Time-Domain Simulation for Coupled Motions of Three Barges Moored Side-by-Side in Floatover Operation

Simulating the coupled motions of multiple bodies in the time domain is a complex problem because of the strong hydrodynamic interactions and coupled effect of various mechanical connectors. In this study, we investigate the hydrodynamic responses of three barges moored side-by-side in a floatover operation in the frequency and time domains. In the frequency domain, the damping lid method is adopted to improve the overestimated hydrodynamic coefficients calculated from conventional potential flow theory. A time-domain computing program based on potential flow theory and impulse theory is compiled for analyses that consider multibody hydrodynamic interactions and mechanical effects from lines and fenders. Correspondingly, an experiment is carried out for comparison with the numerical results. All statistics, time series, and power density spectra from decay and irregular wave tests are in a fairly good agreement.

Experimental Study on Coupled Motions of Mother Ship Launching and Recovering of Human-Occupied Vehicle in Regular Waves

The launching and recovery process of a human-occupied vehicle(HOV)faces more complex wave effects than other types of submersible operations.However,due to the nonlinearity between the HOV and its mother ship,difficulties occur in theoretically simulating their coupled motion and hydrodynamics.The coupled motion responses and the load under different regular wave conditions are investigated experimentally in this study.The optimized design of the experimental scheme simulated the launching and recovery process of the mother ship and HOV in regular waves.The attitude sensor performed synchronous real-time measurement of the coupled motion between the mother ship and HOV as well as obtained the load data on the coupled motion under different cable lengths.The results show that models in heading waves mainly lead to the vertical motion of the hoisting point.In beam waves,the transverse and vertical motions of the hoisting point occur in a certain frequency of waves.Under the heading and beam wave conditions,the longer the hoisting cable is,the greater the movement amplitude of the submersible is.Moreover,compared with the condition of the beam waves,the hoisting submersible has less influence on the mother ship under the condition of the heading waves.The findings provide theoretical support for the design optimization of the launching and recovery operation.

A Coupled Analysis of Nonlinear Sloshing and Ship Motion

Nonlinear interactions among incident wave, tank-sloshing and floating body coupling motion are investigated. The fully nonlinear sloshing and body-surface nonlinear free surface hydrodynamics is simulated using a Non-Uniform Rational B-Spline （NURBS） higher-order panel method in time domain based on the potential theory. A robust and stable improved iterative procedure （Yan and Ma, 2007） for floating bodies is used for calculating the time derivative of velocity potential and floating body motion. An energy dissipation condition based on linear theory adopted by Huang （2011） is developed to consider flow viscosity effects of sloshing flow in nonlinear model. A two-dimensional tank model test was performed to identify its validity. The present nonlinear coupling sway motion results are subsequently compared with the corresponding Rognebakke and Faltinsen （2003）＇s experimental results, showing fair agreement. Thus, the numerical approach presented in this paper is expected to be very efficient and realistic in evaluating the coupling effects of nonlinear sloshing and body motion.

Boundary Control of Coupled Nonlinear Three Dimensional Marine Risers

This paper presents a design of boundary controllers implemented at the top end for global stabilization of a marine riser in a three dimensional space under environmental loadings. Based on the energy approach, nonlinear partial differential equations of motion, including bending-bending and longitudinal-bending couplings for the risers are derived. The couplings cause mutual effects between the three independent directions in the riser＇s motions, and make it difficult to minimize its vibrations. The Lyapunov direct method is employed to design the boundary controller. It is shown that the proposed boundary controllers can effectively reduce the riser＇s vibration. Stability analysis of the closed-loop system is performed using the Lyapunov direct method. Numerical simulations illustrate the results.

