Pitch Mode Research Articles

The semi-phenomenological model of antiferroelectricity in chiral smectic liquid crystals III. Dielectric spectroscopy

In the framework of the model of short pitch modes (SPM) developed for antiferroelectric liquid crystals, the sets of various relaxation modes related to ferro-, antiferro- and ferrielectric phases are explained. The 'soft-like' modes describe the amplitude perturbations of short pitch modes, while the Goldstone modes describe the azimuthal perturbations of the molecular packings related to short pitch modes. The frequencies of the Goldstone modes are mainly determined by the chirality parameter, depending on the number of short pitch modes. The relaxation modes described correspond to the observed phase diagrams in liquid crystal materials for which the measurements of dielectric spectra are presented.

The semi-phenomenological model of antiferroelectricity in chiral smectic liquid crystals I. The structure of short pitch modes and a thermodynamical approach

The development of the model of short pitch modes for ferro-, antiferro- and ferri-electric chiral smectic liquid crystals is presented. Prediction of the structures of the subphases is made. The pure short pitch mode having an n-ray star structure of the n-layers of the unit cell appears to possess antiferroelectric properties. Ferrielectricity is assumed to arise as a result of the coexistence and interaction of the short pitch mode with a long pitch helix. Corresponding polarizational properties and fine structure of the peaks of the resonant X-ray scattering from such structures are calculated.

Hingeless-Rotor Aeromechanical Stability in Axial and Forward Flight With Wake Dynamics

A finite-state wake model is used to investigate aeromechanical stability of hingeless-rotor helicopters in the ground-contact, hover and trimmed-night conditions. The investigation covers three items: (1) the convergence of the damping with increasing number of wake harmonics for the lag regressing, and body pitch and roll modes; (2) a parametric study of the damping over a range of thrust level, advance ratio and number of blades; and (3) correlations, primarily with the damping and frequency measurements of these lag and body modes. The convergence and parametric studies are conducted in the hover and trimmed-flight conditions; they include predictions from the widely used dynamic inflow model. The correlations are conducted in the ground-contact conditions and include predictions from the dynamic inflow and vortex models; recently, this vortex model is proposed for the axial-flight conditions and is used to investigate the coupled free vibrations of rotor flapping and body modes. The convergence and parametric studies show that a finite-state wake model that goes well beyond the dynamic inflow model is required for fairly converged damping, Moreover, the correlations from the finite-state wake, dynamic inflow and vortex models are generally satisfactory.

Multichannel feedback control for the isolation of equipment from base vibration

Passive systems for the isolation of equipment from base vibration involve an inherent compromise between good high-frequency isolation, which requires low values of isolator damping, and limited excitation of the rigid body modes, which requires high values of isolator damping. It is known that a single-channel active control system using ‘‘skyhook damping,’’ in which a secondary force acts in proportion to the absolute velocity of the equipment, can give good damping in a lumped mass-spring-damper system without compromising the high-frequency isolation. In this experimental study a multichannel skyhook damper was used to study the isolation of a rigid mass from the vibrations of a flexible base plate. With the actuators and sensors wired together and the system excited symmetrically, a single-channel controller was initially implemented which not only showed reductions in the equipment vibration of up to 40 dB at the heave resonance at 15 Hz, but also showed substantial reductions at modes of the flexible base plate below about 200 Hz. The multichannel controller was also able to control the pitching mode of the equipment which is apparent when the system is not excited symmetrically.

Investigation of the helix unwinding process in thick freely suspended smectic films

Optical and electro-optical measurements have been performed on free-standing chiral smectic films sufficiently thick (10 000 layers) to preserve the natural smectic helix. The Goldstone mode appears at about 200Hz, showing that these films are a much better approximation of the 'ideal' smectic bulk state than a thick planar sample between glass plates (where the Goldstone mode is found at about 3 kHz). In these films the unwinding of the helix is studied, as a function of applied electric field, by monitoring Bragg reflections and their Fourier components. When the helix deforms, a reflection appears which at first sight might be taken for a subharmonic, but must be interpreted as the main 'full pitch mode' reflection relative to the 'half pitch' reflection from the undeformed helix. Our measurements further confirm that in anticlinic materials no helix unwinding takes place prior to the antiferroelectric-ferroelectric transition.

Human energy expenditure when walking on a moving platform.

