichloride molecules was studied experimentally. The cross sections for the population of the metastable a ⁶ D levels (the lower levels of the laser transitions) by cascade transitions have been determined. It is established that for the z ⁶ F° and z ⁶ D° levels, the cross sections for both the dissociative and direct excitation, Q _m and Q _a , respectively, differ only slightly in absolute value. For the x ⁶ P° levels, the ratio Q _a /Q _m amounts to 9–11, but for the upper laser levels it is much larger: 33 for the z ⁶ P° level and 240 for the y ⁶ P° level.     

Analysis of signal-to-noise ratio and heterodyne efficiency for reference-beam laser Doppler velocimeter

Heterodyne efficiency is a very important factor in a laser Doppler velocimeter (LDV). Gaussian-Airy mode is put forward to analyze the heterodyne efficiency. By studying the distribution of the optical field, the mathematic expression and simulation results of heterodyne efficiency are given under the conditions of both exact match and mismatch. The results of numerical analysis show that heterodyne efficiency of LDV depends on Gaussian beam's parameter Q, detector's parameter X₀, angle of collimation mismatching θ_a, parameter of offset mismatching X_a and the radius of curvature of the reference beam on the detector R(z). Heterodyne efficiency can reach 83.39% when Q=4.15×10^?7, X₀=6.1×10^?7, θ_a=X_a=0, R(z)=∞. But it declines to 0.5 when Fθ_a enhances to 0.28. It decreases with the increment of the offset X_a and the diminishment of the radius of curvature R(z). Results of experiment are in good accordance with the theoretical analysis.     

Specific features of the ferroelastic phase transition in CsLiS1−z CrzO4 solid solutions

Single crystals of the CsLiS_1?z Cr_zO₄ solid solutions (z = 0, 0.1, 0.4, 0.5, 0.9, 1.0) are grown, optical polarization studies are performed, and the birefringence and the angle of rotation of the optical indicatrix φ(T) are measured. A (z?T) phase diagram is constructed in the temperature range from 77 to ～550 K. It is established that substitution of chromium for sulfur has practically no effect on the shape of the optical indicatrix in the initial phase with Pmcn symmetry but produces strong distortions in the monoclinic phase with P112₁/n symmetry. The unusual shape of the curve φ(T) for compositions with z ≈ 1 is accounted for by the interaction of the polarization-constant tensor components a _ij. No radical differences in the patterns of the ferroelastic phase transition between CsLiSO₄ and CsLiCrO₄ are revealed (the critical exponent for the transition parameter is β = 0.33 ± 0.01). These crystals differ only in the magnitudes of the anomalies, which is associated with the large difference between the ionic radii of sulfur and chromium.     

Vibrations of bonded beams with a single lap adhesive joint

The natural frequencies and loss factors of the coupled longitudinal and flexural vibrations of a system consisting of a pair of parallel and identical elastic cantilevers which are lap-jointed by viscoelastic material over a length a_c from their free ends have been investigated. A complete set of equations of motion and boundary conditions governing the vibration of the system are derived. The solution of these equations, subject to satisfying the boundary conditions, yields the desired natural frequencies and associated composite loss factors. The numerical results have been compared with those from two other approximate methods.     

Higher-order fine structure of the a4Πu state of O2+

It is shown that the quality of the fit of frequencies for the (4, 4) band of the b⁴Σ_g^?-a⁴Π_u transition of O₂⁺, obtained in an ion-beam experiment, can be significantly improved by the inclusion of a fine structure term of the form L_zS_z³ in the effective Hamiltonian for the a⁴Π_u state, where L_z and S_z are respectively the components of the total orbital and spin angular momenta along the internuclear axis. The various contributions to this term in the Hamiltonian are assessed from a general standpoint by the use of a new order-of-magnitude scheme. The separate contributions to the parameter involved, η, are then considered in detail by means of a perturbation treatment of the spin-orbit and spin-spin interactions through third order. Attempts to interpret the parameter values determined for the a⁴Π_u state of O₂⁺ are severely limited by the present lack of detailed knowledge of the properties of the various electronic states of O₂⁺.     

The sign of the quadrupole interaction of the 828 keV state of115In in Zn

Sign and magnitude of the electric quadrupole interaction of the 828 keV state of¹¹⁵In in a Zn single crystal was determined by aβ-γ TDPAC measurement. The result:v _Q =e·'Q _I V _zz /h=?193(13)MH_z confirms the universal correlation between the electronic and ionic contributions to the total electric field gradient proposed by R.S. Raghavan et al.