Complete geometric nonlinear formulation for rigid-flexible coupling dynamics

A complete geometric nonlinear formulation for rigid-flexible coupling dynamics of a flexible beam undergoing large overall motion was proposed based on virtual work principle, in which all the high-order terms related to coupling deformation were included in dynamic equations. Simulation examples of the flexible beam with prescribed rotation and free rotation were investigated. Numerical results show that the use of the first-order approximation coupling (FOAC) model may lead to a significant error when the flexible beam experiences large deformation or large deformation velocity. However, the correct solutions can always be obtained by using the present complete model. The difference in essence between this model and the FOAC model is revealed. These coupling high-order terms, which are ignored in FOAC model, have a remarkable effect on the dynamic behavior of the flexible body. Therefore, these terms should be included for the rigid-flexible dynamic modeling and analysis of flexible body undergoing motions with high speed.

Rigid-Flexible Coupling Dynamic Analysis of Sub-Launched Vehicle During the Vertical Tube-Exit Stage

During the launching stage,hydrodynamic pressure and adapters' reaction loads can influence the vehicle's rigid motion as well as cause its structural vibration,which is a typical rigid-flexible coupling dynamic problem. This paper presents a 2-D rigid-flexible coupling model to calculate the vehicle's dynamic responses in that period.The vehicle was equivalent to a flexure beam with axial deformation. Hybrid coordinate and modal superposition methods were used to describe its large rigid displacement and small deformation. By the second Lagrange equation,the vehicle centroid's displacements,rotational angle and modal coordinates were chosen as generalized coordinates and then the vehicle 's rigid-flexible coupling dynamic equations were obtained. By numerical simulation,the results of vehicle's motion parameters and transverse internal loads were acquired.The calculation results showed that differences of the vehicle's motion parameters between the rigid-flexible coupling model and the rigid body assumption are noticeable and the peak magnitude of the vehicle's transverse internal loads in the rigid-flexible coupling model is higher remarkably than that in the rigid body assumption.

A rigid-flexible coupling finite element model of coupler for analyzing train instability behavior during collision

Rail vehicles generate huge longitudinal impact loads in collisions.If unreasonable matching exists between the compressive strength of the intermediate coupler and the structural strength of the car body,the risk of car body structure damage and train derailment will increase.Herein,a four-stage rigid-flexible coupling finite element model of the coupler is established considering the coupler buckling load.The influence of the coupler buckling load on the train longitudinal-vertical-hori-zontal buckling behavior was studied,and the mechanism of the train horizontal buckling instability in train collisions was revealed.Analysis results show that an intermediate coupler should be designed to ensure that the actual buckling load is less than the compressive load when the car body structure begins to deform plastically.The actual buckling load of the coupler and the asymmetry of the structural strength of the car body in the lateral direction are two important influencing factors for the lateral buckling of a train collision.If the strength of the two sides of the car body structure in the lateral direction is asymmetrical,the deformation on the weaker side will be larger,and the end of the car body will begin to deflect under the action of the coupler force,which in turn causes the train to undergo sawtooth buckling.

Multi-Body Dynamics Modeling of Heavy Goods Vehicle-Rail Interaction

Based on the principle of vehicle-track coupling dynamics, SIMPACK multi-body dynamics software is used to establish a C80 wagon line-coupled multi-body dynamics model with 73 degrees of freedom. And the reasonableness of the line-coupled dynamics model is verified by using the maximum residual acceleration, the nonlinear critical speed of the wagon. The experimental results show that the established vehicle line coupling dynamics model meets the requirements of vehicle line coupling dynamics modeling.

The dynamic coupling model and its application of urbanization and eco-environment in Hexi Corridor

