方法论在理论力学课程教学中的应用

针对理论力学课程内容多,学生不易掌握的特点,将科学方法论中的一些方法引入到理论力 学课程教学之中. 经过对几届学生的教学实践表明：学生们不仅能够掌握该课程的内容,而 且又学到了科学方法. 掌握了方法论的方法,这对学生今后学习新知识、新技能和培养学生 独立思考解决问题以及创新能力很有益处.     

论城市环境岩土工程研究

城市环境岩士工程问题是当前岩土工程和工程地质界研究的热点。本文认为,大城市不稳定性、环境水利与环境污染是其三个主要问题,并做了分析论证。根据系统科学思维原则,文中对人们感兴趣的研究方法论问题,提出了五点基本认识。     

方法论在材料力学课程教学中的应用

将科学方法论中的一些方法引入到材料力学课程教学之中. 经过对几届学生的教学实践表明： 学生们不仅能够掌握该课程的内容,而且还能学到科学方法. 掌握了方法论的方法,这对学 生今后学习新知识、新技能和培养学生独立思考解决问题以及创新能力很有益处.     

作大范围运动弹性梁的动力刚化分析

刚体大范围运动与弹性梁的变形运动的相互耦合将产生动力刚化现象，在经典的动力学理论中无法解释这种现象。本文给出了该系统的运动描述方法，利用Ｈａｍｉｌｔｏｎ变分原理建立了动力学控制方程，利用Ｇａｒｌｅｒｋｉｎ模态截断研究了产生动力刚化的原因及其动力学性质，从本质上解释了学者们多年来一直在研究的动力硬化现象，最后用数值模拟验证了理论的正确性。本文所得结论有益于柔性多体系统动力学的发展。     

谈谈实验与观察

<正>实验和观察是科学方法的一个重要的方面。从17世纪开始的近代科学革命,就是基于系统的实验和观察。为了比较深入一点地了解实验和观察,以及它们在科学方法中的地位,我们需要把话说得长一点,先从什么是科学和什么是科学方法谈起。通俗说来,科学方法包含摆事实、讲道理两个方面。所谓摆事实,就是我们这里要讲的实验与观察;而讲道理就是严格的逻辑推理,包括演绎推理和归纳推理,还包括数学计算和论证。用科学方法去探索客观规律的活动,以及所得到的规律本身,     

板弯曲求解新体系及其应用

建立平面弹性与板弯曲的相似性理论,给出了板弯曲经典理论的另一套基本方程与求解方法,然后进入哈密顿体系用直接法研究板弯曲问题．新方法论应用分离变量、本征函数展开方法给出了条形板问题的分析解,突破了传统半逆解法的限制．结果表明新方法论有广阔的应用前景．     

数学模拟和计算实验

物理学中的理论研究总是建立在数学的基础上,建立在所研究现象的主要数量特性的计算上。同时,采用的数学工具的复杂程度,通常由所研究物理对象的复杂程度以及获得研究结果时所要求的精确度来决定。而精确度又取决于研究的应用特性,取决于研究的实践目的。随着科学的发展,对理论物理研究的精确度的要求不断地增长,这是因为在设计和建造现      

摩擦磨损试验机设计的基础 Ⅱ.摩擦磨损试验机设计方法的研究

本讲介绍采用设计方法学的方法对摩擦磨损试验机设计进行研究的结果,建立了摩擦磨损试验机的要求明细表,功能结构图、设计模幅箱和方案评价目标树。根据本讲所阐述的方法,既可使摩擦磨损试验机的设计程序和方案评价建立在一套比较科学的和行之有效的方法上,又能作为建立摩擦磨损试验机CAD(计算机辅助设计)系统的基础。     

时间尺度上Herglotz变分原理及其Noether定理

Herglotz变分原理的作用量是由微分方程定义的,不仅可以描述所有经典变分原理能够描述的动力学过程,还可以对经典变分原理不能适用的非保守系统或耗散系统进行变分描述．时间尺度上微积分理论提供了一种可同时研究离散系统和连续系统的有效方法．本文结合Herglotz变分原理和时间尺度微积分理论来研究时间尺度上的Herglotz变分原理及其Noether定理．首先,给出时间尺度上Lagrange系统的Herglotz变分原理．其次,根据Herglotz变分原理和Dubois-Reymond引理,推导出时间尺度上Lagrange系统的Herglotz变分问题的运动微分方程．再次,基于时间尺度上Hamilton-Herglotz作用量在群的无限小变换下的不变性,给出Noether对称性的定义并导出其Noether等式．最后,建立了时间尺度上Lagrange系统的Herglotz变分问题的Noether定理,给出了连续和离散两种情况下基于Herglotz变分问题的Noether守恒量．文末举例说明结果的应用．     

