Translational Oscillations Research Articles

Dynamical Modelling and Controllability Analysis of an Underactuated 2-Dimensional TORA System on a Slope

The 2-Dimensional Translational Oscillators with Rotating Actuator (2DTORA) is a novel underactuated system which has one actuated rotor and two unactuated translational carts. This paper focuses on dynamical modelling and simulation analysis of the underactuated 2DTORA on a slope. Based on Lagrange equations, the dynamics of the 2DTORA is achieved by selecting a transverse position of a cart, a travelling position of a cart, and the rotor angle as the general coordinates and torque acting on the rotor as the general force. When the slope angle is set to zero, the dynamics of 2DTORA on a slope is reduced to that of 2DTORA on the horizontal plane. Moreover, by eliminating one degree of translational cart motion, the dynamics of 2DTORA is reduced to that of TORA which is a benchmark of underactuated systems. In addition, the equilibrium and controllability of the 2DTORA system on a slop are discussed. Finally, numerical simulations are performed to verify the feasibility of the developed dynamic models.

Semi-global output regulation for linear systems with input saturation by composite nonlinear feedback control

To improve transient performance of output response, this paper applies composite nonlinear feedback (CNF) control technique to investigate semi-global output regulation problems for linear systems with input saturation. Based on a linear state feedback control law for a semi-global output regulation problem, a state feedback CNF control law is constructed by adding a nonlinear feedback part. The extra nonlinear feedback part can be applied to improve the transient performance of the closed-loop system. Moreover, an observer is designed to construct an output feedback CNF control law that also solves the semi-global output regulation problem. The sufficient solvability condition of the semi-global output regulation problem by CNF control is the same as that by linear control, but the CNF control technique can improve the transient performance. The effectiveness of the proposed method is illustrated by a disturbance rejection problem of a translational oscillator with rotational actuator system.

Complex density of a suspension in an oscillatiory wave process

The effective viscous inertia properties exhibited by suspensions in the presence of oscillatory wave processes are considered. A cell model of a concentrated suspension is used to derive the dependence for the complex density, whose real and imaginary parts characterize the effective inertia and the bulk viscous resistance to oscillatory motion, respectively. From hydrodynamic models of low-frequency and high-frequency translatory oscillations of spherical inclusions in the host liquid, estimates are obtained for the internal dynamic parameters of the suspension, namely, the apparent mass factor and the inclusion relaxation time, which specify the general formulas for the complex density.

Effect of a distant rigid wall on microstreaming generated by an acoustically driven gas bubble

AbstractA theory is developed that describes acoustic microstreaming around a gas bubble undergoing small radial and translational oscillations in the presence of a distant rigid wall. It is shown that the presence of the wall can change the amplitude and the phase of the bubble oscillations in such a way that the intensity of acoustic microstreaming is increased considerably as compared with that generated by the same bubble in an infinite liquid. This occurs if the driving frequency is close to the resonance frequency that the bubble has in the presence of the wall. Equations for acoustic microstreaming in the boundary layer at the wall are also provided.

Surface atmospheric pressure excitation of the translational mode of the inner core

Using hourly atmospheric surface pressure field from ECMWF (European Centre for Medium-Range Weather Forecasts) and from NCEP (National Centers for Environmental Prediction) Climate Forecast System Reanalysis (CFSR) models, we show that atmospheric pressure fluctuations excite the translational oscillation of the inner core, the so-called Slichter mode, to the sub-nanogal level at the Earth surface. The computation is performed using a normal-mode formalism for a spherical, self-gravitating anelastic PREM-like Earth model. We determine the statistical response in the form of power spectral densities of the degree-one spherical harmonic components of the observed pressure field. Both hypotheses of inverted and non-inverted barometer for the ocean response to pressure forcing are considered. Based on previously computed noise levels, we show that the surface excitation amplitude is below the limit of detection of the superconducting gravimeters, making the Slichter mode detection a challenging instrumental task for the near future.

The smooth switching gain-scheduled control with H<SUP align="right">∞</SUP> performance to the application of TORA systems

The function of switching logics is crucial to the operation of switching control systems. This paper investigates the smooth switching control approach for linear parameter varying systems, in which the control law for neighbouring subsystems is smoothly switched or scheduled in the overlapped region instead of employing the usual instant switching methods. The proposed approach is designed in terms of the achieved ∞ performance level under control input and system output variable constraints. The control law is constructed based on the parameterised linear matrix inequality conditions. The effectiveness of the proposed approach is demonstrated by disturbance attenuation of the non-linear translational oscillator with rotational actuator systems in a quasi-linear parameter varying system representation.