This paper, taking Hexi Corridor as an example, analyzes the altemating intimidation and the dynamic evolving relation between urbanization and eco-environment in arid area of West China. We argue that the harmonious development system of the urbanization and eco-environment would go through four phases： rudimentary symbiotic phase, harmonious developmental phase, utmost increasing phase and spiral type rising phase. Throughout the four phases, the elements of the system would influence each other, coerce each other, and complete the spiral type rising process from low-grade symbiosis to high-grade harmony together. The study on Hexi Corridor shows that the urbanization level in Hexi Corridor has increased gradually from 1985 to 2003 accompanied with the fluctuations of eco-environment state. The response of eco-environment to urbanization has been evident, but lagged behind the urbanization course. At present, the harmonious development system in Hexi Corridor was in its harmonious developmental phase. However, the coupling degree has increased quickly and approached 90 yet, which is signaling that the system is about to enter the utmost increasing phase, and the ecological crisis will enter the latent period. We have found that the coupling degree can well reflect the interactive coercing and dynamic evolving situation between urbanization and eco-environment in Hexi Corridor. From the temporal change of the coupling degree, it can be concluded that urbanization sometimes needs to pay a certain cost for the damage of the eco-environment in its initial stages, but as the urbanization continues, the state of the eco-environment would be meliorated.

Fully fluid-solid coupling dynamic model for seismic response of underground structures in saturated soils

The seismic response characteristics of underground structures in saturated soils are investigated.A fully fluid-solid coupling dynamic model is developed and implemented into ABAQUS with a user-defined element to simulate the dynamic behavior of saturated soils.The accuracy of the model is validated using a classic example in literature.The performance of the model is verified by its application on simulating the seismic response characteristics of a subway station built in saturated soils.The merits of the model are demonstrated by comparing the difference of the seismic response of an underground structure in saturated soils between using the fully coupling model and a single-phase medium model.The study finds that the fully coupling model developed herein can simulate the dynamic response characteristics of the underground structures in saturated soils with high accuracy.The seismic response of the underground structure tends to be underestimated by using the single-phase medium model compared with using the fully coupling model,which provides a weaker confining action to the underground structure.

Roll System and Stock's Multi-parameter Coupling Dynamic Modeling Based on the Shape Control of Steel Strip

The existence of rolling deformation area in the rolling mill system is the main characteristic which dis- tinguishes the other machinery. In order to analyze the dynamic property of roll system＇s flexural deformation, it is necessary to consider the transverse periodic movement of stock in the rolling deformation area which is caused by the flexural deformation movement of roll system simul- taneously. Therefore, the displacement field of roll system and flow of metal in the deformation area is described by kinematic analysis in the dynamic system. Through intro- ducing the lateral displacement function of metal in the deformation area, the dynamic variation of per unit width rolling force can be determined at the same time. Then the coupling law caused by the co-effect of rigid movement and flexural deformation of the system structural elements is determined. Furthermore, a multi-parameter coupling dynamic model of the roll system and stock is established by the principle of virtual work. More explicitly, the cou- pled motion modal analysis was made for the roll system. Meanwhile, the analytical solutions for the flexural defor- mation movement＇s mode shape functions of rolls are discussed. In addition, the dynamic characteristic of the lateral flow of metal in the rolling deformation area has been analyzed at the same time. The establishment ofdynamic lateral displacement function of metal in the deformation area makes the foundation for analyzing the coupling law between roll system and rolling deformation area, and provides a theoretical basis for the realization of the dynamic shape control of steel strip.

Study on Rigid-Flexible Coupling Effects of Floating Offshore Wind Turbines

In order to account for rigid-flexible coupling effects of floating offshore wind turbines, a nonlinear rigid-flexible coupled dynamic model is proposed in this paper. The proposed nonlinear coupled model takes the higher-order axial displacements into account, which are usually neglected in the conventional linear dynamic model. Subsequently,investigations on the dynamic differences between the proposed nonlinear dynamic model and the linear one are conducted. The results demonstrate that the stiffness of the turbine blades in the proposed nonlinear dynamic model increases with larger overall motions but that in the linear dynamic model declines with larger overall motions.Deformation of the blades in the nonlinear dynamic model is more reasonable than that in the linear model as well.Additionally, more distinct coupling effects are observed in the proposed nonlinear model than those in the linear model. Finally, it shows that the aerodynamic loads, the structural loads and global dynamic responses of floating offshore wind turbines using the nonlinear dynamic model are slightly smaller than those using the linear dynamic model. In summary, compared with the conventional linear dynamic model, the proposed nonlinear coupling dynamic model is a higher-order dynamic model in consideration of the rigid-flexible coupling effects of floating offshore wind turbines, and accord more perfectly with the engineering facts.

