《微分方程的分析力学方法》内容简介

《微分方程的分析力学方法》,梅风翔,吴惠彬著,本书全面系统地论述常微分方程的分析力学方法,包括常微分方程的力学化、降阶法、Hamilton-Jacobi方法、Poisson方法、Noether方法、Hojman方法、场方法、势积分方法、共形不变性、Jacobi最终乘子、Lagrange方法与Birkhoff方法、力学化与稳定性等．     

一种计算三维附面层的新方法

方法概貌机翼的三维附面层计算在美国已经有了三种主要方法,它们在计算公式、坐标系、有限差分格式以及湍流模型上相互区别。这三种方法是纳希(Nash)方法,塞比西(Cebeci)方法和麦克林(McLean)方法。但这些方法都有一定缺点,至今不能提供设计飞机所满意的计算精度。本文推荐的新计算方法吸收了上述三种方法以及在附面层计算中其他隐式差分方法的      

弹性动力学反问题的数值反演方法

系统介绍了弹性动力学反问题中各种数值反演方法,包括各种近似下的线性化反演方法;非线性迭代反演方法;确定性和非确定性搜索的优化反演方法;大范围收敛的同伦反演方法以及多尺度反演方法。阐述了各类反演方法的原理、特点、适用范围和存在的局限性,指出了数值反演方法进一步研究的方向。      

数值模拟界面流方法进展

用数值模拟方法研究界面流,对于工程设计和理论分析复杂流动都是非常重要的.单纯用现有的高分辨格式无法清晰定出流体界面,故此对界面必须进行特殊的处理,例如界面跟踪(front tracking)方法．本文对界面流的各种数值模拟方法进行了综述．这些方法包括锋面跟踪法、移动网格法、基於粒子法、边界积方法、连续对流格式、体积跟踪方法和水平集的方法．我们着重介绍了现阶段处理流体界面问题使用较多的方法:体积跟踪方法和水平集方法．同时我们也对各种方法的优缺点作了评述.      

时间推进方法在叶轮机械内部流场计算中的进展

时间推进方法目前广泛应用于叶轮机械内部流场的计算,这种方法可以划分成显式时间推进方法和隐式时间推进方法．本文简要介绍了时间推进方法用于叶轮机械内部流场计算的起源及这种方法的优点和缺点,重点记述了国内外叶轮机界应用显式时间推进方法和隐式时间推进方法计算叶轮机内部流场的最新进展,并简要介绍世界上一些著名的研究机构开发的时间推进方法计算程序所采用的数值计算方法      

一种可考虑界面不连续的改进SPH方法

SPH方法模拟工程问题时通常遇到不连续的物理量,因此有必要引入不连续的SPH方法.本文基于Taylor展开公式推导了2D和3D的不连续SPH公式.针对越过材料界面不连续物理量的计算,给出了大变形计算中确定不连续位置的方法,基于Taylor展开公式,从理论上给出了确定不连续公式中x_(k)点的方法,并用数值方法验证了此方法的有效性.比较和讨论了初始SPH方法,CSPM方法与不连续SPH方法处理不连续量的效果.结果显示不连续SPH方法在计算不连续量时有较大的优势.     

计算结构动力响应的分段精细时程积分方法

利用钟万勰等发展的精细时程积分方法，提出了解线性定常结构动力系统响应的分段精细进程积分方法，它能适用于各种激励作用下系统的动力响应。对于载荷项采用线性和两次多项式进行拟合，采用精细时程积分方法和叠代方法对动力响应进行计算，与传统的离散积分方法如纽马克方法和威尔逊方法等及状态方程直接积分方法进行数值比较，本方法具有很高的精度和计算效率。     

胞映射方法的研究和进展

介绍了胞映射方法的研究和进展. 归纳了目前胞映射方法的几种主要研究方法, 主要包括简单胞映射、广义胞映射、图胞映射、图胞映射的符号分析方法、图胞映射的面向集合方法、邻接胞映射、庞加莱型的简单胞映射、插值胞映射以及胞参照点映射方法, 分析了各类方法的基本特点和特色, 简述了这几种胞映射方法的最新国内外进展, 综述了胞映射方法在控制及相关领域的应用研究及进展, 给出了胞映射方法研究的一些展望, 提出了胞映射方法研究可能率先突破的几个研究方向.     

关于力学系统的守恒量--分析力学札记之四

利用牛顿力学方法,分析力学经典方法与分析力学近代方法都可以求得力学系统的守恒量,中讨论了３种方法的优缺点。     

工程力学中的互补问题:算法

工程力学里很多问题存在互补关系,文献[1]介绍了有关的数学模型。本文介绍了近年来求解互补问题的几种主要方法,包括投影方法、内点方法、方程组方法、延拓方法以及无约束优化方法。与此同时,也介绍了作者近期在互补问题算法方面的一些研究工作。     

Global qualitative analysis of new Monod type chemostat model with delayed growth response and pulsed input in polluted environment

In this paper, we consider a new Monod type chemostat model with time delay and impulsive input concentration of the nutrient in a polluted environment. Using the discrete dynamical system determined by the stroboscopic map, we obtain a ＂microorganism-extinction＂ periodic solution. Further, we establish the sufficient conditions for the global attractivity of the microorganism-extinction periodic solution. Using new computational techniques for impulsive and delayed differential equation, we prove that the system is permanent under appropriate conditions. Our results show that time delay is ＂profitless＂.     

