Translational Oscillations Research Articles

Advanced robust control techniques for the stabilization of translational oscillator with rotational actuator based barge-type OFWT

In recent times, renewable energy demand is rapidly increasing worldwide. Offshore wind energy is one of the alternative solutions to the problems posed by non-renewable energy resources. The kinetic energy of the wind is converted to mechanical energy by using an offshore floating wind turbine (OFWT). The efficiency of the OFWT is dependent upon the vibrational effect induced by the environment. In this paper, for the mitigation of this vibrational effect, a new model of barge-type OFWT is designed by using an active control strategy called translational oscillator with a rotational actuator (TORA). The disturbance observer (DO) based advanced control techniques including robust backstepping sliding mode control (BSMC), backstepping integral sliding mode control (BISMC), backstepping nonsingular terminal sliding mode control (BNTSMC), and a new backstepping integral nonsingular terminal sliding mode control (BINTSMC) technique, are devised for the stabilization of OFWT model. The comparison of these techniques is carried out by using MATLAB/SIMULINK which validates the feasibility and correctness of the proposed OFWT model and control techniques.

A time-implicit representation of the lift force for coupled translational–rotational galloping

The lift force acting on a purely translational galloping oscillator can be well approximated by using the quasi-steady theory, which states that the flow around a galloping body in motion is very similar to the known flow around a fixed body provided a minimum free stream velocity threshold and a similarity principle are satisfied. However, for oscillators undergoing coupled translational–rotational galloping, the rotation of the bluff body breaks the similarity principle, and therewith the quasi-steady assumption. Traditionally, the effects of rotation are accounted for by including explicit time-dependent terms in the lift force. However, we argue that the time-explicit representation of the lift force is unnecessary because the phenomenon of galloping is not time-explicit and acts only as a function of the body motion. Thus, we propose a modified time-implicit lift force representation, which has the same form of the quasi-steady theory, but with an additional dependence on the free stream velocity. The modified lift force is obtained by studying the transient growth of the amplitude of the bluff body oscillation. The proposed approach is used to model the lift force for square and trapezoidal prisms undergoing coupled translational–rotational galloping showing excellent prediction capabilities.

Influence of Rotational and Translational Oscillations on the Drainage of Liquid in Floating Packed Beds

A marinization test rig comprising a hexapod/column/wire-mesh-sensor assemblage was used to emulate the liquid drainage onboard floating packed columns. Single and compounded rotations and translat...

Translation and nonspherical oscillation of single bubble in ultrasound field

Based on the perturbation theory and generalized Bernoulli equation, the equations describing the radius, translation and deformation of a single gas bubble in ultrasonic field are derived. The evolutions of the radius, displacement and deformation of the bubble with time can be obtained by numerically calculating these equations. The calculation results show that when the initial radius of the bubble and the driving pressure both keep constant, the displacement and shape variable of the bubble increase with the augment of the initial translational velocity of the bubble’s center, and the non-spherical vibration of the bubble becomes more intense. However, the radial vibration of the bubble almost remains unchanged. When the initial translation velocity of the bubble is relatively small, the unstable region is concentrated only in the region of high driving sound pressure in the <inline-formula><tex-math id="M3">\begin{document}$R_{0}\text-p_{\rm a}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210513_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210513_M3.png"/></alternatives></inline-formula> phase diagram of the bubble. As the initial translational velocity increases, the region with small radius and driving sound pressure begins to show instability, and the overall unstable region gradually increases. In addition, a bubble presents different vibration characteristics at different positions in the acoustic standing wave field. The closer to the antinode of sound wave the bubble is, the greater the radial amplitude of the bubble’s vibration is. However, the variable of the translation and shape of the bubble are very small. The error between the plane fractions of the unstable region in the phase diagram of <inline-formula><tex-math id="M4">\begin{document}$R_{0}\text{-} p_ {\rm a}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210513_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210513_M4.png"/></alternatives></inline-formula> is less than 4%.

