Coupling Dynamic Equations Research Articles

Boundary-layer eigen solutions for multi-field coupled equations in the contact interface

The dissipative equilibrium dynamics studies the law of fluid motion under constraints in the contact interface of the coupling system. It needs to examine how constraints act upon the fluid movement, while the fluid movement reacts to the constraint field. It also needs to examine the coupling fluid field and media within the contact interface, and to use the multi-scale analysis to solve the regular and singular perturbation problems in micro-phenomena of laboratories and macro-phenomena of nature. This paper describes the field affected by the gravity constraints. Applying the multi-scale analysis to the complex Fourier harmonic analysis, scale changes, and the introduction of new parameters, the complex three-dimensional coupling dynamic equations are transformed into a boundary layer problem in the one-dimensional complex space. Asymptotic analysis is carried out for inter and outer solutions to the perturbation characteristic function of the boundary layer equations in multi-field coupling. Examples are given for disturbance analysis in the flow field, showing the turning point from the index oscillation solution to the algebraic solution. With further analysis and calculation on nonlinear eigenfunctions of the contact interface dynamic problems by the eigenvalue relation, an asymptotic perturbation solution is obtained. Finally, a boundary layer solution to multi-field coupling problems in the contact interface is obtained by asymptotic estimates of eigenvalues for the G-N mode in the large flow limit. Characteristic parameters in the final form of the eigenvalue relation are key factors of the dissipative dynamics in the contact interface.

Dynamic modeling of a flexible beam with large overall motion and nonlinear deformation using the finite element method

In this paper, the dynamic modeling theory of a flexible beam, which incorporates large overall motion and nonlinear deformation, is investigated. As we knows, in spacecraft and space station, there are a lot of flexible appendices, the dynamic modeling of a flexible beam is essential. Yet existing such models, in our opinion, lack several important coupling terms. This paper supplies these important coupling terms. It is reasonable to use geometrically nonlinear deformation fields to demonstrate and simplify a flexible beam undergoing large overall motion. In this paper, the finite element method is used for the system discretization and the coupling dynamic equations of flexible beam are obtained by Lagrange’s equations. The complete expression of stiffness matrix and all coupling terms are included in the dynamic equations. The second order coupling terms among rigid large overall motion, arc length stretch, lateral flexible deformation kinematics and torsional deformation terms are concluded in the present exact coupling model to expand the theory of one-order coupling model. The dynamic properties of a planar flexible rotating beam in the non-inertial reference frame are developed.

Exact dynamic modeling of a spatial flexible beam with large overall motion and nonlinear deformation

In this paper, the dynamic modeling theory of a spatial flexible beam, which undergoes large overall motion and nonlinear deformation, is investigated. As we know, in spacecraft and space station, there are a lot of flexible appendices so the dynamic modeling of a flexible beam is essential. Yet the existing models, in our opinion, lack several important coupling terms. This paper supplies these important coupling terms. Based on the new approach of deformation of fully geometrically nonlinear beam model developed，the finite element method is used for the system discretization and the coupling dynamic equations of flexible beam are obtained by Lagrange’s equations. The complete expression of stiffness matrix and all coupling terms are included in the dynamic equations. The second order coupling terms between rigid large overall motion, arc length stretch, lateral flexible deformation kinematics and torsional deformation terms are included in the present exact coupling model to expand the theory of one-order coupling model. The dynamic modeling method in this paper is of theoretical significance and has reference value for the rigid-flexible coupling system dynamic investigation .

Frequency Reliability Analysis of Francis Turbine-Generator Units Based on Nonlinear Vibration

This paper studies the frequency reliability of the main shaft system of Francis turbine-generator units based on nonlinear vibration. Taking the generator and turbine as an integrated system, the nonlinear coupling dynamic equations of the system are established by the finite element method. According to the dynamic equations, the frequent factors of system are obtained by the method of multiple scales. The criterion is used that the difference between the natural frequencies and driving frequencies including the frequent factors should be less than specific values. The reliability mode and the safety probability of the main shaft system of Francis turbine-generator units are defined as a series mode, and the frequency reliability analysis method for avoiding the resonance is proposed. Finally, an example is presented.

