一类含平方、立方非线性质项1：2内共振两自由度系统的全局分岔

研究了一类含平方、立方非线性项的两自由度系统全局分岔。首先应用多尺度法求解其平均方程，然后通过一系列变换得到一个近似可积的两自由度系统。应用能量-相位准则，确定了在哈密顿共振时Silnikov轨道存在的条件。通过数值计算验证了此条件。     

两个薄板弯曲广义协调三角形元

本文根据修正势能原理,应用结点挠度的协调条件以及各边平均挠度和平均法向转角的广义协调条件导出两个九自由度三角形薄板位移型单元LZ1和LZ2.这两个广义协调元是低阶次高精度单元,能够通过分片检验。从精度、简便性和可靠性全面衡量,它们是两个优质的九自由度三角形薄板单元。     

带非线性弹簧的两自由度准零刚度隔振系统力传递率特性

基于多自由度系统中的反共振特性,分别在传统线性隔振系统的上、下两层引入非线性倾斜弹簧负刚度机构,构成两自由度准零刚度隔振器。通过静态特性分析,推导出系统满足零刚度条件时,各参数之间的关系,分析了力学参数及结构参数对系统刚度特性的影响。建立两自由度准零刚度隔振系统的非线性动力学方程,利用平均法求解,推导出力传递率表达式,结合数值分析方法,探讨系统在不同的上、下层隔振器阻尼比、竖直刚度比及质量比情况下的力传递率特性,并与单自由度准零刚度隔振系统及线性斜弹簧两自由度准零刚度隔振系统进行对比研究。结果表明：当结构参数 （即：倾斜弹簧处于静平衡位置的长度与倾斜弹簧原长的比值）较小且倾斜弹簧为软化弹簧时,可在平衡位置附近获得较小的系统刚度及较大的低刚度区间;通过选择适当的上、下层隔振器阻尼比、竖直刚度比与质量比,可减小系统的起始隔振频率,增宽隔振频带,加快系统力传递率在特定频段内的衰减速率,改善系统的低频隔振性能。     

含机械调频式动力吸振器的准零刚度隔振系统隔振性能分析

基于动力吸振器原理,在单自由度准零刚度隔振器基础上耦合可调频动力吸振器构成两自由度隔振系统。首先,对动力吸振器工作原理进行理论分析并提出其力学模型;其次,通过静力学分析,推导出系统满足零刚度条件时,各参数间的关系并分析其对系统刚度特性的影响;然后,建立两自由度隔振系统非线性动力学方程,利用谐波平衡法进行幅频响应解析分析,得到力传递率表达式;最后,数值分析动力吸振器阻尼、刚度、质量、激励力幅值和弹簧片有效长度对力传递率的影响规律,并与单自由度准零刚度隔振系统及两自由度线性隔振系统对比分析。结果表明：通过选择适当的动力吸振器参数不仅可以减小系统的起始隔振频率,增宽隔振频带,且还能加快系统力传递率在特定频段内的衰减速率,改善系统的低频隔振性能,实现激励频率的可适应性。     

存在间隙的多自由度系统的周期运动及Robust稳定性

研究一类存在间隙的多自由度振动系统的动态响应．系统由线性元件构成，但其中一个元件的最大位移不能超过由刚性平面约束所确定的阀值．应用模态矩阵方法将系统解耦，并根据碰撞条件和由碰撞规律所确定的衔接条件求得系统的周期运动及其稳定条件．将Ｌｙａｐｕｎｏｖ方法应用于周期运动的扰动差分方程，导出了含不确定参数的碰撞振动系统周期运动的鲁棒（Ｒｏｂｕｓｔ）稳定性条件．文末用一个二自由度系统阐明了方法的有效性     

两自由度耦合van der Pol振子的拟主振动解

本文运用非线性系统的模态方法研究了两自由度耦合van der Pol振子。从退化系统稳定的主振动解出发,得到了原系统的拟主振动解,并给出了系统周期运动的条件,讨论了系统周期解、概周期解的分叉。     

电磁力作用下发电机定子端部绕组的两自由度主共振

对压板松动时大型汽轮发电机定子端部单根绕组的两自由度主共振问题进行了研究．在给出定子端部绕组区域磁感应强度表达式、绕组所受电磁力以及与松动压板间摩擦力计算式的基础上,建立了研究绕组非线性电磁振动的力学分析模型．采用多尺度法对两自由度主、内共振问题进行求解,得到了稳态运动下的幅频响应方程和解的稳定性判定条件．通过算例,得到了反应系统跳跃现象和软硬特性的幅频响应曲线图,以及响应图、相图、Poincare映射图和频谱图,并阐述了系统可能存在的周期运动和锁模现象。     