Optimal Design of a Fuzzy Controller Based on the Imperialist Competitive Algorithm for Fourth-order Nonlinear Systems

Nowadays, control and optimization of systems are two important and noticeable topics in all fields of science and engineering. One of the control methods, widely used because of its simplicity and accuracy, is the fuzzy control, which is based on the fuzzy logic theory. In the uncertainty conditions, this theory is able to formulate many inaccurate and vague implications, variables and systems in mathematical language, and provides requirements for reasoning, inference, control and decision making. This paper studies the stabilization of a Translation Oscillations with a Rotational Actuator (TORA) nonlinear fourth-order system by using a new fuzzy control technique which utilizes the small number of membership functions and rules. Besides, to determine the proper values for the controller parameters, the Imperialist Competitive Algorithm (ICA) is employed. Unlike the other optimization algorithms, ICA is not originated from evolutionary behavior of nature, but it is inspired by a human natural phenomenon called imperialism. In the optimization procedure, the objective function is defined as the sum of integrals of the rotor angle and the cart position. Finally, the comparison between the results obtained by the proposed strategy and some other researchers’ methods is provided, which shows the superiority of this work.

THE MOTION OF A PARTICLE ON A WAVY SURFACE DURING ITS TRANSLATIONAL CIRCULAR OSCILLATIONS IN HORIZONTAL PLANES

The rough plane is a universal structural element of many machines and devices for sifting and separation of parts of technological material. The motion of particles on the horizontal plane, which performs oscillating rectilinear or circular motion, is the most studied. A wavy surface with a sinusoidal cross-sectional line as a working surface will significantly change the trajectories of their motion. The mathematical description of such a motion will change accordingly. The sliding of a particle in a plane will be a partial case of sliding on a wavy surface when the amplitude of the sinusoid is equal to zero. When the wavy surface oscillates and all its points describe circles, the motion of the technological material changes significantly. The regularities of the motion of material particles on such a surface during its circular translational oscillations in the horizontal planes are investigated in the article. Differential equations of relative particle displacement are compiled and solved by numerical methods. The trajectories of the particle sliding on the surface and the graphs of its reaction are constructed. A partial case of a surface is a plane, and the sliding trajectory of a particle is a circle. An analytical expression to determine its radius is found. During circular oscillations of a wavy linear surface with a cross section in the form of a sinusoid relative trajectory of a particle after stabilization of the motion can be closed or periodic spatial curves. To avoid the breakaway of the particle from the surface, the oscillation mode should be set, which takes into account the shape of the surface and the kinematic parameters of oscillations. With the diameter of the circle, which is described by all points of the surface during its oscillation, is equal to the period of the sinusoid, the trajectory of the relative motion of the particle can be a periodic curve. In this case, the particle moves in a direction close to the transverse, overcoming depressions and ridges. In other cases, the trajectory is a closed spatial curve, the horizontal projection of which is close to a circle. The found analytical dependencies allow determining the influence of structural and technological parameters of the surface on the trajectory of the particle.

Diagnostics of dissipative characteristics of friction damper

The aim of our study was to broaden current knowledge of characteristics of friction damper that acts to dissipate the energy of small translational oscillations in friction pairs and to convert it into significant angular shaft movements. We have devised a novel methodology to evaluate elastic-dissipative characteristics of the damper, which provides real-time identification of the stability of these characteristics, as well as running-in periods, stable operation, and catastrophic wear. It is shown that plan bearings made of antifriction self-lubricating organic-fiber composite are more effective than plain bearings made of metal-fluoroplastic tape since their use causes less high-frequency noises that affect the quality of transient response.

Nonlinear disturbance observer based sliding mode control for a benchmark system with uncertain disturbances

Taking uncertain disturbances into account, the control problem of the translational oscillator with a rotational actuator (TORA) is considered in this paper. Motivated by the desire to attenuate influences from unknown disturbances/uncertainties, the disturbance-observer-based methodology is utilized. Specifically, a system model with a cascade structure for the TORA system is obtained after a series of coordinate transformations. Then, inspired by the backstepping control technique, for the first subsystem, a virtual control variable is introduced and an error-signal-based system is designed. Next, an estimator is presented and used to estimate unknown disturbances, based upon which a sliding mode control approach is devised to ensure the underactuated TORA system is asymptotically stable at the origin. Finally, the applicability and robustness of the designed control method are examined via three group numerical simulation tests.