The assumption that working on board ship is more strenuous than comparable work ashore was investigated in this study. Various physiological parameters (VO2, VCO2, VE and HR) have been measured to determine the energy expenditure of subjects walking slowly on a moving platform (ship motion simulator). Twelve subjects (eight men and four women) walked either freely on the floor or on a treadmill at a speed of 1 m x s(-1). Platform motion was either in a heave, pitch or roll mode. These three conditions were compared with a control condition in which the platform remained stationary. The results showed that during pitch and roll movements of the platform, the energy expenditure for the same walking task was about 30% higher than under the stationary control condition (3.6 J x kg[-1] x m[-1] vs 2.5 J x kg[-1] x m[-1], P < 0.05) for both walking on a treadmill and free walking. The heart rate data supported the higher energy expenditure results with an elevation of the heart rate (112 beats x min[-1] vs 103 beats x min[-1], P < 0.05). The heave condition did not differ significantly from the stationary control condition. Pitch and roll were not significantly different from each other. During all experimental conditions free walking resulted in a higher energy cost of walking than treadmill walking (3.5 J x kg[-1] x m[-1] vs 2.7 J x kg[-1] x m[-1], P < 0.05) at the same average speed. The results of this experiment were interpreted as indicating that the muscular effort, needed for maintaining balance when walking on a pitching or rolling platform, resulted in a significantly higher work load than similar walking on a stable or a heaving floor, independent of the mode of walking. These results explain in part the increased fatigue observed when a task is performed on a moving platform.

Resonance behaviour of the seated human body and effects of posture

Understanding of the resonance behaviour of the human body is important in the identification of vibration frequencies and body postures associated with back problems. In this study, experimental modal analysis was applied to whole-body vibration. Eight subjects were exposed to vertical random vibration while adopting three different postures on a rigid seat without a backrest. Motions of the spine, pelvis and viscera in the mid-sagittal plane were derived from skin-mounted accelerometers; head responses were measured using a bite-bar. Eight modes of vibration response were extracted below 10 Hz. A principal resonance of the human body at about 5 Hz consisted of an entire body mode, in which the skeleton moved vertically due to axial and shear deformations of buttocks tissue, in phase with a vertical visceral mode, and a bending mode of the upper thoracic and cervical spine. A bending mode of the lumbar and lower thoracic spine was found with a pitching mode of the head in the next higher mode located close to the principal mode. The second principal resonance at about 8 Hz corresponded to pitching modes of the pelvis and a second visceral mode. When subjects changed posture from erect to slouched, the natural frequency of the entire body mode decreased, resulting in a decrease in the principal resonance frequency. Shear deformation of buttocks tissue increased in the entire body mode due to the same change of posture. The complex body motions suggest that any forces causing injury from whole-body vibration will not be well-predicted by biodynamic models incapable of representing the appropriate body motions and the effects of body posture. It seems likely that the greatest risk of back problems will arise from the bending deformations of the spine.

二重平行リンクサスペンション形対物レンズアクチュエータの減衰設計

A damping design is developed to achieve heavy damping of an objective-lens actuator with dual-parallel link suspensions for CD and CD-ROM drives. The actuator is supported by four suspensions of straight bars for reducing directionally-coupled vibration. An objective value analysis is conducted to determine the desirable damping ratio at the lowest mode as well as at higher modes for high-speed access and stability of the servo system. To construct an actuator of the damping terget, we developed a damping box with gel. This system ensures heavy damping at the lowest mode ζ0 of 0.13 and at the pitching mode ζpit, of O.1. To make the damping coefficient of pitching mode, upper suspensions have slightly elastic bending. The heavy damping of the pitching mode in the frequency band of around 1 kHz can allow the assembly error of normalized center of gravity by 10%. We also developed a heavy-damping actuator with a good frequency response and with no phase disturbance.

Air–Ice–Ocean Momentum Exchange. Part 1:Energy Transfer between Waves and Ice Floes

Abstract The energy exchange between ocean surface waves and ice floes in the marginal ice zone (MIZ) involves the scattering and attenuation of wave energy and the excitation of oscillation modes of the ice floes, as open ocean waves propagate into the MIZ. Heave, pitch, and roll modes of oscillation are linked to estimation of wave scattering and attenuation. A model is presented for wave attenuation and compared to measurements from the Marginal Ice Zone Experiments in the Greenland Sea, as reported by Wadhams et al.