Solution of the Rayleigh problem for a powerlaw non-Newtonian conducting fluid via group method

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On the Rocking Behavior of Rigid Objects

A novel formulation for the rocking motion of a rigid block on a rigid foundation is presented in this work. The traditional piecewise equations are replaced by a single ordinary differential equation. In addition, damping effects are no longer introduced by means of a coefficient of restitution but understood as the presence of impulsive forces. The agreement with the classical formalism is very good for both free rocking regime and harmonic forcing excitation.     

Magnetohydrodynamic transient flows of a non-Newtonian fluid

Some exact solutions of the time-dependent partial differential equations are discussed for flows of an Oldroyd-B fluid. The fluid is electrically conducting and incompressible. The flows are generated by the impulsive motion of a boundary or by application of a constant pressure gradient. The method of Laplace transform is applied to obtain exact solutions. It is observed from the analysis that the governing differential equation for steady flow in an Oldroyd-B fluid is identical to that of the viscous fluid. Several results of interest are obtained as special cases of the presented analysis.     

弹性——粘弹性复合结构模态理论

本文研究弹性-粘弹性复合结构动力学基本问题.复合结构动力学方程是一组微分积分方程,引入增广状态变量.将其变换为常规的状态方程.研究了状态方程特征解的性质.提出了"振荡模态"和"蠕变模态"慨念.给出了脉冲响应矩阵和传递函数矩阵,讨论了它们的特性.复合结构模态理论为其动特性和动响应分析提供理论依据.     

Modal theory of elastic-viscoelastic composite structures

The present paper investigates the vibration modal theory of composite structures constructed with elastic and viscoelastic materials. The equation of motion that comes in the form of integrodifferential equations is transformed into the first order differential equation in state space. Then modal analysis is carried out. The concepts of vibrating modal set and creeping modal set are proposed. And impulsive response matrix and transfer function matrix are defined and discussed in detail. Finally sample problems are given to support the theory developed in this paper.     

Finite and impulsive motion of constrained mechanical systems via Jourdain's principle: discrete and hybrid parameter models

The main purpose of this paper is to present a unified analytical dynamics framework for the analysis of finite and impulsive motion of mechanical systems using Jourdain's principle. Emphasis is given to the general case when a mechanical system is described by a hybrid (discrete-distributed) parameter model. A large group of finite and impulsive, generally non-holonomic, constraints are analysed in detail and a so-called extended Appellian classification is presented for these constrained motion problems. The fundamental dynamic equation of constrained systems is developed in terms of velocity variations (Jourdain's principle). Based on this equation and the constraints, the methods of quasivelocities and Lagrangian multipliers are adopted and interpreted for the finite motion of hybrid parameter models of mechanical systems; and the methods of independent quasivelocity variations and Lagrangian multipliers are introduced for the analysis of impulsive motion of such models. To illustrate the proposed material, an example of a one-link flexible arm intercepting and capturing a moving target is considered.     

Discontinuous and impulsive excitation

In this paper, we study the solution of differential equation with Dirac function and Heaviside function, arising from discontinuous and impulsive excitation. Firstly, according to the theory of differential equation, we suggest, then we derive the equation of x ₁ (t) and x ₂ (t) by terms of property of distribution, and by solving x ₁ (t) and x ₂ (t) we obtain x(t); finally, we make a thorough investigation about periodic impulsive parametric excitation.     

Adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling

This paper investigates the adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling, in which the weights of links between two connected nodes are time varying. By the stability analysis of the impulsive functional differential equation, the sufficient conditions for achieving projective synchronization are obtained, and a hybrid controller, that is, an adaptive feedback controller with impulsive control effects is designed. The numerical examples are presented to illustrate the effectiveness and advantage of the proposed synchronization criteria.     

Mixed outer synchronization of dynamical networks with nonidentical nodes and output coupling

Outer synchronization between the drive network and the response network has attracted much more attention in various fields of science and engineering. In this paper, mixed outer synchronization between two complex dynamical networks with nonidentical nodes and output coupling is investigated via impulsive hybrid control, that is, an adaptive feedback controller with impulsive control effects. Moreover, both the cases of complex networks without and with coupling delay are considered. According to the stability analysis of the impulsive functional differential equation, several sufficient conditions for the networks to achieve mixed outer synchronization are derived. Numerical examples are presented finally to illustrate the effectiveness and advantage of the proposed synchronization criteria.