Friction Influenced by Vibrations: A Refined Contact-Mechanics View on Lateral and Rotational Oscillations

It is known that superposed movements can lower the friction felt at the macroscale. This is well documented for in-plane and normal translatory oscillations. Contact mechanics are a suitable approach to model this effect but so far have not gone beyond single-slider dynamics. In this study, we make use of 3D Boundary Elements Simulations to study the macroscopic friction reduction. This approach allows us to take into account also partial sliding of the contact zone. We first revisit the case of transversal in-plane translatory oscillations. Here, we argue that the behavior at small velocities can best be described when partial slip is indeed taken into account. Next, we investigate the frictional response of a Hertzian indenter when the lateral movement is superposed with a rotational bore movement. An analytical approximation is given for the steady state solution with constant angular velocity. The third case under investigation is an oscillating bore rotation. We present numerical results for the reduction of the macroscopic friction. In two limiting cases, an analytical prediction is given, following the lines used in the translatory case. For extremely large amplitudes, it is based on the idea that a rotational steady state is assumed at every instant. For small velocities we adapt our new approach including partial sliding. We find these predictions to be good but not perfect, slightly underestimating the reduction that rotational oscillations can provide.

Robust global stabilization of a class of underactuated mechanical systems of two degrees of freedom

SummaryIn this article, the global stabilization of a class of underactuated mechanical systems of two degrees of freedom (DoF) is addressed, despite the presence of Lipschitz disturbances and/or uncertainties and uncertain control coefficient in the model. Using two second‐order continuous sliding modes algorithms, the control task is performed, reaching finite‐time convergence in one part of the dynamics and generating a continuous control signal. The efficacy of the proposed controllers is illustrated via simulations for the reaction wheel pendulum (RWP) and the translational oscillator with rotational actuator (TORA) systems, and by means of experiments on the RWP system, comparing the presented algorithms with a linearizing controller.

Global sliding mode control for the underactuated translational oscillator with rotational actuator system

This article is motivated by the control issues of the translational oscillator with rotational actuator system in the existence of uncertain disturbances. A nonlinear disturbance observer and a global sliding mode control method are proposed for the disturbance estimation and stabilization of the translational oscillator with rotational actuator system. Compared with the existing control methods, uncertain disturbances are estimated by the proposed nonlinear disturbance observer. In addition, the sliding mode control method is continuous and global robustness with respect to disturbances. Specifically, to facilitate the controller design, the dynamics of the translational oscillator with rotational actuator system are rearranged as the cascade form first. Then, a virtual signal is constructed and corresponding error dynamics are derived. Subsequently, a nonlinear disturbance observer and a continuous global sliding mode control method are proposed for the disturbance rejection and stabilization of the translational oscillator with rotational actuator system. Finally, simulation results are provided to verify the effectiveness and robustness of the proposed controller.

Influence of the torsional vibration of the periodically attached perpendicular beam resonator on the flexural band of a Euler-Bernoulli beam

The bending and torsional vibration of the periodic perpendicular cantilever beam-mass resonators (PCBMR) is idealized as translational and rotational oscillators attached to the main beam. In this paper, the effect of that torsional vibration of the PCBMR on the dynamics of an infinitely long Euler-Bernoulli beam is evaluated. The band-structure is explored by implementing the transfer matrix method in conjunction with Bloch-Floquet's theorem. The combination of the translational and rotational oscillator modifies the relative position of the coupling coefficient in the transfer matrix, which plays a pivotal role in the band-gap formation. The flexural band-structure is highly sensitive to the torsional vibration while the radius of gyration of the tip mass is considerably higher than the length of the PCBMR. Ill-tuning leads to split and reduction of attenuation band to 50%; whereas, around 38% elongation of the attenuation band in the low frequency regime can be achieved by proper tuning.

