谐和与随机噪声联合作用下Duffing振子的双峰稳态密度

研究Duffing振子在谐和与随机噪声联合作用下系统响应的双峰稳态概率密度问题．用多尺度法分离了系统的快变项,得到了系统慢变项满足的随机微分方程．用线性化方法求出了双峰稳态概率密度的表达式．数值模拟表明提出的方法是有效的．     

裂缝三级摩擦因数及影响因素研究(以砂岩（颗粒胶结体）为例)

讨论摩擦面的摩擦因数模型．认为砂岩的摩擦因数分为砂粒球面摩擦因数、微裂纹平面摩擦因数、凸凹构成的裂缝摩擦因数3个层次,分别代表3类不同的成因,3个层次的耦合是真实岩石摩擦因数的决定因素．岩石摩擦因数是在砂粒球面材料摩擦因数基础上,经过后两种形式的放大而形成岩石的宏观摩擦因数．裂纹表面凸起的平均角度或者分形维数是影响岩石摩擦因数分异的最大影响因素,而颗粒排布模式导致的分异相对小得多．颗粒接触的静摩擦因数大于动摩擦因数的成因与颗粒的平均接触角度有关．     

幂律流体边界层方程的近似解析解和壁摩擦因数的近似值

对幂率流体层流平板边界层的解析解进行了研究．对该问题提供了Adomian分解方法并且推导出了问题的级数形式的近似解析解,该近似解析解具有快速收敛性和易于计算性．对不同的幂率给出了方程的近似解析解和相应的壁摩擦因数近似值,最后对近似解所推出结果和所得壁摩擦因数与文献中的数值解进行了比较验证,证实了该文提出的解析近似方法的准确性和可靠性,说明了该近似解能够应用于提供所研究问题的壁摩擦因数．     

一类超线性收敛的既约变尺度法

本文将既约梯度法与Ｈｕａｎｇ族变尺度法相结合，给出标准型线性约束规划问题的一类既约变尺度法．在较温和的假设下，算法具有全局收敛性和超线性收敛速度，最后指出本文算法包含和改进几个己有的有效算法．     

广义投影梯度型约束变尺度法

本文将广义投影梯度方向移植到约束变尺度算法之中，得到了一类新型算法：广义投影梯度型约束变尺度算法，并成功的使用了Ａｒｍｉｊｏ规则．该算法将广义投影类可行方向法和约束变尺度算法的优点溶为一体．并且由于使用了拟下降的概念，算法变得更为灵活．     

二次回归正交组合设计在消除试验机摩擦振动中的应用

本文采用二次回归正交组合设计的原理，在Ｍ２摩擦试验机上，对消除低速滑动时的摩擦振动所需要的激振力与试验机系统参数之间的关系，进行了多因素优化试验回归，得到了二者之间的非线性回归方程．利用方程能对试验机在各种系统参数组合下需要的激振力作出比较准确的预报，使激振消除摩擦振动这一新技术，在摩擦试验机上得到了更为有效的应用．     

关于几种有限元方法的注记

§1.引言 在许多种解椭圆边值问题的有限元法中,比较成功的方法有非协调元、拟协调元、广义杂交应力元及混合刚度元等.这些方法是从不完全相同的观点出发得到的.例如,从势能原理出发,放宽势能的定义域而得到的,有非协调元方法和拟协调元方法;从Reissuer原理出发而得到的,有广义杂交应力元和混合刚度元方法.实际上,这些方法都可以从势能原理出发放宽势能定义域而得到(见[2]).本文企图用多套函数有限元逼近的思想,将上述方法统一在一个有限元模型EFE方法中,从而看出这几种方法的关系.为此目的,我们以线弹性力学方程组为例,阐述本文的结果.对于其它椭圆边值问题,例如薄板弯曲问题,可以得到类似的结果.     