Coupling numerical simulation with remotely sensed information for the study of frozen soil dynamics

The acquisition of spatial-temporal information of frozen soil is fundamental for the study of frozen soil dynamics and its feedback to climate change in cold regions.With advancement of remote sensing and better understanding of frozen soil dynamics,discrimination of freeze and thaw status of surface soil based on passive microwave remote sensing and numerical simulation of frozen soil processes under water and heat transfer principles provides valuable means for regional and global frozen soil dynamic monitoring and systematic spatial-temporal responses to global change.However,as an important data source of frozen soil processes,remotely sensed information has not yet been fully utilized in the numerical simulation of frozen soil processes.Although great progress has been made in remote sensing and frozen soil physics,yet few frozen soil research has been done on the application of remotely sensed information in association with the numerical model for frozen soil process studies.In the present study,a distributed numerical model for frozen soil dynamic studies based on coupled water-heat transferring theory in association with remotely sensed frozen soil datasets was developed.In order to reduce the uncertainty of the simulation,the remotely sensed frozen soil information was used to monitor and modify relevant parameters in the process of model simulation.The remotely sensed information and numerically simulated spatial-temporal frozen soil processes were validated by in-situ field observations in cold regions near the town of Naqu on the East-Central Tibetan Plateau.The results suggest that the overall accuracy of the algorithm for discriminating freeze and thaw status of surface soil based on passive microwave remote sensing was more than 95%.These results provided an accurate initial freeze and thaw status of surface soil for coupling and calibrating the numerical model of this study.The numerically simulated frozen soil processes demonstrated good performance of the distributed numerical model based on the coupled water-heat transferring theory.The relatively larger uncertainties of the numerical model were found in alternating periods between freezing and thawing of surface soil.The average accuracy increased by about 5%after integrating remotely sensed information on the surface soil.The simulation accuracy was significantly improved,especially in transition periods between freezing and thawing of the surface soil.

A Study of Dynamic Analysis Method for the Rigid-Flexible Coupled Bar Linkage System

In order to present a dynamic analysis method for the rigid-flexible coupled bar linkage system(RFCBLS),the flexible element motion equation was gotten by Lagrange Equation and the rigid element motion equation was gotten based on rigid constraint conditions.The multi-body system(MBS) is a complex mechanism and its components have quite different rigidities.If it is considered as a rigid MBS(RMBS) to do its dynamic analysis,elastic deformation's ignorance will lead to inaccurate analysis.If it is considered as a flexible MBS(FMBS) to establish,analyze,and solve the model,quite large system equations make it difficult to solve.The better method is as follows:the complex mechanism system is regarded as a rigid-flexible coupled system(RFCS) to make dynamic characteristic of rigid components be equivalent,system equation is established by FMBS' way,and system equation dimensions are reduced by transition matrices' introduction.A dynamic analysis method for rigid element and flexible element coupling was presented based on the FMBS.The analyzed crank slide-block mechanism results show that the dynamic analysis method for RFCBLS is quick and convenient.

Constitutive model of rock under static-dynamic coupling loading and experimental investigation

The importance of study on constitutive model of statically loaded rock experiencing dynamic load is set forth, and the studying methods on dynamic constitutive model are classified according to the current studying status. By way of combining statistic damage model and viscoelastic model, uni-axial and multi-axial constitutive models of statically loaded rock experiencing dynamic load (static-dynamic coupling constitutive model) under intermediate strain rate are established. The verification experiment on 2D constitutive model under different static stress and dynamic stress with different frequencies is designed and performed. It is found that there is a good agreement between the experimental stress-strain curves and the theoretical stress-strain curves.

THE COUPLING DYNAMICAL MODELING THEORY OF FLEXIBLE MULTIBODY SYSTEM

Based on the deformation theory of elastic beams, the coupling effect between the coupling displacements of a point on the middle line of beam and large overall motion is presented. The 'coupling matrix library' and Jourdain's variation principle and single direction recursive formulation method are used to establish the general coupling dynamical equations of flexible multibody system. Two typical examples show the coupling effect between coupling displacements and large overall motion on the dynamics of flexible multibody system consisting of beams.