The fundamental solution of poroelastic plate saturated by fluid and its applications

AbstractIn this paper, the numerical model of the transverse vibrations of a thin poroelastic plate saturated by a fluid was proposed. Two coupled dynamic equations of equilibrium related to the plate deflection and the equivalent moment were established for an isotropic porous medium with uniform porosity. The fundamental solutions for a porous plate were derived both in the Laplace transform domain and in the time domain. A meshless method was developed and demonstrated in the Laplace transform domain for solving two coupled dynamic equations. Numerical examples demonstrated the accuracy of the method of the fundamental solutions and comparisons were made with analytical solutions. The proposed meshless method was shown to be simple to implement and gave satisfactory results for a poroelastic plate dynamic analysis. Copyright © 2009 John Wiley & Sons, Ltd.

Rigid-flexible coupling dynamics of three-dimensional hub-beams system

In the previous research of the coupling dynamics of a hub-beam system, coupling between the rotational motion of hub and the torsion deformation of beam is not taken into account since the system undergoes planar motion. Due to the small longitudinal deformation, coupling between the rotational motion of hub and the longitudinal deformation of beam is also neglected. In this paper, rigid-flexible coupling dynamics is extended to a hub-beams system with three-dimensional large overall motion. Not only coupling between the large overall motion and the bending deformation, but also coupling between the large overall motion and the torsional deformation are taken into account. In case of temperature increase, the longitudinal deformation caused by the thermal expansion is significant, such that coupling between the large overall motion and the longitudinal deformation is also investigated. Combining the characteristics of the hybrid coordinate formulation and the absolute nodal coordinate formulation, the system generalized coordinates include the relative nodal displacement and the slope of each beam element with respect to the body-fixed frame of the hub, and the variables related to the spatial large overall motion of the hub and beams. Based on precise strain-displacement relation, the geometric stiffening effect is taken into account, and the rigid-flexible coupling dynamic equations are derived using velocity variational principle. Finite element method is employed for discretization. Simulation of a hub-beams system is used to show the coupling effect between the large overall motion and the torsional deformation as well as the longitudinal deformation. Furthermore, conservation of energy in case of free motion is shown to verify the formulation.

Dynamic response of liquid-filled rectangular tank with elastic appendages under pitching excitation

Nonlinear dynamics of liquid-filled rectangular tank with elastic appendages are studied. Based on the assumption of ideal fluid, the coupling dynamic equations of rigid tank, elastic appendages and liquid fuel are derived using H-O principle. In the case of pitch excitation, the modified potential function and wave height function are introduced to describe the moving boundary of fluid, then Galerkin’s method is used to discretize the dynamic equations into ordinary differential equations. The natural frequencies of the coupling system are formulated in liquid depth, the length of the tank, etc. The formulae are confirmed by numerical simulations, which also show that the effects of liquid and elastic appendages on the attitude angular of rigid.

Study of pore pressure variation during liquefaction using two constitutive models for sand

Numerical analyses of liquefiable sand are presented in this paper. Liquefaction phenomenon is an undrained response of saturated sandy soils when they are subjected to static or dynamic loads. A fully coupled dynamic computer code is developed to predict the liquefaction potential of a saturated sandy layer. Coupled dynamic field equations of extended Biot's theory with u– P formulation are used to determine the responses of pore fluid and soil skeleton. Generalized Newmark method is employed for integration in time. The soil behavior is modelled by two constitutive models; a critical state two-surface plasticity model, and a densification model. A class ‘B’ analysis of a centrifuge experiment is performed to simulate the dynamic response of level ground sites. The results of the numerical analyses demonstrate the capability of the critical sate two-surface plasticity model in producing pore pressures that are consistent with observations of the behavior of liquefiable sand in the centrifuge test.

Low-temperature dynamic behavior of a spherical p-spin model of glass in an alternating field

Coupled dynamic Schwinger-Dyson equations for autocorrelation and linear-response functions are used for studying nonequilibrium dynamics of a p-spin model of glass. The numerical solution of these equations reveals an interesting dynamic behavior of the system in the external alternating field. The behavior is also shown to depend on the amplitude and frequency of the foregoing field and on the value of coupling between the spins.

