RELATIVISTIC VARIATION PRINCIPLES AND EQUATION OF MOTION FOR VARIABLE MASS CONTROLLABLE MECHANICAL SYSTEM

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Space time on the Poincare diagrams

Relations between the experience of space technology and theory of space and time arefound in this paper.A nontraditional approach to the concepts of space and time isintroduced.The approach is based upon the the analysis of the detailed mechanism of radarmeasurement and nonlinear Doppler effects as measured by an astronaut.The Lorentzfactor and four-dimensional interval t~2-x~2/c~2 may be interpreted fromthe point of view of a space technologist.A“geometrical mean”notion for computing timeinterval is introduced parallelly with the usual arithmetic mean formulas,giving resultscomparable with those of special relativity theory.Space time relationships aredemonstrated on the Poincare diagrams.     

Convection and heat/mass transfer processes under space flight conditions

A simulation of 3D convective flows and heat/mass transfer processes under space flight conditions on the basis of hydrodynamic models and a numerical analysis of these models is discussed. The significance of the methods of mechanics in microgravity sciences and the role of the journal “Fluid Dynamics” in the development of this branch of science is examined. The results of recent investigations of certain problems are presented.     

Numerical analysis of added mass and damping of floating production, storage and offloading system

An integral equation approach is utilized to investigate the added mass and damping of floating production,storage and offloading system(FPSO system).Finite water depth Green function and higher-order boundary element method are used to solve integral equation.Numerical results about added mass and damping are presented for odd and even mode motions of FPSO.The results show robust convergence in high frequency range and can be used in wave load analysis for FPSO designing and operation.     

在应力空间描述岩体损伤本构关系的一种模型

在分析岩体经观和宏观损伤特征及其与岩体非弹性变形之间关系的基础上,运用损伤面来定义生－－损伤准则,建立了在应力空间描述岩体损伤本构关系一种模型,并对该模型在工程中的应用进行了讨论。     

相对论性定轴转动变质量系统的广义Noether定理

研究相对论性定轴转动变质量系统的广义Noether定理,首先给出相对论性定轴转动变质量非完整系统的运动方程的Routh形式;其次利用Hamilton作用量在无限小变换下的不变性,研究了相对论性定轴转动变质量非完整系统的广义Noether定理和相对论性定轴转动变质量非完整系统的广义Noether逆定理;结论具有普遍意义,对于经典情形和相对论情形都适用,若m_(oi)为常量,结果化为相对论性定轴转动常质量的Noether定理;若θ《Г_i,ω_i《Г_i结果化为经典定轴转动变质量系统的初Noether定理;若m_(oi)为常量,且θ_i《Г_i,ω_i《Г_i,则结果化为经典定轴转动常质量系统的Noether定理。     

Conservation of mass for a particle moving with high velocity

I.IntroductionItiswell-knownthatthe"lassofaparticleoranoh.jectisstrictlytoobservethelawofcollservatiollof1llasswbedmovewitlllowvelocity.Butathighvelocity,particularlynearthevelocityoflight,themass(restmass)oftheparticle,accordingtothetheoryofspecialrelativity,increasesrapidlywithitsincrementofthevelocity.Inotherwords,themassisnotinconservatioll\vitllitsvelocity.However.withtheoriesandresearchmethodsbringingforthflewideasandcomplement,andthehumanthoughtdevelopingconstantlywhatthemassisnotconse…     

岩体施工过程损伤演化预测的时变力学分析

由建立的岩体损伤本构模型，依据时变力学理论对岩体进行不同施工路径下的分步开挖计算，并对施工过程中各点损伤演化历程进行计算机仿真模拟，以预测后续开挖的损伤状态及寻求较优施工步序。理论及算例分析均表明：存在损伤演化时，不同施工步序下岩体终应力位移和损伤状态均不同，设计与施工应进行损伤演化的时变力学分析，以保证施工安全。     

The conservation law and the radiation of general relativity

ＴＨＥＣＯＮＳＥＲＶＡＴＩＯＮＬＡＷＡＮＤＴＨＥＲＡＤＩＡＴＩＯＮＯＦＧＥＮＥＲＡＬＲＥＬＡＴＩＶＩＴＹＬａｍＹｕ－ｙｉｕ（林汝耀）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ）ＨｏｎｇＫｏｎｇＰｏｌｙｔｅｃｈｎｉｃ．ＨｏｎｇＫｏｎ...     