Dynamic Positioning Control of Surge−Pitch Coupled Motion for Small-Waterplane-Area Marine Structures

For general dynamic positioning systems,controllers are mainly based on the feedback of motions only in the horizontal plane.However,for marine structures with a small water plane area and low metacentric height,undesirable surge and pitch oscillations may be induced by the thruster actions.In this paper,three control laws are investigated to suppress the induced pitch motion by adding pitch rate,pitch angle or pitch acceleration into the feedback control loop.Extensive numerical simulations are conducted with a semi-submersible platform for each control law.The influences of additional terms on surge−pitch coupled motions are analyzed in both frequency and time domain.The mechanical constraints of the thrust allocation and the frequency characters of external forces are simultaneously considered.It is concluded that adding pitch angle or pitch acceleration into the feedback loop changes the natural frequency in pitch,and its performance is highly dependent on the frequency distribution of external forces,while adding pitch rate into the feedback loop is always effective in mitigating surge−pitch coupled motions.

Numerical Study on Motion Responses of Two Parallel Ships During Underway Replenishment by the Semi-Analytical HOTP Method

Motion responses of two ships advancing parallel in waves with hydrodynamic interactions are investigated in this paper. Within the framework of the frequency-domain potential flow theory, a semi-analytical higher-order translating-pulsating source(HOTP) method is presented to solve the problems of coupled radiation and diffraction potential. The method employs nine-node bi-quadratic curvilinear elements to discretize the boundary integral equations(BIEs) constructed over the mean wetted surface of the two ship hulls. In order to eliminate the numerical oscillation, analytical quadrature formulas are derived and adopted to evaluate the integrals related to the Froudedependent part of the Green’s function along the horizontal direction in the BIEs. Based on the method, a numerical program is originally coded. Through the calculations of hydrodynamic responses of single ships, the numerical implementation is proved successful. Then the validated program is applied in the investigations on the hydrodynamic interactions of two identical Wigley Ⅲ hulls and the underway replenishment of a frigate and a supply ship in waves with and without stagger, respectively. The comparison between the present computed results with experimental data and numerical solutions of other methods shows that the semi-analytical HOTP method is of higher accuracy than the pulsating source Green’s function method with speed correction and better stability than the traditional HOTP method based on Gauss quadrature. In addition, for two ships with obviously different dimensions,the influence of hydrodynamic interactions on the smaller ship is found to be more noticeable than that on the larger ship, which leads to the differences between the motions of frigate with and without the presence of supply ship.

Over-Constraints and a Unified Mobility Method for General Spatial Mechanisms Part 2:Application of the Principle

The pre-research on mobility analysis presented a unified-mobility formula and a methodology based on reciprocal screw theory by HUANG, which focused on classical and modem parallel mechanisms. However its range of application needs to further extend to general multi-loop spatial mechanism. This kind of mechanism is not only more complex in structure but also with strong motion coupling among loops, making the mobility analysis even more complicated, and the relevant research has long been ignored. It is focused on how to apply the new principle for general spatial mechanism to those various multi-loop spatial mechanisms, and some new meaningful knowledge is further found. Several typical examples of the genera/multi-loop spatial mechanisms with motion couple even strong motion couple are considered. These spatial mechanisms include different closing way： over-constraint appearing in rigid closure, in movable closure, and in dynamic closure as well; these examples also include two different new methods to solve this kind of issue： the way to recognize over-constraints by analyzing relative movement between two connected links and by constructing a virtual loop to recognize over-constraints. In addition, over-constraint determination tabulation is brought to analyze the motion couple. The researches above are all based upon the screw theory. All these multi-loop spatial mechanisms with different kinds of structures can completely be solved by following the directions and examples, and the new mobility theory based on the screw theory is also proved to be valid. This study not only enriches and develops the theory and makes the theory more universal, but also has a special meaning for innovation in mechanical engineering.

Nonlinear Random Motion Analysis of A Tension Leg Platform Consider- ing the Set-down Motion of A Floating Body

The dynamic analysis of a Tension Leg Platform （TLP） in random wave is investigated by considering the set-down of a floating body. The nonlinear restoring stiffness is derived with the set-down motion of a floating body and the coupled motion of the tension leg and platform and the differential equations of the motion are established. The study focuses on the influence of the set-down motion on the nonlinear response of the platform. By considering different significant wave heights and currents, motion responses of the platform are calculated and compared. The analysis shows that the set-down motion significantly increases the heave motion with low frequency and the equilibrium position of the heave motion with the set-down motion is much lower than that without set-down motion. The results in this paper indicate that the set-down motion has a major impact on the safety of the platform inproduction operation, and it is also a threat to the strength of tension legs and risers.