Laboratory measurement of electrification of wind‐blown sands and simulation of its effect on sand saltation movement

This article presents a measurement of electrification generated by wind‐blown sands in a field wind tunnel and a numerical methodology to simulate the effect of electrification on the sand saltation movement after the mutual couple interaction between the sand movement and the wind flow is taken into account. The measured data of electric charge on the “uniform” sands in the wind‐tunnel tests show that the sign of electric charge, either negative or positive, is mainly dependent on the diameter size of sand particles, i.e., negative charge is gained when the diameter is smaller than 250 μm and positive charge is obtained if the diameter is larger than 500 μm, and that for both “uniform” and mixed sands, the average charge‐to‐mass ratio decreases with increasing the wind velocity, and increases with height from sand bed. Meanwhile, the measurement of electric field in wind‐sand cloud related to the electric charge displays that the magnitude of electric field increases generally as the wind velocity and the height increase, and the direction of the field is always upwardly vertical to the Earth's surface, which is opposite to that of the fair‐weather field. In order to exhibit the effect of electrification on sand saltation movement, a theoretical model by considering the mutual coupling interaction between wind flow and sand movement is proposed after the electric force exerted on the moving sands is considered. Through solving the nonlinear coupling dynamic equations by a proposed program, the effect of electrification on sand saltation motion, e.g., trajectory, is discussed quantitatively. After that, its effect on wind‐sand transport flux, sand ejecta flux, and wind profile is also displayed. The results show that the prediction for the Bagnold's kink is good agreement with the measurement in literature.

TRANSVERSE VIBRATIONS OF A THIN RECTANGULAR POROUS PLATE SATURATED BY A FLUID

A simple model of the transverse vibrations of a thin rectangular porous plate saturated by a fluid is proposed. The model is based on the classical theory of homogeneous plates and on Biot's stress–strain relations in an isotropic porous medium with a uniform porosity. Two coupled dynamic equations of equilibrium relating the plate deflection and the fluid/solid relative displacement are found and their physical interpretation is given. The energy dissipation by viscous friction is included in the model. An approximate calculation of the natural frequencies of vibration is given for rigid plates with various boundary conditions at the edges. The influence of porosity, tortuosity and permeability on the resonances is studied and a condition of maximum damping involving these parameters is given.

Transient Response Analysis of Nonlinear Modally Coupled Structural Dynamics Equations of Motion

The solution of the structural dynamics matrix differential equations of motion in the presence of general structural damping, aerodynamic stiffness and damping, and nonlinear generalized forces is discussed. An intuitive and easy-to-use method of Picard iteration by Dawson is shown to provide exponential convergence to the exact solution of quasilinear second-order matrix differential equations with general modal coupling, and the first mathematical proof of convergence is presented. It is demonstrated, for the special case of general structural damping without aerodynamic forces but with forcing functions that depend only on time, that the method of Picard iteration agrees to within machine accuracy with the method of linear modal velocity of Henkel and Mar. Thomson's coupled damping problem is solved using both methods and percent errors resulting from ignoring modal coupling are quantified. Possible areas of future research are discussed.

Monomer–excimer kinetics in solution. I. Stochastic many-particle approach

A stochastic many-particle approach is applied to study the kinetics of reversible excimer formation in solution. Coupled dynamic equations for the macroscopic concentrations and for the radial distribution function are derived, and applied to analyze (i) time resolved kinetics after a short pulse, and (ii) steady-state kinetics. Renormalization of the phenomenological excimer dissociation rate coefficient due to nonequilibrium effects is discussed. A relation is demonstrated between steady-state, reversible monomer–excimer kinetics and irreversible fluorescence kinetics. Explicit results are given for the excimer fluorescence yield, assuming the Smoluchowski–Collins–Kimball reactivity model.