An improved algorithm for calculating relaxation time spectra from material functions of polymers with monodisperse and bimodal molar mass distributions

Using the basic concept of Emri and Tschoegl, the algorithm for calculating relaxation time spectra has been improved such that excellent results are provided in the difficult case of polymers with narrow molar mass distributions. These spectra can be compared with those calculated by nonlinear regularization (Weese 1992), which we regard as a very exact method, and show equally good results with even less mathematical effort. Examples of dense relaxation time spectra (up to eight points per decade) are given for nearly monodisperse polystyrene melts and for mixtures of these up to four components. The relaxation time spectra describe the dynamic mechanical experimental data in each case with an overall error of less than 3%. The filtering method used to avoid physically senseless oscillations has been proven to resolve the characteristic peaks contributed by monodisperse polymers accurately.     

Gurtin变分原理在矩形板动力初值问题中的应用

结构动力分析是工程设计中的重要组成部分,传统动力分析方法并不能全面反映动力初值特征,而Ｇｕｒｔｉｎ变分原理则被认为是目前唯一能全面反映动力初值特征的变分原理。本文基于位移型Ｇｕｒｔｉｎ变分原理,对空间和时间同时离散,建立了一种求解板的动力初值问题的时空有限元法,并对两种边界情况板的振动问题进行了编程计算,计算结果表明时空元法精确度很高且稳定收敛。     

FIRST INTEGRALS AND INTEGRAL INVARIANTS FOR VARIABLE MASS NONHOLONOMIC SYSTEM IN NONINERTIAL REFERENCE FRAMES

ＦＩＲＳＴＩＮＴＥＧＲＡＬＳＡＮＤＩＮＴＥＧＲＡＬＩＮＶＡＲＩＡＮＴＳＦＯＲＶＡＲＩＡＢＬＥＭＡＳＳＮＯＮＨＯＬＯＮＯＭＩＣＳＹＳＴＥＭＩＮＮＯＮＩＮＥＲＴＩＡＬＲＥＦＥＲＥＮＣＥＦＲＡＭＥＳＬｕｏＳｈａｏ－ｋａｉ（罗绍凯）（Ｓｈａｎｇｑｉｕ,Ｎｏｒ...     

结构主动开闭环多重调谐质量阻尼器（AMTMD）新控制策略

提出了一种新控制策略——主动开闭环多重调谐质量阻尼器(AMTMD)。AMTMD控制系统频率呈线性分布。AMTMD中的MTMD保持相同的刚度和阻尼系数但质量变化。基于TMD的工作原理定义了AMTMD的主动控制力构成即保持相同的位移和速度反馈增益系数但变化结构和地震加速度反馈增益系数。基于结构的广义振型模型，导出了设置AMTMD时结构的动力放大系数(DMF)，于是优化准则可定义为：Min．Min．Max．DMF．通过最优搜寻，研究了反映AMTMD有效性和鲁棒性的参数。这些参数包括：频率间隔、平均阻尼比、调谐频率比、总数、质量比和标准化加速度反馈增益系数。为了比较，多重调谐质量阻尼器(MTMD)和主动开闭环调谐质量阻尼器(ATMD)也被考虑。     

Dynamic properties of a body with discontinual mass variation

In this paper the procedure for the dynamic analysis of body separation is introduced. Based on the general laws of classical dynamics, the method for obtaining the velocity and the angular velocity of the remainder body during separation is developed. Due to the discontinual mass variation, the jump-like change of the velocity and the angular velocity of the body is evident. Various types of motion of the separated body are considered. Depending on the type of motion of the separated body the dynamic properties of the remainder body are obtained. As a special case the in-plane motion of the body before and after separation is considered. The theoretical considerations are applied for the separation analysis of a rotor (a shaft-disc system). The transient motion of the body after separation is investigated. To prove the correctness of the procedure suggested in the paper, the case when the mass and the moment of inertia of the separated body are infinitesimal is analyzed. The obtained differential equations are the same as those previously obtained.     