OPCL控制方法在准零刚度隔振系统中的应用研究

为了降低船舶动力机械的振动噪声和线谱信号,解决常见线谱控制方法存在的小能量控制混沌化、变工况下持续混沌化和小振幅混沌化的难题,采用开环加闭环(OPCL)控制方法进行了两自由度准零刚度隔振系统的吸引子迁移控制和广义混沌同步化研究。首先,建立了两自由度准零刚度隔振系统的动力学模型,进行了全局性态分析;然后,利用OPCL控制方法将系统从大振幅吸引子迁移至小振幅吸引子,从而减小了系统振幅;最后,在单向耦合系统中,利用OPCL控制方法施加主动控制,实现了系统在大参数范围内的小振幅广义混沌同步化。结果表明,将OPCL控制方法应用于两自由度准零刚度隔振系统的吸引子迁移控制和广义混沌同步化,能够同时实现隔振系统的线谱控制和振动隔离,从而进一步扩大了OPCL控制方法的应用范围。     

均质简支梁简化为单自由度系统条件研究

简支梁是土木工程中的常见结构形式，工程计算中常将其简化为单自由度系统进行初步分析和计算．本文系统地讨论了简谐荷载作用下将简支梁简化为单自由度系统进行竖向位移计算的限定条件．对限定条件分析发现将梁上质量的一半集中到梁跨中处所得近似结果精度最好．给出公式可以通过单自由度系统的位移得到梁上任意点处的竖向位移．本文对结构力学教材中的集中质量法进行了进一步的分析和讨论，给出的近似计算公式对土木工程中简支梁在简谐力作用下竖向位移的快速估算具有一定的参考价值．     

耦合van der Pol振子的数值解

本文简要介绍ＮＮＲ方法，用以求解非线性系统的时间历程．求出二自由度耦合ｖａｎｄｅｒＰｏｌ振子的两组极限环；分析了出现不同极限环的初值条件．     

The numerical method for analysing the transient temperature field and transient phase transformation of metal materials in heat treating

In this paper,the Kirchhoffs transformation is popularized to the nonlinear heat conduction problem which the heat conductivity can be expressd as a multinomial of temperature firstly,the boundary condition of heat conduction problem is determined by analytics.Secondly,the incubation peroid superposition and the linear combination law is employed to simulate the transient phasses transformation in the process of heat treatment of materials.That the begin time of phase transformation,the type of phase transformation and the amount of phase constitution is determined simply.Finally,the three-dimension Dual Reciprocity Boundary Element Method is usedto analysis the total process of various heat treatment of component,the results of numerical calculation of examples show that the method provided in this paper is effectivce.     

On the derivation of an admissibility condition for phase boundary propagation in an SMA bar based on a 3-D formulation

There is some considerable difficulty in determining the solution uniquely for a propagating phase boundary in shape memory alloy (SMA) bar. In this paper, we establish an admissibility condition starting from a three-dimensional (3-D) internal-variable formulation to resolve this issue. We adopt a 3-D formulation in literature which is based on a constitutive model with specific forms of the Helmholtz free energy and dissipation rate. Then the 3-D dynamical equations are reduced to the 1-D rod equations for three phase regions (coupled with the radial effect and surface condition) by using two small parameters. Connection conditions at the phase interfaces are determined. By considering the traveling-wave solution for the rod system, we eventually derive three conditions across a sharp phase boundary corresponding to the 1-D sharp-interface model, including the two usual jump conditions and an additional condition. The third condition is then used to supplement the 1-D sharp-interface model to study an impact problem. The unique solution is constructed analytically for all possible impact velocity, including three kinds of wave patterns according to different levels of the impact velocity. The results are compared with those obtained by the maximal dissipation rate criterion.     

钢筋与混凝土粘结试验及有限元模拟

建立了一种按接触条件模拟钢筋与混凝土之间相互作用的模型。通过试验确定钢筋与混凝土的一些基本力学参数:粘结刚度、摩擦系数、抗剪强度、径向挤压力和软化系数;进而通过有限元模拟分析了试件的拔出过程:弹性阶段、局部开裂阶段、内部拥塞阶段以及完全脱粘阶段。计算结果与试验结果符合较好,验证了本文计算模型的合理性,解决了传统连续体理论所无法解释的现象。     

An Eulerian model for the motion of granular material with a large Stokes number in fluid flow

This study introduced a novel Euler–Euler approach for modeling granular multiphase flow. The motion of particles with a large Stokes number was investigated assuming that granular material has unilateral compressibility. Solid pressure in the momentum equations for granular multiphase flow was determined so that the unilateral incompressibility condition was satisfied. Using the continuity condition of the granular phase, the equation was rewritten in the optimal form to calculate the solid pressure. A discrete formulation of smoothed particle hydrodynamics was applied for the convective terms so that the discrete matrix was positive semidefinite for the convergence and the discretization for an unstructured mesh was allowed. Frictional stress was then determined from solid pressure and, by using the solid pressure and frictional stress, momentum equations for the granular phase were solved. The method was incorporated into ANSYS FLUENT by a UDF (user defined function). Model validation was performed through a comparison with two previous results, and efficacy of the proposed model was confirmed.     