Kinetics of nonstationary, diffusion-influenced reversible reactions in solution

The statistical nonequilibrium thermodynamic theory of diffusion-influenced reactions is extended to nonstationary situations. Coupled dynamic equations for the average concentrations and the radial distribution function are derived, and, in the low density limit, applied to study the approach of the reversible reaction A+B⇄C to equilibrium. Two types of rate coefficients for the bimolecular reaction are discussed: (i) molecular rate coefficient describing the rates of elementary reactive events, and (ii) phenomenological rate constants defined via the macroscopic rate equations. In contrast to the phenomenological rate constant, the molecular forward rate coefficient ceases to depend on diffusion when the reaction reaches equilibrium. If the relaxation time for the reaction is much greater than that for diffusion, the classical expressions of Eigen for the linearized relaxation rate near equilibrium are recovered. A close relationship between the classical approach, the pseudo-steady-state approximation, and Onsager’s regression hypothesis is demonstrated. The relation between the present results and those recently put forward in the literature is discussed.

Parallel computation of robot inverse dynamics for high speed motions

The computation of the highly coupled dynamic equations has always posed a bottleneck in real-time dynamic control of robot manipulators. Recent advances in VLSI technology make it possible to implement new algorithms that compute these equations and meet real-time constraints. Parallel processing techniques can now be used to reduce the computation time for models of a highly mathematical nature such as the dynamical modelling of robot manipulators. In this paper an attempt is made to review the subject of the parallel computation of robot dynamics. Moreover, a new and highly efficient technique is introduced to solve this problem. A simplified form of the Lagrange-Euler is divided into subtasks and distributed on to a parallel processing system. The development (parallel processor) system employs several INMOS transputers running the OCCAM concurrent programming language. Further, the system is used to introduce parallelism to robot dynamics through different task allocation strategies. These strategies flow naturally from the Lagrange-Euler formulation. The cost effectiveness and speed of the algorithm are demonstrated by a case study (Stanford arm). Comparisons are made between uniprocessor (von Neumann) and parallel implementations of the algorithm. Several measures such as utilisation, efficiency, and speed up are used to evaluate the performance of the employed networks and task allocations.

Application of statistical narrow-band model to coupled radiation and convection at high temperature

The use of wide-band or gray-gas models in coupled heat transfer calculations frequently leads to significant errors due to spectral correlations between the emitted flux intensity and gas transmissivity. In the present study, the random statistical narrow-band model with the exponential-tailed-inverse distribution and the Curtis-Godson approximation are used with a 25cm −1 spectral resolution; our parameters are generated from a line-by-line calculation. Coupled dynamic and energy equations are solved for an emitting and absorbing laminar gas flow between two parallel walls at fixed temperature. The influence of radiative and thermophysical property variations with temperature is analysed for H 2O-air mixtures under strong temperature gradients. A large range of optical thickness is studied. Different temperature and heat flux profiles are found when the walls are heated or cooled. Finally, results obtained with the statistical narrow-band model and the exponential wide-band model are compared.

THE INTERACTION OF PARTICLES WITH CAVITONS IN PLASMA

Starting from Vlasov-Doisson equations, the coupled dynamics equations for slowly varying electron distribution function δFe, slowly varying field Es and fast varying field E are derived and the system of above equations is analytically solved. Thus, the interactions of the particles distribution functions with solitons are revealed. Furthermore, the collapse motions of δFe Es. E for higher dimensions and their many cavitons behavior are discussed.

A procedure for coupling dynamical equations

The analytical formulation for coupling dynamical equations having general linear constraints is a highly relevant structural problem which is often encountered in modal synthesis procedures. Computational difficulties arise in reducing the total number of unknowns in the dynamical equations to an independent set. Here a simple, general and powerful procedure is presented which can be easily introduced in existing finite element programs. This method will be implemented in ASKA, which has excellent substructuring techniques and is available in the European Space Agency.

Liquefaction Analysis of Horizontally Layered Sands

A method is presented for analysis of seismic response and liquefaction of the horizontally layered saturated soils that are modeled as fluid saturated porous solids. Coupled dynamic equations of motion are used and nonlinear material properties are assigned to the solid granular portion. The paper describes the theory and the material model used. The proposed method is used in case studies, including a Niigata like soil profile and the results of the analyses are considered.