位移时空综合分析法及其在深基坑中的应用

对于岩土工程设计和施工来说,如何对监测所获的位移信息进行分析十分重要。以往主要采用位移-时间的分析方法。但为了使信息在修改设计和指导施工方面起更大作用,本文提出位移空间比较分析法,并主张与常用的位移-时间分析方法结合使用,以形成所谓位移时空综合分析法。在济南彩云大厦深基坑等的成功应用,表明该法是可行的。     

Particle flow study on strength and meso-mechanism of Brazilian splitting test for jointed rock mass

A discrete element method （DEM） called particle flow code （PFC2D） was used to construct a model for Brazilian disc splitting test in the present study. Based on the experimental results of intact Brazilian disc of rock-like material, a set of micro-parameters in PFC2D that reflected the macro-mechanical behavior of rock-like materials were obtained. And then PFC2D was used to simulate Brazilian splitting test for jointed rock mass specimens and specimen containing a central straight notch. The effect of joint angle and notch angle on the tensile strength and failure mode of jointed rock specimens was detailed analyzed. In order to reveal the meso-mechanical mechanism of crack coalescence, displacement trend lines were applied to analyze the displacement evolution during the crack initiation and propagation. The investigated conclusions can be described as follows. （1） The tensile strength of jointed rock mass disc specimen is dependent to the joint angle. As the joint angle increases, the tensile strength of jointed rock specimen takes on a nonlinear variance. （2） The tensile strength of jointed rock mass disc specimen containing a central straight notch distributes as a function of both joint angle and notch angle. （3） Three major failure modes, i.e., pure tensile failure, shear failure and mixed tension and shear failure mode are observed in jointed rock mass disc specimens under Brazilian test. （4） The notch angle roles on crack initiation and and joint angle play important propagation characteristics of jointed rock mass disc specimen containing a central straight notch under Brazilian test.     

埃尔米特梁单元的分块对角与高阶质量矩阵

埃尔米特梁单元常用的集中质量矩阵,是由挠度自由度对应的一致质量矩阵元素通过行求和或节点积分构造。然而,数值结果表明该集中质量矩阵在求解包含自由端的梁振动问题时,会出现频率精度掉阶现象。本文首先从保障质量矩阵最优收敛性的数值积分精度出发,分别针对三次和五次梁单元,发展了质量矩阵的梯度增强节点积分方案。利用梯度增强节点积分方案,可以得到具有分块对角形式的单元质量矩阵,而其组装的整体质量矩阵除边界节点外仍然呈现对角形式。对于两种单元,其分块对角质量矩阵分别具有4阶最优精度和6阶次优精度。再者,将标准一致质量矩阵和具有同阶精度的梯度增强节点积分质量矩阵进行优化组合,建立了具有超收敛特性的高阶质量矩阵。最后,通过数值算例系统验证了三次和五次单元的分块对角与高阶质量矩阵的频率计算精度。     

Evolution of governing mass and momentum balances following an abrupt pressure impact in a porous medium

A mathematical model is developed of an abrupt pressure impact applied to a compressible fluid flowing through a porous medium domain. Nondimensional forms of the macroscopic fluid mass and momentum balance equations yield two new scalar numbers relating storage change to pressure rise. A sequence of four reduced forms of mass and momentum balance equations are shown to be associated with a sequence of four time periods following the onset of a pressure change. At the very first time period, pressure is proven to be distributed uniformly within the affected domain. During the second time interval, the momentum balance equation conforms to a wave form. The behavior during the third time period is governed by the averaged Navier-Stokes equation. After a long time, the fourth period is dominated by a momentum balance similar to Brinkman's equation which may convert to Darcy's equation when friction at the solid-fluid interface dominates.     

The added mass coefficient of a dispersion of spherical gas bubbles in liquid

Models published in the two-phase flow literature for the added mass coefficient of a dilute bubbly dispersion are discussed and compared. It is shown that the differences between the models are mainly due to the different ways in which the added mass is defined. Also, approximate expressions for the added mass coefficient of non-dilute bubbly dispersions are given. Finally, the use of the models in an equation for the average motion of the bubbles is briefly discussed.     

An example of nonlinear toxic mass spreading

A one-dimensional, nonlinear problem of reproductive toxic mass spreading is studied in this paper. The nonlinearity is due to the difference of the reproduction rates in the toxic region and the nontoxic region. Multiple steady state solutions are found and their stability and instability are proved. Due to the instability, there may exist turning points (also called saddle-node bifurcation points), at which an infinitesimal perturbation of some parameters may cause a catastrophic change in the location of the steady state toxic front (the interface of the toxic region and the nontoxic region). For the time dependent case, the propagation of the toxic front is considered. An integral equation is derived to determine the propagation of the toxic front. Some numerical results are found for a specific example.