One-dimensional statistical models

The properties of one-dimensional statistical systems are studied. A consistent comparison of the values of the binary correlation function obtained from the configuration integral and from Bogolyubov chain equations in various approximations is presented. The results obtained here are discussed briefly.The existing methods for studying the behavior of real statistical systems are usually based on perturbation theory, and the presence of small parameters characterizing the proximity of the system to an ideal system is assumed. Strongly interacting systems do not permit the isolation of small parameters; therefore, there are no effective methods for studying them at present. In this connection, it appears to be of interest to turn to one-dimensional systems which enable the investigation to be advanced much further and, in particular, permit a consideration of the case of strong interaction. Comparison of the exact results with approximate results obtained by methods for decomposing chains of recurrence equations for correlation functions [1] may be regarded as a qualitative criterion of the accuracy of the latter.Configuration integrals for one-dimensional statistical systems were first obtained in reference [2]. Papers have recently appeared in which one-dimensional models are studied by methods of the theory of stochastic processes [3–6].     

用实测数据估算直线振动机械的运动学参数的方法

本文给出了一个根据实测数据分析估算直线振动机械的运动学参数的方法。为提高估算的可信度，提出了选择测点、信号和“超定”方程等问题。为评定此类机械的动力特性提供重要的信息。     

多体系统动力学动态最优化设计与灵敏度分析

基于多体系统的动态最优化设计过程包括传统的多体系统仿真分析、系统设计灵敏度分析、 系统最优化设计等过程, 针对多体系统运动学、用二阶常微分方程和微分代数方程描述 的动力学,基于含设计参数的通用数学模型及通用的积分型目标函数,采用高效的系统灵 敏度分析伴随变量方法及易于实施的惩罚函数最优设计方法,建立了多体系统最优设计数学 模型和算法. 通过双摆系统、曲柄-滑块系统、弹簧/阻尼器-滑块系统3个算例对上述 算法的有效性进行了验证.     

Finite elasto-viscoplastic modeling of polymers including asymmetric effects

Asymmetric effects between compression and tension are a pronounced behavior for glassy polymers such as polycarbonate. For its simulation an elasto-viscoplastic framework is formulated within a geometrically nonlinear theory. Here a new approach within the concept of stress mode dependent weighting functions is used, where each material parameter is additively decomposed into a sum of weighted stress mode-related quantities. The characterization of the stress modes is obtained in the octahedral plane of the deviatoric stress space in terms of the mode angle, such that stress mode dependent scalar weighting functions can be constructed. The constitutive equations are formulated for large strains in terms of logarithmic Hencky strains and its work conjugated Hill stresses. The resulting evolution equations are updated using a semi-implicit Euler scheme, and the algorithmic tangent operator is derived for the finite element equilibrium iteration. The numerical implementation is also used to identify the material parameters thus resulting into a good agreement with experimental data. Furthermore, the model is used to simulate the cold drawing processes for a dumbbell-shaped specimen in tension and a perforated strip in compression and tension.     

Amplitude bounds of linear forced vibrations

Summary For reasons of safety and reliability, the maximum amplitudes of vibration responses must be taken into account in engineering. The exact maximum amplitudes are available from solving linear differential equations. However, for large scale systems, it requires too much computation time to be useful. Therefore, simple amplitude bounds are of great interest for engineers. Up to now, only for classically dampled linear systems, some approximate amplitude bounds were presented. In this paper, amplitude bounds of linear forced vibrations are presented for general dampled linear vibrating systems. For transient, harmonic and step excitations, the presented amplitude bounds show simple relations to the system parameters, and are easy to calculate. The advantage is the possibility to judge the level of vibrations, and to choose appropriate parameters at design. Compared with the approximate underestimating amplitude bounds available in literature, the presented amplitude bounds are overestimating the maximum amplitude and, therefore, can be safely applied to general damped vibrating systems.The paper is dedicated to Prof. Dr.-Ing. Dr.-Ing. E.h. Dr.h.c. mult, Erwin Stein, on the occasion of his 65th birthday.     

Steady laminar flow over a downstream-facing step as a critical test case for the upwind Petrov-Galerkin finite element method

Galerkin finite element methods based on symmetric weighting functions give oscillations in the solution of steady Navier-Stokes equations when the Reynolds number is large. To overcome this difficulty Galerkin methods with asymmetric weighting functions can be used. In the present paper a critical test case is calculated with this so-called Petrov-Galerkin method. Comparison between calculations and experiments proofs that the accuracy of the method is good, even for a Reynolds number based on mesh size as high as two hundred.     