Hydrodynamic Analysis and Power Conversion for Point Absorber WEC with Two Degrees of Freedom Using CFD

Point absorber wave energy device with multiple degrees of freedom(DOF) is assumed to have a better absorption ability of mechanical energy from ocean waves. In this paper, a coaxial symmetric articulated point absorber wave energy converter with two degrees of freedom is presented. The mechanical equations of the oscillation buoy with power take-off mechanism(PTO) in regular waves are established. The three-dimensional numerical wave tank is built in consideration of the buoy motion based upon the CFD method. The appropriate simulation elements are selected for the buoy and wave parameters. The feasibility of the CFD method is verified through the contrast between the numerical simulation results of typical wave conditions and test results. In such case, the buoy with single DOF of heave, pitch and their coupling motion considering free(no PTO damping) and damped oscillations in regular waves are simulated by using the verified CFD method respectively. The hydrodynamic and wave energy conversion characteristics with typical wave conditions are analyzed. The numerical results show that the heave and pitch can affect each other in the buoy coupling motion, hydrodynamic loads, wave energy absorption and flow field.The total capture width ratio with two coupled DOF motion is higher than that with a single DOF motion. The wave energy conversion of a certain DOF motion may be higher than that of the single certain DOF motion even though the wave is at the resonance period. When the wave periods are high enough, the interaction between the coupled DOF motions can be neglected.

Research on Coupling Transfer Characteristics of Vibration Energy of Free Piston Linear Generator

In order to clarify the mechanism and main influencing factors of the vibration energy coupling transmission with a dual-piston structure,a thermodynamic and dynamic coupling model of the free piston linear generator(FPLG)was established.The system energy conversion,vibration energy coupling transmission,and influencing factors were studied in detail.The coupling transmission paths and the secondary influence mechanism from in-cylinder combustion on vibration energy transmission were obtained.In addition,the influence of the movement characteristics of the dual-piston on the vibration energy transmission was studied,and the typical parameter variation law was obtained,which provides theoretical guidance for the subsequent vibration reduction design of the FPLG.

Dynamic modeling and simulation for the flexible spacecraft with dynamic stiffening

A rigid flexible coupling physical model which can represent a flexible spacecraft is investigated in this paper. By applying the mechanics theory in a non-inertial coordinate system,the rigid flexible coupling dynamic model with dynamic stiffening is established via the subsystemmodeling framework. It is clearly elucidated for the first time that,dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beamand the transverse vibration deformation of the beam. The modeling approach in this paper successfully avoids problems which are caused by other popular modeling methods nowadays： the derivation process is too complex by using only one dynamic principle; a clearly theoretical explanation for dynamic stiffening can＇t be provided. First,the continuous dynamic models of the flexible beamand the central rigid body are established via structural dynamics and angular momentumtheory respectively. Then,based on the conclusions of orthogonalization about the normal constrained modes,the finite dimensional dynamic model suitable for controller design is obtained. The numerical simulation validations showthat： dynamic stiffening is successfully incorporated into the dynamic characteristics of the first-order model established in this paper,which can indicate the dynamic responses of the rigid flexible coupling system with large overall motion accurately,and has a clear modeling mechanism,concise expressions and a good convergence.

THE COUPLE MOTION BETWEEN VESSEL WALL AN DBLOOD IN THE ENTRANCE REGION OF A TAPERED VESSEL

A problem of couple motion between vessel wall and blood in the entrance regionof a tapered vessel is considered in this paper A mathematical model of co-coupleaction is formed for both motion of vessel wall and blood flow in the entrance regance regionof elastic vessel with tapered angle. Under the situation that the relative boundary conditions are satisfied a.set of velocity distribution formula. pressure distributionformula for the blood flow in a tapered elastic vessel are derived. Some importantconclusions are obtained.