Responses of a non-linearly coupled pitch-roll ship model under harmonic excitation

Stationary responses of nonlinearly coupled pitch and roll ship modes are studied using a modified averaging method, along with two second order multiple time scale (MTS) methods for comparison. Stability of the solutions is also studied. In the case of harmonic excitation all the three methods give fairly accurate results to the original problem but the averaging method is the most efficient. Analytic solutions are obtained from the averaged equations, which can be used to predict stationary responses both for small and for large excitations. From the averaging method several qualitatively different phenomena which cannot be addressed by the first order theory have been obtained: (i) the saturation phenomenon is lost, (ii) the bifurcation points are altered and (iii) a drift term is present which, although small, appears to have a significant effect on the accuracy of the solutions.

New Class of Sliders Numerically Designed for Maximum Stiffness

The following inverse problem is addressed: given a class of slider geometry for which the gap can only have two values and given its global footprint, where should one distribute the etching (or deposition) of the air bearing surface such that the corresponding stiffness is maximum? First, this optimization problem is mathematically setup and formulated. Then, a simple numerical algorithm is proposed which will generate the desired gap profile, the method is based on an iterative approach on the unknown gap distribution coupled with a finite element solution of the pressure solution. Finally, the canonical example of a simple square slider is treated for various stiffnesses (normal, pitch, roll and mixed modes), and the results illustrate the proposed technique.

Nonlinearly Coupled Pitch and Roll Motions in the Presence of Internal Resonance; Part I, Theory

The dynamic stability and complicated motions of a vessel in following or head regular waves are investigated when the frequency in pitch is nearly twice the frequency in roll. The damping in the pitch mode is modeled by a linear visco ins damping term, whereas that of the roll mode is modeled by the sum of a linear viscous part and a quadratic viscous part. The method of multiple scales is used to determine a system of four nonlinear first-order equations governing the modulation of the amplitudes and phases of the pitch and roll. Force-response andfrequency-response curves are generated. Coexistence of multiple solutions is found. The jump phenomenon continues to exist, whereas the saturation phenomenon ceases in the presence of quadratic damping. Hopf bifurcations are found. Near these bifurcations, the modulation equations possess limit-cycle solutions and hence the steady-state motion is a periodically modulated pitch and roll motion. Numerical simulations are used to investigate the bifurcations of these limit cycles and how they lead to chaos and hence chaotically modulated pitch and roll motions.

A New Theory for Oscillating and Translating Slender Ships

A new theory is presented for the radiation problem of heave and pitch modes of a slender ship advancing at arbitrary forward speed. The theory has no restrictions on the order of forward speed and oscillation frequency, embracing both of unified theory developed by Newman and high-speed slender-body theory (HSSBT). The inner velocity potential consists of a particular solution, which is the same as that of HSSBT, and a homogeneous component, which is constructed by the superposition of the real-flow velocity potential and the reverse-flow reverse-time velocity potential.Since precise computations of HSSBT are prerequisite for the present theory, the calculation procedure adopted for HSSBT is described, converting the formulation into an equivalent initial-value problem in the time domain and applying the higher-order boundary-element method at each time step.Numerical results of added-mass and damping coefficients based on the present theory are shown for a modified Wigley model and compared with corresponding experiments and other computed results by the strip method, HSSBT, and 3-D Rankine-panel method.

Non-Stationary Oscillations About a Simple Bifurcation

The non-stationary response of a non-linear oscillator that exhibits a simple bifurcation from one stable root to another is discussed. The discussion is motivated by previous work on the coupled pitch and role modes of a ship. Two aspects of the analysis are emphasized: (i) aspects of the response described numerically by others are described analytically; and (ii) analysis of the response using only local stability of the two response solutions is inadequate. A global stability criterion is obtained, and it is shown that what appear to be rapid jumps from one solution to another are in fact smooth transitions on the phase plane.

A Study on Active Suspension for Large-Scale Buses Using Fuzzy Reasoning. Design of Active Controls Considering Pitch Mode.

This paper presents a design for an active suspension for large-scale buses using the concept of fuzzy set theory. The model is described by a nonlinear system with six degrees of freedom subject to irregular excitation from the road surface. The active control of position type consists of principal and supplementary controls. In the fuzzy control rules, the vertical velocity and its time increment of vehicle body are treated as the input variables in the principal control, and the pitch-angle velocity and its time increment of vehicle body are done as the input variables in the supplementary control. The computer simulation indicates that the proposed active suspension provides more effective performance than the passive suspension.