可渗透收缩薄膜引起的三维不稳定边界层流动

研究可渗透收缩薄膜上的不稳定粘性流动．通过相似变换得到相似方程．在不同的不稳定参数、质量吸入参数、收缩参数、Prandtl数下,数值地求解相似方程,得到速度和温度的分布,以及表面摩擦因数和Nusselt数等．结果发现,与不稳定的伸展薄膜不同,在质量吸入参数和不稳定参数的某一范围内,可渗透收缩薄膜上的不稳定流动存在双重解．     

差商变尺度法的整体收敛性

对于求解无约束最优化问题,变尺度法被公认为是最有效的方法之一,从1971年Powell的开创性工作以来,关于变尺度法收敛性的研究已形成了系统的理论,由于精确导数难以得到,常用差商代替,称为差商变尺度法,对其收敛性理论的研究,尚相当薄弱,本文证明了差商变尺度法的整体收敛性,同时给出了保证收敛的差商步长条件。     

含摩擦的多刚体系统碰撞问题的滑动状态步进法

研究了含铰摩擦的多刚体系统的碰撞动力学问题．在保留了关于处理冲击问题的经典近似假定的基础上,给出了计算冲击后系统广义速度的滑动模式步进算法．该算法避免了求解变尺度的微分方程的困难,同时由于考虑了切向模式的复杂性,从而使计算结果避免了碰撞前后能量的不协调性．算例描述了该算法的实现过程．     

三维非定常/定常不可压缩流动N-S方程基于人工压缩性方法的数值模拟

基于人工压缩性方法提出—中心与迎风混合的算法,以数值模拟N-S方程的定常/非定常解．对半离散方程的左端采用中心差分, 方程右端数值流量采用迎风Roe近似算法,其精度可达三阶．湍流模式利用Baldwin-Lomax代数模式．计算例子包括二维平板、机翼剖面、扁椭球、颅动脉瘤等．计算结果表明,压力和摩擦系数与实验符合,在分离涡旋区计算值与实验有差别,这或许是由于湍流模式不够精确的缘故．     

Multiscale simulation for description of rubber friction

The interaction between tire and road generates the transferable forces, which are necessary for driving dynamics and safety. These forces are based on friction between rubber material and pavement surface and depend on the roughness of the pavement, the slip velocity, the contact pressure and the temperature. Based on the finite element method, the friction coefficient is calculated by numerical simulation. The roughness of the pavement surface is described by the height difference correlation function (HDCF), which allows partitioning into different length scales. This multiscale approach is suitable to understand and to evaluate friction phenomena. These phenomena are hysteresis friction based on dissipation inside the rubber material and adhesion friction, which describes the direct bonding between two materials. Given, that the material parameters of rubber highly depend on temperature and the frictional dissipation leads to a warming of the rubber, the provision for these effects is necessary for a realistic desciption of friction. The method allows an understanding of friction phenomena on the micro-scale like the real contact area or the microscopic contact pressure. Also, the temperature distribution inside the tire cross-section can be illustrated. The resulting coefficient of friction is validated by experimental data based on linear friction tests and compared to analytical solutions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

面内平动黏弹性板非线性振动的内-外联合共振

研究了同时存在受迫共振和1∶3内共振时的面内平动黏弹性板的横向非线性振动问题．板的黏弹性材料用Kelvin本构关系描述．基于系统的运动方程和四边简支的边界条件,对偏微分方程应用直接多尺度法建立了联合共振时的可解性条件．应用Routh-Hurvitz判据对系统幅频响应的稳定性进行了判别．给出了黏弹性系数、面内平动速度和激励幅值3个参数对幅频响应的影响．最后,应用微分求积数值方法验证了近似解析方法的结论.     

Multiscale Rubber Friction Analysis on Rough and Flexible Surfaces

In this work, a multiscale homogenization approach is introduced to provide friction features between rubber and rough contact partners. Different length scales of the rough surface are considered by using a decomposition of the height difference correlation (HDCF) or the power spectral density function (PSDF) in several sinusoidal waves to accumulate the micro- and mesoscopic friction into a macroscopic friction coefficient. By using the finite element method (FEM), the sensitivity of the influencing factors for instance slip velocity and contact pressure may be investigated for rigid and flexible surfaces in the two- and the three-dimensional case. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermoelastic rolling contact problem with temperature dependent friction