Linear Mathematical Models for the Aerodynamics of Three-Dimensional Lifting Systems in an Unsteady Subsonic Gas Flow

A complex of linear mathematical models for the processes associated with unsteady compressible subsonic flow past three-dimensional lifting systems is developed. The models make it possible to determine the aerodynamic transfer functions over their entire range of definition with respect to Mach, Strouhal, and decrement numbers. The corresponding boundary value problems for the Laplace and Helmholtz equations are formulated and a technique of reducing them to systems of singular integral equations is developed. The questions of the construction and mathematical validation of numerical methods of solution of these systems are discussed. The technique developed is an outgrowth of the discrete vortex method, as applied to the class of the problems under consideration. Examples of calculations are presented.     

ARC-length method for differential equations

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An iterative parallel algorithm of finite element method

In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in this method. Also by using the weighted residual method and choosing the appropriate weighting functions, the finite element basic form of parallel algorithm is deduced. The program of this algorithm has been realized on the ELXSI-6400 parallel computer of Xi'an Jiaotong University. The computational results show the operational speed will be raised and the CPU time will be cut down effectively. So this method is one kind of effective parallel algorithm for solving the finite element equations of large-scale structures.     

Synchronization of three homodromy coupled exciters in a non-resonant vibrating system of plane motion

In this paper, the synchronization problem of three homodromy coupled exciters in a non-resonant vibrating system of plane motion is studied. By introducing the average method of modified small parameters, we deduced dimensionless coupling equation of three exciters, which converted the problem of synchronization into that of the existence and stability of zero solutions for the average differential equations of the small parameters. Based on the dimensionless coupling torques and characteristics of the corresponding limited functions, the synchronization criterion for three exciters was derived as the absolute value of dimensionless residual torque difference between arbitrary two motors being less than the maximum of their dimensionless coupling torques. The stability criterion of its synchronous state lies in the double-condition that the inertia coupling matrix is positive definite and all its elements are positive as well. The synchronization determinants are the coefficients of synchronization ability, also called as the general dynamical symmetry coefficients. The double-equilibrium state of the vibrating system is manifested by numeric method, and the numeric and simulation results derived thereof indicate the indispensable and crucial role the structural parameters of the vibrating system play in the stability criterion of synchronous operation. Besides, by adjusting its structural parameters, the elliptical motion of the vibrating system successfully met the requirements in engineering applications.     

Stiffness and Damping Identification from Full Field Measurements on Vibrating Plates

The paper presents an experimental application of a method leading to the identification of the elastic and damping material properties of isotropic vibrating plates. The theory assumes that the searched parameters can be extracted from curvature and deflection fields measured on the whole surface of the plate at two particular instants of the vibrating motion. The experimental application consists in an original excitation fixture, a particular adaptation of an optical full-field measurement technique, a data preprocessing giving the curvature and deflection fields and finally in the identification process using the Virtual Fields Method (VFM). The principle of the deflectometry technique used for the measurements is presented. First results of identification on an acrylic plate are presented and compared to reference values. Results are discussed and improvements of the method are proposed.     

Construction of Basis Functions and Their Application to Boundary-Value Problems of Mechanics of Continuous Media

A unified method for constructing basis (eigen) functions is proposed to solve problems of mechanics of continuous media, problems of cubature and quadrature, and problems of approximation of hypersurfaces. Numerical-analytical methods are described, which allow obtaining approximate solutions of internal and external boundary-value problems of mechanics of continuous media of a certain class (both linear and nonlinear). The method is based on decomposition of the sought solutions of the considered partial differential equations into series in basis functions. An algorithm is presented for linearization of partial differential equations and reduction of nonlinear boundary-value problems, which are reduced to systems of linear algebraic equations with respect to unknown coefficients without using traditional methods of linearization.     

Unilateral Multibody Dynamics

Contact processes may be represented by local discretization, by a rigid body approach or by a mixed method using both ideas. For the dynamics of mechanical systems a rigid body approach is described achieving good results also for multiple contact problems. This paper considers mainly contacts in multi-body systems where the corresponding contact constraints vary with time thus generating structure-variant systems. The equations of motion for dynamical systems with such an unilateral behavior are discussed, solution methods and applications are presented.     

