Modified Equations of Motion of the Hydrogen Maser

We demonstrate that in the currently used equations of motion for the hydrogen maser (in relative units) the scale along the coordinate axes dependeds on the q factor of the hydrogen maser. This makes it difficult to analyze the H-maser operation and to optimize its parameters. We propose modified equations of motion equations without this shortcoming.     

Oscillating two-phase flow in a prestressed thick elastic tube

Summary The pulsating flow of a fluid with dusty particles in a prestressed thick walled elastic tube has been studied. The tube, subjected to a static inner pressure P_i and an axial stretch λ, is taken to be an incompressible, isotropic, elastic material. The fluid with particles is treated as incompressible Newtonian. Employing the theory of small deformation superimposed on large initial deformations, for an axially symmetric perturbed motion the governing equations are obtained in cylindrical polar coordinates. The analytical solutions of the equations of motion for the dust and the fluid have been obtained. Because of the variable character of the coefficients of the resulting equations for the solid body they are solved numerically. The dispersion relation is obtained as a function of the stretch, the thickness ratio and the parameters for dusty particles.     

New predictor/corrector algorithms with improved energy balance for a recent formulation of dynamic vehicle/structure interaction

A new class of predictor/corrector algorithms is proposed to solve the complex system of differential equations that arises from a Galerkin spatial discretization of the equations of motion in a recent formulation of dynamic vehicle/structure interaction. The applicability of the concept of a building-block vehicle/structure interaction model developed in our previous work—where the vehicle nominal motion is not prescribed a priori, but is part of the unknown motion of the system—is demonstrated through the construction of a simple vehicle model. In the new algorithms, the presence of the accelerations of the vehicle component is eliminated in the predictor structural equations, making these equations different from the corrector structural equations. The special treatment of the predicted axial motion that provides an artificial damping to eliminate unstable oscillations in the numerical results as proposed in the old algorithms is avoided. Accurate results from numerical simulations using the new algorithms are obtained, and there are no unstable oscillations that were observed in some other predictor/corrector schemes. The system energy balance is also better preserved compared with the old algorithms.     

A hybrid variational method for multibody dynamics

This paper presents a hybrid variational method to minimize computational effort in forming and solving the equations of motion for broad classes of rigid multibody mechanical systems. The hybrid method combines the O(n) and O(n³) recursive variational methods for forming the equations of motion in terms of joint relative co-ordinates. While the O(n³) method is more efficient than the O(n) method for systems with short chains and decoupled loops, the converse is true when the number of bodies in chains is large. The computational complexity of the O(n³) and O(n) methods in forming and solving the equations of motion is analysed as a function of the numbers of bodies, decoupled loops, joints, cut joints, cut-joint constraint equations and force elements. Based on complexity estimates, the method presented in this paper uses either the O(n) or O(n³) variational method to formulate the equations of motion for each open chain and decoupled loop in the system, to minimize the computational effort.     

Unsteady axisymmetric creeping flow from an orifice

Summary The slow unsteady motion of a viscous incompressible fluid which issues from a finite orifice into the half-space,x>0 is considered. By slow it is meant that the convective acceleration (i.e. nonlinear) terms in the Navier-Stokes equations are of negligible magnitude in comparison with terms attributable to viscosity. Only axisymmetric motions will be considered. The assumed nature of the motion along with the resultant linearization of the Navier-Stokes equations allows the construction of the Stokes stream function for the flow. Others have discussed this problem when the motion is steady. A general representation for the flow is given when the motion is unsteady and numerical results are presented for the resulting evolutionary motion of specific flows issuing from the orifice.     

Unification of Free Electron Laser Theories

The quantum mechanical equations of motion of the electron in a standing wave pattern are discussed in connection with the free electron laser. The reference frame where quantization is performed is the frame in which an electron with zero initial momentum does not cause, on the average, gain or loss of the laser field. The quantum features of the electron motion are retained, while quantum fluctuations of the fields are neglected. The validity of the fully classical approach is also discussed. In the pure momentum representation the density matrix is found to be characterized by a pair of integers, (μ, v). The classical, single particle motion is recovered if one considers the index μ as a continuous parameter, i.e. in the limit of little momentum transfer, ?k→0. If, in addition one retains only the terms with v=0, ±1, the classical equations of motion for the quasi Bloch vector, previously derived by the Arizona group, can be recovered.     