一类双边碰撞振动系统的随机响应研究

碰撞过程凭借瞬时冲击模型得以简化,但采用经典的Newton恢复系数模型为计算带来了误差。本研究引入修正的恢复系数模型取代经典的Newton恢复系数模型,预测了一类宽带噪声激励下双边碰撞振动系统的随机动力学响应。位移的碰撞条件借助自由振动系统被转化为能量的碰撞条件。根据系统的能量水平,系统的运动可被分为双边碰撞和无碰撞振动两类。进一步地,两类运动的平均漂移系数和扩散系数可借助能量包线随机平均法求解获得。在此基础上,建立并求解对应的Fokker-Plank-Kolmogorov (FPK)方程,进而得到系统的稳态响应。最后,将所提方法应用于Duffing振子,讨论了屈服速度、挡板间距和噪声激励对响应的影响,并用蒙特卡罗模拟验证了所述方法的有效性。     

Bridging reductionism and holism — multi-scale methodology with applications to particle-fluid systems

While science continues to extend to two extremes — micro-scale towards dimensions even smaller than elemental particles and mega-scale even beyond the universe, one recognizes that reductionism is not sufficient to solve many problems we encounter in engineering, which are likely characterized by nonlinearity, nonequilibrium and dissipative multi-scale structures. On the other hand, the common features of these nonlinear systems, such as bifurcation, state multiplicity and self-organization, have attracted much attention, leading to the approaches of the so-called complexity science which has become a focus not only in natural science and engineering science, but also in social science.However, no effective methodology has been established to understand these complex systems, though noticeable progress has been achieved in studying these systems, such as particle-fluid multi-phase systems. Multi-scale methodology has been considered as a promising methodology to tackle complex systems due to its capability in correlating phenomena at different scales. In this presentation, we shall review the development of the multi-scale methodology and its applications to particle-fluid systems, elucidating the essential relevance of complex systems and the challenging problems in chemical engineering.Multi-scale structure is considered to be the focus in studying complex systems, particularly, correlation between phenomena at different scales, compromise between different dominant mechanisms, coupling between spatial and temporal structural changes and critical phenomena occurring in these systems — these are the four critical issues in understanding complex systems. We first propose that by analyzing particle-fluid systems complex systems can be formulated as a multi-objective variational problem. Such an analytical multi-scale method will be reviewed in particular by analyzing the above four critical issues and by showing its 20-year development at IPE from a rough idea to modeling approaches, softwares and finally to industrial applications as well as its extension to different chemical and physical systems. The strategy of “from the particular to the general” in developing this multi-scale methodology is emphasized and challenges to mathematicians and physicists are identified to show the necessity of transdisciplinary cooperation. This presentation will be concluded by prospects and suggestions.     

Promising Future, yet More Efforts Needed

The Research Collaboration Group on multi-scale methodology and complex systems was financed by the Chinese Academy of Sciences in recognition of the challenge of multi-scale spatio-temporal structure in the 21st-century chemical engineering science with the hope of possible breakthrough and new opportunities through better understanding and correlation of phenomena occurring at different scales.     

INVESTIGATION AND APPLICATIONS OF PANSYSTEMS RECOGNITION THEORY AND PANSYSTEMS-OPERATIONS RESEARCH OF LARGE-SCALE SYSTEMS(Ⅰ)

In this work, a sort of recognition theory and operations research of large scale systems are developed within the framework of pansystems methodology. We establish a series of theorems concerning pansystems relations, which discuss some fundamental problems of interdisciplines from the viewpoint of generalized system-transformation-symmetry in things mechanism, and are connected closely with mathematical physics systems thinking science bioecological sciences and the methodological investigation of mechanical foundation. This paper offers 100 pansystems theorems.     