The paper is concerned with the numerical solution of a thermoelastic rolling contact problem with wear. The friction between the bodies is governed by Coulomb law. A frictional heat generation and heat transfer across the contact surface as well as Archard's law of wear in contact zone are assumed. The friction coefficient is assumed to depend on temperature. In the paper quasistatic approach to solve this contact problem is employed. This approach is based on the assumption that for the observer moving with the rolling body the displacement of the supporting foundation is independent on time. The original thermoelastic contact problem described by the hyperbolic inequality governing the displacement and the parabolic equation governing the heat flow is transformed into elliptic inequality and elliptic equation, respectively. In order to solve numerically this system we decouple it into mechanical and thermal parts. Finite element method is used as a discretization method. Numerical examples showing the influence of the temperature dependent friction coefficient on the temperature distribution and the length of the contact zone are provided. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiparameter regularization for Volterra kernel identification via multiscale collocation methods

Identification of the Volterra system is an ill-posed problem. We propose a regularization method for solving this ill-posed problem via a multiscale collocation method with multiple regularization parameters corresponding to the multiple scales. Many highly nonlinear problems such as flight data analysis demand identifying the system of a high order. This task requires huge computational costs due to processing a dense matrix of a large order. To overcome this difficulty a compression strategy is introduced to approximate the full matrix resulted in collocation of the Volterra kernel by an appropriate sparse matrix. A numerical quadrature strategy is designed to efficiently compute the entries of the compressed matrix. Finally, numerical results of three simulation experiments are presented to demonstrate the accuracy and efficiency of the proposed method.     

Finite element analysis of a static contact problem with Coulomb friction

A unilateral contact problem with a variable coefficient of friction is solved by a simplest variant of the finite element technique. The coefficient of friction may depend on the magnitude of the tangential displacement. The existence of an approximate solution and some a priori estimates are proved.     

Comparison of approximate symmetry and approximate homotopy symmetry to the Cahn–Hilliard equation

Complete infinite order approximate symmetry and approximate homotopy symmetry classifications of the Cahn–Hilliard equation are performed and the reductions are constructed by an optimal system of one-dimensional subalgebras. Zero order similarity reduced equations are nonlinear ordinary differential equations while higher order similarity solutions can be obtained by solving linear variable coefficient ordinary differential equations. The relationship between two methods for different order are studied and the results show that the approximate homotopy symmetry method is more effective to control the convergence of series solutions than the approximate symmetry one.     

On methods for continuous systems with quadratic,cubic and quantic nonlinearities

Methods for study of weakly nonlinear continuous systems are discussed. The method of multiple scales is used to analyze the nonlinear response of a relief valve under combined static and dynamic loadings. We determine a second-order approximation to the response of the system for the case of primary resonance. Second, we derive a second-order nonlinear ordinary differential equation that describes the time evolution of a single-mode, the so-called single-mode discretization. Then, we use the multiple scales method to determine second-order approximate solutions of this equation, thereby obtaining the equations describe the modulations of the amplitude and phase of the response. We show that the results of the second approach are erroneous.     

Techniques for approximating a spatially varying Euler-Bernoulli model with a constant coefficient model

Developing accurate models to describe the behaviour of a physical system often results in differential equations with spatially varying coefficients. A notable example of this that appears in many applications is the Euler-Bernoulli beam equation for transverse vibrations. This equation with spatially varying coefficients, such as when the bending stiffness or mass per unit length varies along the length of the beam, is of interest in the current research. Methods for approximating the Euler-Bernoulli equation with periodically varying coefficients have been proposed yet there is still a need for methods that approximate the more general, non-periodically varying, cases. The goal of this research is to obtain a constant coefficient Euler-Bernoulli equation that accurately approximates the original spatially varying equation using an inverse problem approach. Obtaining such an approximation has advantages in control applications where a constant coefficient model is strongly preferred for computational efficiency. The motivation for this research stems from previous work by the authors on modelling cable-harnessed structures. The spatially varying equation is solved using the Lindstedt-Poincaré perturbation method and these results are used to determine the approximate model. Multiple inverse problem methods for determining the coefficients in the approximate model are considered including metric minimization, the modal participation factor (MPF), and the proper orthogonal decomposition (POD). Continuous version of POD and MPF methods are obtained. Several wrapping patterns and boundary conditions are considered for comparison and the results are in good agreement with analytical and finite element analysis (FEA) results.