Early stimulated emission amplification by an inverted nuclear spin population and the H-maser

Two different topics are discussed: (1) early (1950) stimulated emission amplification observed with a pure LiF crystal having an inverted population of the nuclear spin system and (2) the atomic H-maser.     

Perfectly matched layers for transient elastodynamics of unbounded domains

One approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outward from the bounded domain. A perfectly matched layer (PML) is an unphysical absorbing layer model for linear wave equations that absorbs, almost perfectly, outgoing waves of all non‐tangential angles‐of‐incidence and of all non‐zero frequencies. In a recent work [Computer Methods in Applied Mechanics and Engineering 2003; 192: 1337–1375], the authors presented, inter alia, time‐harmonic governing equations of PMLs for anti‐plane and for plane‐strain motion of (visco‐) elastic media. This paper presents (a) corresponding time‐domain, displacement‐based governing equations of these PMLs and (b) displacement‐based finite element implementations of these equations, suitable for direct transient analysis. The finite element implementation of the anti‐plane PML is found to be symmetric, whereas that of the plane‐strain PML is not. Numerical results are presented for the anti‐plane motion of a semi‐infinite layer on a rigid base, and for the classical soil–structure interaction problems of a rigid strip‐footing on (i) a half‐plane, (ii) a layer on a half‐plane, and (iii) a layer on a rigid base. These results demonstrate the high accuracy achievable by PML models even with small bounded domains. Copyright © 2004 John Wiley & Sons, Ltd.     

Concerning the alternating-sign dissipation of energy in a fluid with relaxing viscous stresses

Total equations of motion of an incompressible fluid are investigated taking account of relaxation phenomena for viscous stresses and heat flux. In the K. I. Strakhovich class of solutions the fluid flows are considered that contain a strong hydrodynamic discontinuity. The conditions of motion are analyzed under which the dissipative function is negative. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 6, pp. 967–974, November–December, 1997.     

流动VLBI站氢原子钟的研制与性能测试

氢脉泽是至今为止除极短时间测量间隔之外最稳定的频率标准 ,它是射电天文所必需的频率标准。本文讨论了为流动VLBI站研制的新一代氢脉泽的物理结构特点 ,包括对腔泡结构、磁屏蔽、原子束光学系统等采用的新技术。性能测试表明 ,在 80s到 1d之间其频率稳定度优于 1× 10 - 1 4 ,有了较大的提高。     

Hybrid state‐space time integration in a rotating frame of reference

A time integration algorithm is developed for the equations of motion of a flexible body in a rotating frame of reference. The equations are formulated in a hybrid state‐space, formed by the local displacement components and the global velocity components. In the spatial discretization the local displacements and the global velocities are represented by the same shape functions. This leads to a simple generalization of the corresponding equations of motion in a stationary frame in which all inertial effects are represented via the classic global mass matrix. The formulation introduces two gyroscopic terms, while the centrifugal forces are represented implicitly via the hybrid state‐space format. An angular momentum and energy conserving algorithm is developed, in which the angular velocity of the frame is represented by its mean value. A consistent algorithmic damping scheme is identified by applying the conservative algorithm to a decaying response, which is rendered stationary by an increasing exponential factor that compensates the decay. The algorithmic damping is implemented by introducing forward weighting of the mean values appearing in the algorithm. Numerical examples illustrate the simplicity and accuracy of the algorithm. Copyright © 2011 John Wiley & Sons, Ltd.     