ELECTROMECHANICAL COUPLING MODEL AND ANALYSIS OF TRANSIENT BEHAVIOR FOR INERTIAL RECIPROCATION MACHINES

Introduction Inertialvibratingmachinesexcitedbytworotatingeccentricweightsarewidelyusedto siftmaterialsinindustriessuchasmine,metallurgy,chemicalindustry,foodstuff,etc.The eccentricweightisgenerallydrivenbyanasynchronouselectromotor,anditssteady state ope…     

Separation of principal stresses by SOR technique over arbitrary boundaries

A computerized method is presented that generates a grid mesh within the digitized boundary of a photoelastic specimen as it appears in the single viewing through an overhead polariscope. The second-order partial differential equation for the first linear invariant of stress which satisfies the Laplace equation is solved from the boundary values for the digitized domain by the finite-difference method. Connectivity and the weighting functions that are required for the iterative solution of the systems of linear equations are generated from the digitized information along the boundary. Isochromatic values at each nodal point within the boundary are estimated from the digitized fringe patterns by a scanning technique, and the individual values of principal stresses are determined. To enhance convergence, the method of successive over relaxation is applied with an optimum accelerating factor determined in the course of the solution process. The accuracy and the speed of the solution are tested with three different examples. Paper was presented at the 1989 SEM Spring Conference on Experimental Mechanics held in Cambridge, MA on May 28–June 1.     

The Method of Abel-Type Integral Equations for Identification of Nonlinear Systems of Structural Seismodynamics

The problem on determination of the nonlinear dissipative and elastic characteristics of some vibrating systems that are encountered in structural seismodynamics is considered. Systems of integral Volterra equations of the first kind (Abel-type equations) are constructed on the basis of approximate analytical solutions to problems on the forced vibration of quasilinear vibrating systems. Such equations relate the nonlinear stiffness and dissipation characteristics with the characteristics of motion, which can be obtained experimentally. The solutions of the integral equations derived are represented in the form of quadrature Stieltjes-integral formulas     

Dynamical behaviors of nonlinear viscoelastic thick plates with damage

Based on the deformation hypothesis of Timoshenko's plates and the Boltzmann's superposition principles for linear viscoelastic materials, the nonlinear equations governing the dynamical behavior of Timoshenko's viscoelastic thick plates with damage are presented. The Galerkin method is applied to simplify the set of equations. The numerical methods in nonlinear dynamics are used to solve the simplified systems. It could be seen that there are plenty of dynamical properties for dynamical systems formed by this kind of viscoelastic thick plate with damage under a transverse harmonic load. The influences of load, geometry and material parameters on the dynamical behavior of the nonlinear system are investigated in detail. At the same time, the effect of damage on the dynamical behavior of plate is also discussed.     

An identification method of generalized modal parameters of linear vibrating defective systems

Based on the generalized mode theory of linear vibrating defective systems, an identification method of generalized modal parameters is presented in this paper. By the use of this method, which combines the direct method with the iteration method in frequency domain, all the generalized modal parameters can be identified without any initial value. It is shown that the present method is effective and useful.     

A numerical treatment of the periodic solutions of non-linear vibration systems

Direct numerical integration can be used to find the periodicsolutions for the equations of motion of nonlinear vibrationsystems.The initial conditions are iterated so that theycoincide With the terminal conditions.The time interval ofthe integration(i.e.,the period)and certain parameters ofthe equations of motion can be included in the iterations.Theintegration method has a variable stoplength.This Sbooting method can produce periodic solutions witha shorter computex time.The only error occurs in the numeri-cal integration and it can therefore be estimated and madesmall enough.Using this method one can treat a variety ofvibration problems.such as free conservative.forced.para-meter-excited and self-sustained vibrations with one or se-veral degrees-of-freedom.Unstable solutions and those Whichare sensitive to parameter Changes can also be calculated.Thestability of the solutions is investigated based on the thecryof differential equations with periodic coefficients.The ex-trapolation method and the proc     

Unilateral problems of dynamics

Summary Contact processes may be described by local discretizations, by rigid representation or by mixed methods incorporating both ideas. A rigid body approach is proposed for the dynamics of mechanical systems, achieving good results also for multiple-contact problems. Contacts in multibody systems are mainly considered, with the corresponding contact constraints varying with time, thus generating structure-variant systems. The equations of motion for dynamical systems with such unilateral behavior are discussed, solution methods and applications are presented. Received 3 March 1999; accepted for publication 5 May 1999