Contouring error modeling and simulation of a four-axis motion control system

A layered modeling method is proposed to resolve the problems resulting from the complexity of the error model of a multi-axis motion control system. In this model, a low level layer can be used as a virtual axis by the high level layer. The first advantage of this model is that the complex error model of a four-axis motion control system can be divided into several simple layers and each layer has different coupling strength to match the real control system. The second advantage lies in the fact that the controller in each layer can be designed specifically for a certain purpose. In this research, a three-layered cross coupling scheme in a four-axis motion control system is proposed to compensate the contouring error of the motion control system. Simulation results show that the maximum contouring error is reduced from 0.208 mm to 0.022 mm and the integration of absolute error is reduced from 0.108 mm to 0.015 mm, which are respectively better than 0.027 mm and 0.037 mm by the traditional method. And in the bottom layer the proposed method also has remarkable ability to achieve high contouring accuracy.

Optimization of body configuration and joint-driven attitude stabilization for transformable spacecraft under solar radiation pressure

The solar sail is one of the most promising space exploration systems due to its theoretically infinite specific impulse achieved through solar radiation pressure(SRP).Recently,researchers have proposed“transformable spacecraft”capable of actively reconfiguring their body configurations using actuatable joints.Transformable spacecraft,if used similarly to solar sails,are expected to significantly enhance orbit and attitude control capabilities owing to their high redundancy in control degrees of freedom.However,controlling them becomes challenging due to their large number of inputs,leading previous researchers to impose strong constraints to limit their potential control capabilities.This study focuses on novel attitude control techniques for transformable spacecraft under SRP.We developed two methods,namely,joint angle optimization to obtain arbitrary SRP force and torque,and momentum damping control driven by joint angle actuation.Our proposed methods are formulated in a general manner and can be applied to any transformable spacecraft comprising front faces that can predominantly receive the SRP on each body.The validity of our proposed method is confirmed through numerical simulations.Our study contributes to making most of the high control redundancy of transformable spacecraft without the need for expendable propellants,thus significantly enhancing the orbit and attitude control capabilities.

A MULTI-BODY SPACE-COUPLED MOTION SIMULATION FOR A DEEP-SEA TETHERED REMOTELY OPERATED VEHICLE

A multi-body coupled dynamic model is developed （TROV） system. A strong nonlinear coupling motion between to simulate the motion of a Tethered Remotely Operated Vehicle umbilical tether and ROV is discussed .The movement of ROV is considered as six-degrees of freedom. The lumped mass model is applied and an averaged tangential vector technique is included in the three-dimensional dynamic response equations of the cable-segments. The model can simulate the three-dimensional transient coupled motion of the complex multi-body system in typical ship maneuvering conditions and can be used in either a towing problem or a tethered underwater vehicle problem. Simulation results are seen to fit well with the experiment.

Intrinsic Kinematics of the Tibiotalar and Subtalar Joints during Human Walking based on Dynamic Biplanar Fluoroscopy

Accurate knowledge of the kinematics of the in vivo Ankle Joint Complex(AJC)is critical for understanding the biomechanical function of the foot and assessing postoperative rehabilitation of ankle disorders,as well as an essential guide to the design of ankle–foot assistant devices.However,detailed analysis of the continuous 3D motion of the tibiotalar and subtalar joints during normal walking throughout the stance phase is still considered to be lacking.In this study,dynamic radiographs of the hindfoot were acquired from eight subjects during normal walking.Natural motions with six Degrees of Freedom(DOF)and the coupled patterns of the two joints were analyzed.It was found that the movements of the two joints were mostly in opposite directions(including rotation and translation),mainly in the early and late stages.There were significant differences in the Range of Motion(ROM)in Dorsiflexion/Plantarflexion(D/P),Inversion/Eversion(In/Ev),and Anterior–Posterior(AP)and Medial–Lateral(ML)translation of the tibiotalar and subtalar joints(p<0.05).Plantarflexion of the tibiotalar joint was coupled with eversion and posterior translation of the subtalar joint during the impact phase(R^(2)=0.87 and 0.86,respectively),and plantarflexion of the tibiotalar joint was coupled with inversion and anterior translation of the subtalar joint during the push-off phase(R^(2)=0.93 and 0.75,respectively).This coordinated coupled motion of the two joints may be a manifestation of the AJC to move flexibly while bearing weight and still have stability.