Contact forces in the non-linear dynamic analysis of tracked vehicles

It is known that when two springs are connected in series, the stiffness coefficient of an equivalent system that consists of one spring is less than the stiffness coefficients of the original springs. Experimental observations indicate that this fact can be very useful in determining the overall vibration characteristics of tracked vehicles. This simple fact is used in this investigation to develop a computer aided analysis procedure for the dynamic simulation of large-scale tracked vehicles. The track is considered as a closed kinematic chain that consists of rigid bodies connected by revolute joints. The contacts between the track links and the rollers, the sprocket, and the idler are represented by non-linear continuous force models. The stiffness and damping coefficients in these contact force models are determined by studying the viberation characteristics of the tracked vehicle. The tooth of the sprocket is defined using three surfaces. These are the left, the bottom, and the fight surfaces. Three successive transformations are used to define the contact kinematic relationships between the sprocket teeth and the pins of the track links. The equations of motions of the vehicle are formulated using the Lagrangian approach. Non-linear constraint equations that describe mechanical joints and specified motion trajectories in the system are adjoined to the differential equations of motion using the technique of Lagrange multipliers. The resulting mixed system of differential and algebraic equations is solved numerically using a direct numerical integration method. A Newton–Raphson algorithm is used to check on the violations in the kinematic constraints. The results presented in this paper are obtained using a 54 body planer tracked vehicle in which the track consists of 42 rigid links connected by revolute joints.     

Motion of N articulated rigid bodies with chain structure in the field of two mutually attracting massive centers: General formalism and a survey of the chain's planar motion

Summary In this paper we describe a new model consisting of N articulated rigid bodies with open chain structure, that move in the combined gravitational field of two mutually attracting massive centers. We derive the general equations of motion of the chain and we study the conditions for the planar motion of the individual centers of mass of the links.     

Ventricular segmentation and modeling using topological watershed transformation and harmonic state model

This paper proposes an adapted ventricular segmentation method based on topological watershed transform. Segmentation will allow spatio-temporal modeling of trajectories of the different points belonging to the borders of the ventricle using a harmonic motion model that is able to describe such motion over the entire cardiac cycle. In addition, extraction of the adopted canonical state vector and the corresponding state equations guarantees an optimal efficacy and a gradual transition from order n to order n + 1. To validate the proposed approach, an intern-image base was used. Our results show a promising ability to discern whether subjects are healthy or pathological with an 80% success rate.     

Roughness effect on squeeze film pressure

The Stokes equations for the axial symmetric slow motion generated by a plane, approaching towards a solid surface allowing slippage, have been solved in this paper by using finite Hankel transform. The squeeze film pressure between the two rigid faces is then obtained. It is found that the roughness parameter Β ∼ d/4, whered is the separation between the two surfaces, causes an extremely high pressure on the surface.     

Assessment of explicit and semi‐explicit classes of model‐based algorithms for direct integration in structural dynamics

The ‘model‐based’ algorithms available in the literature are primarily developed for the direct integration of the equations of motion for hybrid simulation in earthquake engineering, an experimental method where the system response is simulated by dividing it into a physical and an analytical domain. The term ‘model‐based’ indicates that the algorithmic parameters are functions of the complete model of the system to enable unconditional stability to be achieved within the framework of an explicit formulation. These two features make the model‐based algorithms also potential candidates for computations in structural dynamics. Based on the algorithmic difference equations, these algorithms can be classified as either explicit or semi‐explicit, where the former refers to the algorithms with explicit difference equations for both displacement and velocity, while the latter for displacement only. The algorithms pertaining to each class are reviewed, and a new family of second‐order unconditionally stable parametrically dissipative semi‐explicit algorithms is presented. Numerical characteristics of these two classes of algorithms are assessed under linear and nonlinear structural behavior. Representative numerical examples are presented to complement the analytical findings. The analysis and numerical examples demonstrate the advantages and limitations of these two classes of model‐based algorithms for applications in structural dynamics. Copyright © 2015 John Wiley & Sons, Ltd.     

The dynamics of avalanches of granular materials from initiation to runout. Part I: Analysis