Dynamical correlation functions of the quadratic coupling spin-Boson model

The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method.We focus on the dynamical auto-correlation functions CO（ω）, with the operator taken as σx, σz, and X, respectively. In the weak-coupling regime α 〈 αc, these functions show power law ω-dependence in the small frequency limit, with the powers 1 ＋ 2s, 1 ＋ 2s, and s, respectively. At the critical point α = αc of the boson-unstable quantum phase transition, the critical exponents yO of these correlation functions are obtained as yσx= yσz= 1-2s and yX=-s, respectively. Here s is the bath index and X is the boson displacement operator. Close to the spin flip point, the high frequency peak of Cσx（ω） is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point.

Numerical simulation of aircraft arresting process with an efficient full-scale rigid-flexible coupling dynamic model

The arresting process of carrier-based aircraft is widely recognized as a challenging task,characterized by the highest accident rate among all carrier-based aircraft operations.Dynamic simulation plays a crucial role in assessing the intricate responses of the arresting process,favoring the design of carrier-based aircraft.An efficient and accurate rigid-flexible coupling model for analyzing the dynamic response of the arresting process is proposed.By combining the dynamic characteristics of airframe,landing gear,arresting hook and arresting gear system,the rigid-flexible coupling dynamic model is established to reflect the relative motion of the coupling parts and arresting load.The dynamic model is verified through simulations of landing gear landing drops and by comparing the arresting simulation results with corresponding data in the US military standard.Additionally,simulations of the arresting process under different off-center distance and aircraft yaw angle are conducted to obtain the dynamic response of the aircraft during the arresting process.The result indicates that the rigid-flexible coupling dynamic model proposed is effective for analyzing the arresting dynamics response of carrier-based aircraft.The axial force of the arresting cable on both sides of the hook engagement point,pitch and yaw angle of aircraft are inconsistent under yaw and off-center arresting.The analysis method and obtained results provide valuable references for assessing the dynamic responses of carrier-based aircraft during arresting process and offer valuable in-sights in the design of carrier-based aircraft.

Nonlinear Coupled Dynamics Analysis of A Truss Spar Platform

Accurate prediction of the offshore structure motion response and associate mooring line tension is important in both technical applications and scientific research. In our study, a truss spar platform, operated in Gulf of Mexico, is numerically simulated and analyzed by an in-house numerical code ＇COUPLE＇. Both the platform motion responses and associated mooring line tension are calculated and investigated through a time domain nonlinear coupled dynamic analysis. Satisfactory agreement between the simulation and corresponding field measurements is in general reached, indicating that the numerical code can be used to conduct the time-domain analysis of a truss spar interacting with its mooting and riser system. Based on the comparison between linear and nonlinear results, the relative importance of nonlinearity in predicting the platform motion response and mooring line tensions is assessed and presented. Through the coupled and quasi-static analysis, the importance of the dynamic coupling effect between the platform hull and the mooting/riser system in predicting the mooting line tension and platform motions is quantified. These results may provide essential information pertaining to facilitate the numerical simulation and design of the large scale offshore structures.

Dynamic model of vertical vehicle-subgrade coupled system under secondary suspension

As it is known, track transportation can be divided into track system above and track system below. While the train is moving, the parts above and below are interacted and influenced. Therefore, in fact, the problem of track transportation is the match between the vehicle and the raihvay line system. In this paper, on a basis of dynamic analysis of the vehicle-subgrade model of vertical coupled system under primary suspension, utilizing track maintenance standard and simulating track irregularity excitation, the dynamic interaction of vehicle-track-subgrade system is researched in theory and dynamic model of the vertical vehicle-track-subgrade coupled system under secondary suspension is established by compatibility condition of deformation. Even this model considers the actual structure of a vehicle, also considers vibration characteristic of the substructure of track including subgrade and foundation. All these work want to be benefit for understanding and design about the dynamic characters of subgrade in high speed railway.