A micromechanics-based thermodynamic formulation of isotropic damage with unilateral and friction effects

This paper is devoted to micromechanical modeling of isotropic damage in brittle materials. The damaged materials will be considered as heterogeneous media composed of solid matrix weakened by isotropically distributed microcracks. The original contribution of the present work is to provide a proper micromechanical thermodynamic formulation for damage-friction modeling in brittle materials with the help of Eshelby’s solution to matrix-inclusion problems. The elastic and plastic strain energy involving unilateral effects will be fully determined. The condition of microcrack opening–closure transition will be determined in both strain-based and stress-based forms. The effect of spatial distribution of microcracks will also be taken into account. Further, the damage evolution law is formulated in a sound thermodynamic framework and inherently coupled with frictional sliding. As a first phase of validation, the proposed micromechanical model is finally applied to reproduce basic mechanical responses of ordinary concrete in compression tests.     

On a Model of Heterogenous Deformation of Elastic Bodies by the Mechanism of Multiple Appearance of New Phase Layers

A model describing a possible scenario of martensite type phase transformations is examined. A new phase is supposed to nucleate in the form of plane parallel layers. As the boundary condition, average strains are imposed. Then, the governing parameters of the two-phase structure are the concentration of new phase layers, their orientation and also the orientation of anisotropy axes. The parameters depend on the average strains and are determined by the requirement to minimize the average Helmholtz free-energy function. Once a general procedure has been discussed, average strain–stress diagrams are constructed for two cases. In the first case, for the simplicity sake, both phases are assumed to be isotropic. In the second case anisotropy is produced by a non-spherical phase transformation strain tensor. For both cases phase transition zones (PTZs) are constructed. The PTZ is formed in the space of strains by those which can exist on equilibrium interfaces. Loading and unloading paths, corresponding to uniaxial stretching and plane stretching/compression, are examined and related with the PTZ. Effects of internal stresses induced by the nucleation of new phase areas and the anisotropy of new phase are discussed.     

Predicting failure modes and ductility of dual phase steels using plastic strain localization

Ductile failure of metals is often treated as the result of void nucleation, growth and coalescence. Various criteria have been proposed to capture this failure mechanism for various materials. In this study, ductile failure of dual phase steels is predicted in the form of plastic strain localization resulting from the incompatible deformation between the harder martensite phase and the softer ferrite matrix. Microstructure-level inhomogeneity serves as the initial imperfection triggering the instability in the form of plastic strain localization during the deformation process. Failure modes and ultimate ductility of two dual phase steels are analyzed using finite element analyses based on the actual steel microstructures. The plastic work hardening properties for the constituent phases are determined by the in-situ synchrotron-based high-energy X-ray diffraction technique. Under different loading conditions, different failure modes and ultimate ductility are predicted in the form of plastic strain localization. It is found that the local failure mode and ultimate ductility of dual phase steels are closely related to the stress state in the material. Under plane stress condition with free lateral boundary, one dominant shear band develops and leads to final failure of the material. However, if the lateral boundary is constrained, splitting failure perpendicular to the loading direction is predicted with much reduced ductility. On the other hand, under plane strain loading condition, commonly observed necking phenomenon is predicted which leads to the final failure of the material. These predictions are in reasonably good agreement with experimental observations.     

Equations of heterophase equilibrium of a biomembrane

Summary Phase transitions in a shell are considered within the frame example work of a biomembrane of a general shape divided into parts containing different phases. The configuration of a boundary separating these phases is determined by the condition of minimum of the total membrane free energy with respect to its position. Equations of equilibrium for both the membrane phases and the phase boundary are deduced. They allow to describe the heterophase state of the biomembrane. Received 11 December 1997; accepted for publication 31 July 1998     

ANALYSIS OF THE CHAOTIC MOTION FOR A ROTOR SYSTEM WITH A TRANSVERSE CRACK

The chaotic motion of an elastic shaft-disk rotor system including the geometricnonlinearity of the shaft with a transverse crack is investigated.The critical condition for thesystem to enter chaotic state is given by the Melnikov method.Meanwhile,whether the chaosoccurs is determined by the Poincaré map,phase portrait and time-displacement history diagram.     

Stability of Subsonic Planar Phase Boundaries in a van der Waals Fluid

We are concerned with the structural stability of dynamic phase changes occurring across sharp interfaces in a multidimensional van der Waals fluid. Such phase transitions can be viewed as propagating discontinuities. However, they are usually subsonic, and thus undercompressive. The lacking information lies in an additional jump condition, which may be derived from the viscosity-capillarity criterion. This condition is rather simple in the case of reversible phase transitions, since it reduces to a generalized equal area rule. In a previous work, I proved that reversible planar phase boundaries are weakly linearly stable, in the sense introduced by Majda for shock fronts. This means that they satisfy a generalized Lopatinsky condition but not a uniform one. The aim of this paper is to point out the influence of viscosity on the stability analysis, in order to deal with the more realistic case of dissipative phase transitions. The main difficulty lies in the additional jump condition, which is no longer explicit and depends on the (unknown) internal structure of the interface. We overcome it by using bifurcation arguments on the nondimensional parameter measuring the competition between viscosity and capillarity. We show by perturbation that the positivity of this parameter stabilizes the phase transitions. As a conclusion, we find that dissipative planar phase boundaries are uniformly linearly stable, in the sense of the uniform Lopatinsky condition. Accepted December 14, 1998