Energy-based output feedback control of the underactuated 2DTORA system with saturated inputs

In this paper, we consider the control issues of the two-dimensional translational oscillator with rotational actuator (2DTORA) system, which has two translational carts and one rotational rotor. An output feedback controller for the 2DTORA system is proposed, which can prevent the unwinding behaviour. In addition, the velocity signal unavailability and actuator saturation are taken into account, simultaneously. In particular, the dynamics of the 2DTORA system are given first. On the basis of the passivity and control objectives of the 2DTORA system, an elaborate Lyapunov function is constructed. Then, based on the introduced Lyapunov function, a novel output feedback control method is proposed straightforwardly for the 2DTORA system. Lyapunov theory and LaSalle’s invariance principle are utilized to analyse the stability of the closed-loop system and the convergence of the states. Finally, simulation results are provided to illustrate the excellent control performance of the proposed controller in comparison with the existing method.

Densities of Pt–X (X: Fe, Co, Ni and Cu) binary melts and thermodynamic correlations

The densities of liquid binary Pt–X (X: Fe, Co, Ni and Cu) alloys were measured over a wide temperature range including the supercooled liquid region, using electromagnetic levitation under a static magnetic field. The static magnetic field effectively suppressed translational motion and surface oscillation of the levitated Pt–X sample droplets, enabling high-accuracy density measurement in a non-contact manner. The excess molar volumes (VE) of the liquid alloys were evaluated from the density measurements, and we demonstrated that the liquid Pt–X systems have positive VE with negative excess molar Gibbs energy (GE). The Pt–X systems have the common feature that order–disorder transitions are present in their phase diagrams. It should be also noted that VE decreases and GE increases with increasing number of electrons in the 3d orbital of X. This unique feature in the liquid Pt–X systems was discussed with possible rearrangement of electronic structure caused by alloying Pt with X.

A review of the researches on the added mass and damping coefficients for the heave plates of the offshore platforms at translational and rotational oscillations

A review of the researches on the added mass and damping coefficients for the heave plates of the offshore platforms at translational and rotational oscillations

Saturated stabilization for an uncertain cascaded system subject to an oscillator

This paper investigates saturated stabilization of an uncertain cascaded system that consists of an uncertain double integrator and an uncertain oscillator. The saturation reduction analysis is carried out by using the time-interval based contradiction approach, while the exponential stability analysis of the corresponding reduced system is conducted by using the Hurwitz lemma. In doing the saturation reduction analysis, an intractable problem is how to estimate the states of the oscillator. Fully using the property of saturation functions as well as the technique of Lyapunov inequalities, we can first estimate the states of the oscillator and then achieve the time-derivative bounds that some saturated terms possess in a finite time. This has helped to carry out the saturation reduction analysis. As the applications of the suggested algorithm, the stabilizing controllers have been provided for two benchmark systems — the uncertain two-mass–spring and the translational oscillator with a rotational actuator (TORA).

Output feedback control for an underactuated benchmark system with bounded torques

AbstractIn this paper, we consider the stabilization of the translational oscillator with a rotational actuator (TORA) system. Existing control methods for the TORA system are developed on the basis of the assumptions that full state feedback is available, and the actuator can supply control torques with any bounded amplitudes or system parameters are exactly known. In order to relax these assumptions, an amplitude‐saturated output feedback controller is proposed for the TORA system. Compared with existing control methods, the proposed method exhibits four remarkable features: free of plant parameters, bounded amplitude, output feedback, and unwinding behavior prevention. Specifically, the passivity of the TORA system is analyzed first. Then, a constructive energy‐like function is introduced and a corresponding amplitude‐saturated output feedback control law for the TORA system is proposed on the basis of the constructed energy‐like function. Lyapunov‐based analysis and LaSalle's invariance principle are used to prove the boundedness and convergence of the closed‐loop signals. Finally, numerical simulations with comparisons to previous reported methods are implemented to demonstrate the superior performance of the proposed method.