Passive stabilization of a tethered system in low Earth orbit

In the first part of the paper, the divergence phenomena induced by forcing aerodynamic actions, due to orbital eccentricity and inclination to the equatorial plane, are investigated by a general, three-dimensional dynamic model of the tethered subsatellite system. In the second part, the aerodynamic stabilization of the subsatellite is considered. Although the libration mode appears almost unaffected by the passive control system, longitudinal elastic modes, with frequencies close to that of the pitch mode, can diverge for an energy transfer from the subsatellite to the tether.

Dynamic Characteristics of Hydrostatic Air Slider with Comb-Shaped Grooves.

In this study we develop a new hydrostatic air bearing slider with comb-shaped grooves which can provide high damping ratio in the high-frequency region of resonance, as well as high stffness. The basic idea to increase the air film damping at a high frequency region is to reduce the compressive effect of the air film by a set of parallel inner grooves. Increases in groove number and groove depth generally result in high damping in the high-frequency region, but excessive increases cause negative damping in the low-frequency region. The design procedure to determine the optimal value of the groove parameters is described by the design charts based on numerical calculation. The developed air slider has a high static stiffness of 418 N/μm (non-dimensional stiffness is 0.59) in the vertical direction, Damping ratios are 0.19, 0.12 and 0.07 at the natural frequencies of the roll, pitch and vertical vibration modes, respectively.

The transmission of translational seat vibration to the head: the effect of measurement position at the head.

Head motion has been measured in six axes on twelve subjects exposed to vertical seat vibration in the frequency range 0.5-25 Hz. The subjects sat on a rigid flat seat in two postures: 'back-off' (no backrest) and 'back-on' (subject's back in contact with the seat backrest). Translational acceleration has been calculated for various locations on the head and transmissibilities between vertical seat vibration and translational head motion determined for each location and all axes. The translational motion of the head was most affected by pitch motion of the head. This caused variations in fore-and-aft motion with position along the vertical axis of the head and variations in vertical motion with position along the fore-and-aft axis of the head. These variations are illustrated for each subject in both postures. The individual data allow the identification of various modes of vibration and show that seat-to-head transmissibility is greatly affected by pitch modes of the head and neck. The magnitude of motion occurring in some modes is dependent on body posture.

Domains of Attraction of System of Nonlinearly Coupled Ship Motions by Simple Cell Mapping

A nonlinear dissipative dynamical system can often have multiple attractors. In this case, it is important to study the global behavior of the system by determining the global domain of attraction of each attractor. In this paper we study the global behavior of a two-degree-of freedom system. The specific system examined is a system of nonlinearly coupled ship motions in regular seas. The system is described by two second-order nonlinear nonautonomous ordinary differential equations. When the frequency of the pitch mode is twice the frequency of the roll mode, and is near the encountered wave frequency, the system can have two asymptotically stable steady-state periodic solutions. The one solution has the same period as the encountered wave period and has the pitch motion only. The other solution has twice the period of the encountered wave period and has pitch and roll motions. The harmonic and second-order subharmonic solutions show up as period-1 and period-2 solutions, respectively, in a Poincare´ map. We show how the method of simple cell mapping can be used to determine the two four-dimensional domains of attraction of the two solutions in a very effective way. The results are compared with the ones obtained by direct numerical integration.

Effect of Connecting the Front and Rear Air Suspensions of a Vehicle on the Transmissibility of Road Undulation Inputs

SUMMARY Airsprings have been used for vehicle suspensions over the last 40 years. They are mostly used as independent suspensions. Analysis of air springs available in literature is mostly limited to a single-degree-of-freedom system or a two-degrees-of-freedom system only in the translation mode. This paper deals with a model of a vehicle where the front and the rear springs are connected by a capillary tube. A two-degrees-of-freedom model having motion in bounce and pitch mode is presented. Equations of mass flow are linearized on the assumption of small variations in volume and pressure. Expressions for the transmissibility and the phase angle in the bounce and the pitch mode are derived. Road inputs to the front and the rear axles are assumed to be identical except for a phase difference between them. The effect of the capillary flow coefficient and that of the phase angle between the front and the rear axle excitation are studied. It is shown that an optimum value of the capillary flow coefficient ex...