NANOSCALE PROCESS ENGINEERING

The research of nanoscale process engineering (NPE) is based on the interdisciplinary nature of nanoscale science and technology. It mainly deals with transformation of materials and energy into nanostructured materials and nanodevices, and synergizes the multidisciplinary convergence between materials science and technology, biotechnology, and information technology. The core technologies of NPE concern all aspects of nanodevice construction and operation, such as manufacture of nanomaterials “by design“, concepts and design of nanoarchitectures, and manufacture and control of customizable nanodevices. Two main targets of NPE at present are focused on nanoscale manufacture and concept design of nanodevices. The research progress of nanoscale manufacturing processes focused on creating nanostructures and assembling them into nanosystems and larger scale architectures has built the interdiscipline of NPE. The concepts and design of smart, multi-functional, environmentally compatible and customizable nanodevice prototypes built from the nanostructured systems of nanocrystalline, nanoporous and microemulsion systems are most challenging tasks of NPE. The development of NPE may also impel us to consider the curriculum and educational reform of chemical engineering in universities.     

多尺度科学面向21世纪的挑战

多尺度科学是一门研究各种不同长度尺度或时间尺度相互耦合现象的科学．多尺度科学的研究领域十分宽广，涵盖的学科之多难以一一罗列．对于诸如流体动力学、材料科学、生物学、环境科学、化学、地质学、气象学和高能物理之类的各门科学，多尺度科学是它们的核心．多尺度科学目前在国际上处于刚刚起步的阶段．正如非线性现象和随机现象被认为是属于交叉学科并得到广泛重视一样，多尺度科学因其处于当代科学的许多极富挑战性问题的核心地位，发展前途未可限量．因此，在我国有必要抓住机遇，大力开展多尺度科学及其方法的研究．     

Hagedorn's theorem in some special cases of rheonomic systems

Hagedorn's theorem on instability [Arch. Rational Mech. Anal. 58 (1976) 1], deduced from Jacobi's form of Hamilton's principle, refers to scleronomic mechanical systems. In this paper we shall prove that Hagedorn's methodology can be generalized to a class of rheonomic mechanical systems with differential equations of motion which allow the existence of Painlevé's integral of energy. The application of this methodology to the case of rheonomic systems which allow, together with Painlevé's integral, cyclic integrals, as well as to the mechanical systems having resultant motion, with prescribed transport motion, and, finally, to the systems having Mayer's rheonomic potential, are also considered. Obtained results are illustrated by an example.     

充液系统动力学与航天高技术问题

充液航天器内部液体晃动及其对控制系统的影响,是当前国内外航天高技术研究的重要课题,也是一个比较复杂的问题。本文首先由力学变分原理导出了充液系统的状态方程,其次分析了充液系统的稳定性;特别是,研究了在失重或微重条件下,充液航天器内部液体晃动的动力学特性以及部分充液三轴稳定性问题等。本文的研究结果,对于航天、航空、航海中的充液系统动力学与控制问题,都有重要的参考价值。      

工业化住宅系统建模和控制的初步分析

探索用系统科学原理和方法分析工业化住宅的形成过程，讨论了工业化住宅系统的结构模型，邻接矩阵，数学模型及知识模型，构建了工业化住宅系统的集成模型，提出了工业化住宅系统优化设计原则和目标函数，分析了工业化住宅形成过程的多级递阶协调控制结构．为住宅工业化提供相关的理论指导．     

践行工程科学思想的体会

郑哲敏先生一生积极践行和倡导钱学森先生的工程科学思想, 传承和发扬工程科学思想对推动我国技术创新有十分重要的现实意义. 本文首先阐述了工程科学的定义、方法论和特点, 强调了提出新的解决方案是工程科学的核心内容以及工程科学家对技术创新的作用. 其次通过分析水下爆炸处理地基、三峡围堰相关技术等工程案例, 诠释了工程科学在技术创新中的作用; 讨论了工程计算与数值模拟的理论基础及工程科学属性, 选取广义计算变量、构建解的结构是数值模拟中创造性的工作; 连续非连续计算方法的核心在于构建了计算过程中时域内可增减的广义计算变量, 列举了几个体现工程科学方法论的计算案例; 介绍了滑坡灾害防治关键力学问题研究中践行工程科学思想的工作, 讨论了监测与数值模拟相结合的可行性及渐进破坏和破裂度概念. 最后基于开发高压卸荷矿石粉化技术的认知提出了岩石物理学发展的几个工程科学研究方向.