Micro-Particle Image Velocimetry Investigation of Flow Fields of SonoVue Microbubbles Mediated by Ultrasound and Their Relationship With Delivery

The flow fields generated by the acoustic behavior of microbubbles can significantly increase cell permeability. This facilitates the cellular uptake of external molecules in a process known as ultrasound-mediated drug delivery. To promote its clinical translation, this study investigated the relationships among the ultrasound parameters, acoustic behavior of microbubbles, flow fields, and delivery results. SonoVue microbubbles were activated by 1 MHz pulsed ultrasound with 100 Hz pulse repetition frequency, 1:5 duty cycle, and 0.20/0.35/0.70 MPa peak rarefactional pressure. Micro-particle image velocimetry was used to detect the microbubble behavior and the resulting flow fields. Then HeLa human cervical cancer cells were treated with the same conditions for 2, 4, 10, 30, and 60 s, respectively. Fluorescein isothiocyanate and propidium iodide were used to quantitate the rates of sonoporated cells with a flow cytometer. The results indicate that (1) microbubbles exhibited different behavior in ultrasound fields of different peak rarefactional pressures. At peak rarefactional pressures of 0.20 and 0.35 MPa, the dispersed microbubbles clumped together into clusters, and the clusters showed no apparent movement. At a peak rarefactional pressure of 0.70 MPa, the microbubbles were partially broken, and the remainders underwent clustering and coalescence to form bubble clusters that exhibited translational oscillation. (2) The flow fields were unsteady before the unification of the microbubbles. After that, the flow fields showed a clear pattern. (3)The delivery efficiency improved with the shear stress of the flow fields increased. Before the formation of the microbubble/bubble cluster, the maximum shear stresses of the 0.20, 0.35, and 0.70 MPa groups were 56.0, 87.5 and 406.4 mPa, respectively, and the rates of the reversibly sonoporated cells were 2.4% ± 0.4%, 5.5% ± 1.3%, and 16.6% ± 0.2%. After the cluster formation, the maximum shear stresses of the three groups were 9.1, 8.7, and 71.7 mPa, respectively. The former two could not mediate sonoporation, whereas the last one could. These findings demonstrate the critical role of flow fields in ultrasound-mediated drug delivery and contribute to its clinical applications.

Acoustic streaming outside and inside a fluid particle undergoing monopole and dipole oscillations.

An analytical theory is developed for acoustic streaming induced by an acoustic wave field inside and outside a spherical fluid particle, which can be a liquid droplet or a gas bubble. The particle is assumed to undergo the monopole (pulsation) and the dipole (translation) oscillation modes. The dispersed phase and the carrier medium are considered to be immiscible, compressible, and viscous. The developed theory allows one to calculate the acoustic streaming both outside and inside the fluid particle. In contrast to earlier works, no restrictions are imposed on the thickness of the outer and inner viscous boundary layers with respect to the particle radius. A numerical implementation of the obtained analytical results is used to evaluate the acoustic streaming for different experimentally relevant configurations, such as an air bubble in water, a water droplet in oil, and a water droplet in air, considering both traveling and standing acoustic waves. The results show the richness of streaming pattern variations that arise in bubbles and droplets.

Dynamics of Suspended Nanoparticles in a Time-varyingGradient Magnetic Field: Analytical Results

We study theoretically the deterministic dynamics of single-domain ferromagnetic nanoparticles in dilute ferrofluids, which is induced by a time-varying gradient magnetic field. Using the force and torque balance equations, we derive a set of the first-order differential equations describing the translational and rotational motions of such particles characterized by small Reynolds numbers. Since the gradient magnetic field generates both the translations and rotations of particles, these motions are coupled. Based on the derived set of equations, we demonstrate this fact explicitly by expressing the particle position through the particle orientation angle, and vice versa. The obtained expressions are used to show that the solution of the basic set of equations is periodic in time and to determine the intervals, where the particle coordinate and orientation angle oscillate. In addition, this set of equations is solved approximately for the case of small characteristic frequency of the particle oscillations. With this condition, we find that all particles perform small translational oscillations near their initial positions. In contrast, the orientation angle oscillates near the initial angle only if particles are located in the vicinity of zero point of the gradient magnetic field. The possible applications of the obtained results in biomedicine and separation processes are also discussed.