Slichter modes of large icy satellites

Because of the presence of an ocean below the ice shell of icy satellites such as Europa, Callisto, Ganymede and Titan the solid interior of these satellites can be displaced with respect to the ice shell, similarly to the translational oscillation of the inner core of the Earth called the Slichter modes of the Earth.We construct a set of interior structure models of Europa, Callisto, Ganymede and Titan satisfying the observed mass, radius and moment of inertia and study the properties of the Slichter mode for these models. The periods obtained range from a few hours to a few tens of hours depending mainly on the ocean thickness. Ganymede has two Slichter modes since it is thought to have a liquid outer core besides a global subsurface ocean. The second Slichter mode describes essentially the oscillation of the solid inner core inside the liquid outer core and its period is determined principally by the thickness of the outer core. We study the possible observation of these modes with a lander on the surface or a spacecraft in orbit about Europa, Callisto, Ganymede or Titan. We show that an impactor with a radius of at least a few kilometers to a few tens of kilometers could excite the Slichter modes to a level observable by a lander. Such impacts occur on average once in >30My for Europa, once in >70My for Callisto, once in >40My for Ganymede and once in >0.4Gy for Titan. Observation of the Slichter mode would allow constraining the thickness of the ocean.

Observation of a Geometric Hall Effect in a Spinor Bose-Einstein Condensate with a Skyrmion Spin Texture

For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a Skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of the condensate and the vortex number increases over 100 without significant heating. We attribute the vortex nucleation to the shearing effect of the effective Lorentz force from the inhomogeneous effective magnetic field.

Detection of inner core translational oscillations using superconducting gravimeters

An attempt has been made to search for the translational oscillations of the Earth’s solid inner core in the gravity measurements recorded with the superconducting gravimeters (SG) from the worldwide network of the Global Geodynamics Project (GGP). All the SG data were prepared and analyzed by the same method to remove accurately the signatures related to gravity tides, local barometric pressure, the Earth’s rotation, the long-term trend and so on. We obtained the estimations of the power spectral densities of each residual series and the estimations of the product spectral densities in the subtidal band (0.162–0.285 cph) were obtained by using a multi-station stacking technique after further eliminating atmospheric effects. The inner core translation triplet was detected in the subtidal band. We find 6 groups of signal with high signal-to-noise ratio that are consistent with the characteristics of the triplet, and 4 groups of the results that are close to the previous studies and the differences are less than 0.92%. It implies that the groups of signatures all have the possibility to be related to the inner core translational oscillations.

Passivity-based control of two-dimensional translational oscillator with rotational actuator

An underactuated two-dimensional translational oscillator with rotational actuator (2DTORA) consisting of an actuated rotational proof-mass and two unactuated translational carts is presented. Passivity-based control design is employed for 2DTORA based on its Euler–Lagrange structure and passivity property. Firstly, the dynamics of 2DTORA are derived based on Euler–Lagrange equations. Motivated by constructing a damped close-loop Euler–Lagrange system, the controller dynamics is designed to shape the potential energy and inject the required damping. As a result, the designed controller stabilizes the underactuated 2DTORA with the feedback of the rotational actuator’s position only. Moreover, by modifying controller dynamics with a saturation function, the control input can be constrained to certain bounds. Finally, simulation results demonstrate the feasibility and effectiveness of the proposed controllers.

Additive-state-decomposition-based tracking control for TORA benchmark

In this paper, a new control scheme, called additive-state-decomposition-based tracking control, is proposed to solve the tracking (rejection) problem for rotational position of the translational oscillator with a rotational actuator (TORA, a nonlinear nonminimum phase system). By the additive state decomposition, the tracking (rejection) task for the considered nonlinear system is decomposed into two independent subtasks: a tracking (rejection) subtask for a linear time invariant (LTI) system, leaving a stabilization subtask for a derived nonlinear system. By the decomposition, the proposed tracking control scheme avoids solving regulation equations and can tackle the tracking (rejection) problem in the presence of any external signal (except for the frequencies at±1) generated by a marginally stable autonomous LTI system. To demonstrate the effectiveness, numerical simulation is given.