Summary This paper describes a model to predict the flow of an initially stationary mass of cohesion-less granular material down rough curved beds. This work is of interest in connection with the motion of rock and ice avalanches and dense flow snow avalanches. The constitutive behaviour of the material making up the pile is assumed to be described by a Mohr-Coulomb criterion while the bed boundary condition is treated by a similar Coulomb-type basal friction law assumption. By depth averaging the incompressible conservation of mass and linear momentum equations that are written in terms of a curvilinear coordinate system aligned with the curved bed, we obtain evolution equations for the depthh and the depth averaged velocity. Three characteristic length scales are defined for use in the non-dimensionalization and scaling of the governing equations. These are a characteristic avalanche lengthL, a characteristic heightH, and a characteristic bed radius of curvatureR. Three independent parameters emerge in the non-dimensionalized equations of motion. One, which is the aspect ratio -H/L, is taken to be small. By choosing different orderings for the other two, the tangent of the bed friction angle and the characteristic non-dimensional curvature =L/R, we can obtain different sets of equations of motion which appropriately display the desired importance of bed friction and bed curvature effects. The equations, correct to order for moderate curvature, are discretized in the form of a Lagrangian-type finite difference representation which proved to be successful in the earlier studies of Savage and Hutter [24] for granular flow down rough plane surfaces. Laboratory experiments were performed with plastic particles flowing down a chute having a bed made up of a straight, inclined portion, a curved part and a horizontal portion. Numerical solutions are presented for conditions corresponding to the laboratory experiments. It is found that the predicted temporal-evolutions of the rear and front of the pile of granular material as well as the shape of the pile agree quite well with the laboratory experiments.     

Projection methods in flexible multibody dynamics. Part I: Kinematics

In this paper a recursive projection method for the dynamic analysis of open-loop mechanical systems that consist of a set of interconnected deformable bodies is presented. The configuration of each body in the system is identified using a coupled set of reference and elastic co-ordinates. The absolute velocities and accelerations of leaf or child bodies in the open-loop system are expressed in terms of the absolute velocities and accelerations of the parent bodies and the time derivatives of the relative co-ordinates of the joints between the bodies. The dynamic differential equations of motion are developed for each link using the generalized Newton-Euler equations. The relationship between the actual joint reactions and the generalized forces combined with the kinematic relationships and the generalized Newton-Euler equations are used to develop a system of loosely coupled equations which has a sparse matrix structure. Using matrix partitioning and recursive projection techniques based on optimal block factorization an efficient solution for the system accelerations and joint reaction forces is obtained. This solution technique yields a much smaller operations count and can more effectively exploit vectorization and parallel processing. It also allows a systematic procedure for decoupling the joint and elastic accelerations.     

A simple explicit–implicit finite element tearing and interconnecting transient analysis algorithm

A simple explicit–implicit finite element tearing and interconnecting (FETI) algorithm (AFETI‐EI algorithm) is presented for partitioned transient analysis of linear structural systems. The present algorithm employs two decompositions. First, the total system is partitioned via spatial or domain decomposition to obtain the governing equations of motions for each partitioned domain. Second, for each partitioned subsystem, the governing equations are modally decomposed into the rigid‐body and deformational equations. The resulting rigid‐body equations are integrated by an explicit integrator, for its stability is not affected by step‐size restriction on account of zero‐frequency contents (ω = 0). The modally decomposed partitioned deformation equations of motion are integrated by an unconditionally stable implicit integration algorithm. It is shown that the present AFETI‐EI algorithm exhibits unconditional stability and that the resulting interface problem possesses the same solution matrix profile as the basic FETI static problems. The present simple dynamic algorithm, as expected, falls short of the performance of the FETI‐DP but offers a similar performance of implicit two‐level FETI‐D algorithm with a much cheaper coarse solver; hence, its simplicity may offer relatively easy means for conducting parallel analysis of both static and dynamic problems by employing the same basic scalable FETI solver, especially for research‐mode numerical experiments. Copyright © 2011 John Wiley & Sons, Ltd.     

Effects of transpiration on free convection in an annulus between concentric porous spheres

An analysis is presented to study the effects of transpiration on free convection in an annulus between concentric porous spheres. A regular perturbation technique is applied to solve the steady-state Navier-Stokes equations of motion and the energy equation, whereby the stream-function and temperature are expanded in the form of power series in terms of the Rayleigh number Ra, and injection/suction Reynolds number Re. The analytical solution is valid for small values of Ra and Re, and all values of the Prandtl number Pr. A finite-difference solution of the governing steady-state equations of motion and energy is also provided. The range of validity of the analytical solution is determined by comparison with the numerical solution. Plots of the flow patterns, velocity distributions, temperature profiles, local and overall heat transfer rates are presented for Pr = 0.7 and different values of Re, Ra, and the radius ratio . Results are shown over a range of values of Ra and Re such that the effects of mixed convection in the annulus can be clearly observed.