Improved frequency modeling and solution for parallel liquid-filled pipes considering both fluid-structure interaction and structural coupling

The dynamic characteristics of a single liquid-filled pipe have been broadly studied in the previous literature.The parallel liquid-filled pipe(PLFP)system is also widely used in engineering,and its structure is more complex than that of a single pipe.However,there are few reports about the dynamic characteristics of the PLFPs.Therefore,this paper proposes improved frequency modeling and solution for the PLFPs,involving the logical alignment principle and coupled matrix processing.The established model incorporates both the fluid-structure interaction(FSI)and the structural coupling of the PLFPs.The validity of the established model is verified by modal experiments.The effects of some unique parameters on the dynamic characteristics of the PLFPs are discussed.This work provides a feasible method for solving the FSI of multiple pipes in parallel and potential theoretical guidance for the dynamic analysis of the PLFPs in engineering.

Coupled Dynamics and Integrated Control for Position and Attitude Motions of Spacecraft:A Survey

Inspired by the integrated guidance and control design for endo-atmospheric aircraft,the integrated position and attitude control of spacecraft has attracted increasing attention and gradually induced a wide variety of study results in last over two decades,fully incorporating control requirements and actuator characteristics of space missions.This paper presents a novel and comprehensive survey to the coupled position and attitude motions of spacecraft from the perspective of dynamics and control.To this end,a systematic analysis is firstly conducted in details to show the position and attitude mutual couplings of spacecraft.Particularly,in terms of the time discrepancy between spacecraft position and attitude motions,space missions can be categorized into two types:space proximity operation and space orbital maneuver.Based on this classification,the studies on the coupled dynamic modeling and the integrated control design for position and attitude motions of spacecraft are sequentially summarized and analyzed.On the one hand,various coupled position and dynamic formulations of spacecraft based on various mathematical tools are reviewed and compared from five aspects,including mission applicability,modeling simplicity,physical clearance,information matching and expansibility.On the other hand,the development of the integrated position and attitude control of spacecraft is analyzed for two space missions,and especially,five distinctive development trends are captured for space operation missions.Finally,insightful prospects on future development of the integrated position and attitude control technology of spacecraft are proposed,pointing out current primary technical issues and possible feasible solutions.

Macroscopic damping model for structural dynamics with random polycrystalline configurations

In this paper the macroscopic damping model for dynamical behavior of the structures with random polycrystalline configurations at micro-nano scales is established. First, the global motion equation of a crystal is decomposed into a set of motion equations with independent single degree of freedom （SDOF） along normal discrete modes, and then damping behavior is introduced into each SDOF motion. Through the interpolation of discrete modes, the continuous representation of damping effects for the crystal is obtained. Second, from energy conservation law the expression of the damping coefficient is derived, and the approximate formula of damping coefficient is given. Next, the continuous damping coefficient for polycrystalline cluster is expressed, the continuous dynamical equation with damping term is obtained, and then the concrete damping coefficients for a polycrystalline Cu sample are shown. Finally, by using statistical two-scale homogenization method, the macroscopic homogenized dynamical equation containing damping term for the structures with random polycrystalline configurations at micro-nano scales is set up.

The integration of nitrogen dynamics into a land surface model. Part 1: model description and site-scale validation

Nitrogen cycling has profound effects on carbon uptake in the terrestrial ecosystem and the response of the biosphere to climate changes.However,nutrient cycling is not taken into account in most land surface models for climate change.In this study,a nitrogen model,based on nitrogen transformation processes and nitrogen fluxes exchange between the atmosphere and terrestrial ecosystem,was incorporated into the Atmosphere–Vegetation Interaction Model(AVIM)to simulate the carbon cycle under nitrogen limitation.This new model,AVIM-CN,was evaluated against site-scale eddy covariance–based measurements of an alpine meadow located at Damxung station from the FLUXNET 2015 dataset.Results showed that the annual mean gross primary production simulated by AVIM-CN(0.7073 gC m^-2 d^-1)was in better agreement with the corresponding flux data(0.5407 gC m^-2 d^-1)than the original AVIM(1.1403 gC m^-2 d^-1)at Damxung station.Similarly,ecosystem respiration was also down-regulated,from 1.7695 gC m^-2 d^-1 to 1.0572 gC m^-2 d^-1,after the nitrogen processes were introduced,and the latter was closer to the observed vales(0.8034 gC m^-2 d^-1).Overall,the new results were more consistent with the daily time series of carbon and energy fluxes of observations compared to the former version without nitrogen dynamics.A model that does not incorporate the limitation effects of nitrogen nutrient availability will probably overestimate carbon fluxes by about 40%.