DOMAIN BOUNDARIES IN FERROELECTRICS

Present paper is a brief review of the information and existing approaches in the study of domain walls in ferroelectric materials. In the framework of the continuum approach the structure of 180° and 90° domain walls was considered. The results of calculation of width and energy of domain walls were compared with those obtained from ab initio calculations and experimental data. Factors conducive to the broadening of domain boundaries are discussed such as profile temperature fluctuation, capture to nearby defects and surface impact. The structure of charged domain walls was considered under the conditions of screening by free carriers. The structure and characteristics of the moving domain wall are discussed: the local effective mass, the top speed and the mobility. The lateral motion of domain walls in the lattice potential relief in the general case creeping mode is investigated. The factors that control the macroscopic movement of domain walls are studied: an effective quasi-elasticity coefficient and nonlocal effective mass associated with involvement in the movement of the elastic medium surrounding wall. Natural frequency of translational oscillations of domain boundaries and the influence of the size effect were estimated. The interaction of domain walls with different types of defects and their effect on the deformation profile and features of the motion of domain walls are considered.

Angular Oscillation of Solid Scatterers in Response to Progressive Planar Acoustic Waves: Do Fish Otoliths Rock?

Fish can sense a wide variety of sounds by means of the otolith organs of the inner ear. Among the incompletely understood components of this process are the patterns of movement of the otoliths vis-à-vis fish head or whole-body movement. How complex are the motions? How does the otolith organ respond to sounds from different directions and frequencies? In the present work we examine the responses of a dense rigid scatterer (representing the otolith) suspended in an acoustic fluid to low-frequency planar progressive acoustic waves. A simple mechanical model, which predicts both translational and angular oscillation, is formulated. The responses of simple shapes (sphere and hemisphere) are analyzed with an acoustic finite element model. The hemispherical scatterer is found to oscillate both in the direction of the propagation of the progressive waves and also in the plane of the wavefront as a result of angular motion. The models predict that this characteristic will be shared by other irregularly-shaped scatterers, including fish otoliths, which could provide the fish hearing mechanisms with an additional component of oscillation and therefore one more source of acoustical cues.

Radial and translational oscillations of an acoustically levitated bubble in aqueous ethanol solutions

The radial and translational oscillations of a single cavitation bubble in a standing ultrasound wave were investigated experimentally at various driving acoustic pressures for aqueous ethanol solutions with different bulk molar fractions of ethanol range of 0-1.3 × 10(-3). The results show that both the lower and upper stability thresholds of the acoustic driving pressure decreased as the concentration of ethanol was increased. At a given driving pressure the ambient and maximum bubble sizes increased with increasing ethanol concentration. In addition, as the ethanol was increased, the sonoluminescence intensity decreased while the bubble dynamics remained largely unchanged. The translational oscillation of the levitated bubble, however, became increasingly violent with increasing ethanol concentration. The displacement of the bubble reached 0.7 mm at the highest concentration studied (1.3 × 10(-3)) and the maximum bubble size was found to change as the bubble jumped up and down. This bubble translation may be responsible for the decrease of the acoustic driving pressure threshold and suggests that repetitive injection of ethanol molecules into the bubble takes place. These results may account for the different sensitivities of single bubble and multi-bubble sonoluminescence to the presence of volatile additives.

Stabilizing Control of an Underactuated 2‐dimensional TORA with Only Rotor Angle Measurement

AbstractOne dimensional translational oscillation with a rotational actuator (TORA) system has been used as a benchmark for motivating the study of nonlinear control techniques. In this paper, a novel underactuated 2‐dimensional TORA (2DTORA), which has one actuated rotor and two unactuated translational carts, is presented. The analysis of controllability around the system's equilibriums yielded the controllable equilibriums and the constraint on physical parameters. To stabilize the system to its controllable equilibriums from any initial conditions, we propose a simple linear controller containing the rotor angle and angular velocity. The controller was derived from a proper Lyapunov function, including the system's total energy, that was used to show the passivity property of the system. In addition, a high pass filter was adopted to approximately differentiate the rotor angle so that an estimated angular velocity was used in the controller rather than measuring the actual rotor angular velocity. As a result, only the angle measurement is required for the designed feedback controller to stabilize the underactuated system. Finally, simulation results verify our control design and analysis.

Biosensor platform based on stress-improved piezoelectric membrane

A new design as piezoelectric membrane is introduced to improve the performance of a diaphragm based biosensor platform. In the design, stress is introduced into the diaphragm by a vacuum chamber and makes it work as membrane with a higher sensitivity and a higher Q factor. The mass sensitivity of stress-improved membrane was investigated and an effective mass approach is used to simulate the sensitivity of the device for a point mass load. Piezoelectric membranes with different sizes have been built using PVDF piezo-polymers. These devices were characterized in air and in water. The experimental results are consistent with the theoretical simulation and indicate that the device in liquid can have a higher Q factor than that in air. A theoretical model, which is a sphere executing translatory oscillations in viscous fluid, was used to analyze the Q factor in liquid environment. The results indicated that the large Q factor in liquid can be attributed to the relative large effective mass of membrane in liquid environment.

Use of a Static Magnetic Field in Measuring the Thermal Conductivity of a Levitated Molten Droplet

Numerical models are used to analyze the complex behaviour of magnetically levitated droplets in the context of determining their thermophysical properties. We focus on a novel method reported in Tsukada et al. [4] which uses periodic laser heating to determine the thermal conductivity of an electromagnetically levitated droplet in the presence of a static DC field to suppress convection. The results obtained from the spectral-collocation based free surface code SPHINX and the commercial package COMSOL independently confirm and extend previous findings in [4]. By including the effects of turbulence and movement of the free surface SPHINX can predict the behaviour of the droplet in dynamic regimes with and without the DC magnetic field. COMSOL is used to investigate arbitrary amplitude axial translational oscillations when the spherical droplet is displaced off its equilibrium. The results demonstrate that relatively small amplitude oscillations could cause significant variation in Joule heating and redistribution of the temperature. The effect of translational oscillations on the lumped circuit inductance is analysed. When a fixed voltage drive is applied across the terminals of the levitation coil, this effect will cause the coil current to change and a correction is needed to the electromagnetic force acting on the droplet.

Arbitrary oscillatory Stokes flow past a porous sphere using Brinkman model

The present paper deals with the hydrodynamics of a porous sphere placed in an arbitrary oscillatory Stokes flow. Unsteady Stokes equation is used for the flow outside the porous sphere and Brinkman equation is used for the flow inside the porous sphere. Corresponding Faxen’s law for drag and torque is derived and compared with few existing results in some special cases. Examples like uniform flow, oscillatory shear flow and oscillating Stokeslet are discussed. Also, translational oscillation of a weakly permeable sphere is discussed.

Forced oscillations of two gas bubbles in a fluid in the vicinity of bubble contact

For a theoretical derivation of bubble coalescence conditions, nonlinear forced oscillations of two closely spaced spherical bubbles subjected to the action of a periodic external pressure field are considered. The equations, asymptotic with respect to a small distance between the bubble surfaces, are derived to describe the approach of the bubbles under the action of (i) the Bjerknes attraction force averaged over the oscillation period and (ii) the viscous drag. It is shown that due to nonlinear interaction of the viscous drag with the radial and translational oscillations of the bubbles a unidirectional repulsive force is generated, which prevents the approach of the bubbles. The coalescence of the bubbles is possible when the nondimensional parameter combined from the amplitude and frequency of the external pressure field, the bubble radius, and the fluid viscosity is greater than a certain critical value. The obtained coalescence condition is qualitatively confirmed by experiments.

LMI-based gain scheduling for bridge flutter control using eccentric rotational actuators

SUMMARY Long-span bridge girders can show dangerous instable flutter vibrations caused by aerodynamic forces due to very strong winds. The control objective of flutter control is to enhance the structure-dependent and control-dependent critical wind speed of flutter onset. An active mass damper system with two eccentric rotational actuators (ERA) is presented for flutter control. By using a bridge girder model that moves in two degrees of freedom (DOFs) and is subjected to wind, the equations of motion of the controlled structure equipped with ERA are established. For determination of critical wind speed, a flutter analysis is carried out with the help of a numerical simulation scheme. Considering the plant without the aerodynamic forces and neglecting the interaction effects between the two ERA, the simplified control problem of one ERA is affine to the translational oscillator and rotational actuator (TORA) benchmark problem. LMI-based gain scheduling technique has been used successfully for the TORA and is implemented for flutter control with ERA in this research. For an example, the performance of the controlled bridge girder is investigated. Copyright © 2011 John Wiley & Sons, Ltd.