一类振动方程周期解的全局分岔

本文利用Ｍｅｌｎｉｋｏｖ函数方法，通过分析无穷远处轨线的性质，研究一类柱面振动方程周期解的全局分岔问题，获得了第二类闭轨存在性和唯一性的条件。     

小半径曲线上长大桥梁车桥耦合振动分析

本文基于车辆-直线桥梁的耦合振动分析理论,采用模态叠加法,建立车辆-曲线桥梁的耦合振动方程。采用移动坐标系,通过坐标变换,解决车辆曲线通过时轮轨耦合的几何关系。依据赫兹弹性接触理论,考虑密贴接触和非密贴接触,求解轮轨接触力。基于车辆直线运动的Kalker线形蠕滑理论,修正后得出车辆曲线运行的蠕滑率。同时,在广义力向量中考虑了车辆曲线运动时产生的离心力和超高分力。采用分离迭代法求解运动方程,得出车桥耦合振动响应。基于这些理论分析,结合某小半径曲线上长大桥梁工程实例,进行列车-曲线桥梁的车桥耦合振动数值分析,得出了车辆通过小半径曲线上长大桥梁的一些车桥振动特性和规律。     

混沌振动压实动力学的仿真研究—（I）混沌识别

本文提出了四自由度混沌振动压路机“机架－振动轮－土”系统的力学模型;建立了其数学模型;对数学模型进行了数值仿真;根据振动轮的运动,利用混沌识别的定性方法（相轨图、功率谱图和Ｐｏｉｎｃａｒｅ图）与定量方法（最大Ｌｙａｐｕｎｏｖ指数）,对系统的混沌特征进行了识别。结果表明：系统的运动是混沌的。     

周期Riccati型方程解的振动性及其渐挥性

本文主要利用Ｂｒｏｕｗｅｒ不动点定理和解的交差化积的方法，研究下列周期Ｒｉｃｃａｔｉ型方程ｙ＝ｆ（ｔ，ｙ）＝Ａ（ｔ）ｙ＾ｍ＋Ｂ（ｔ）ｙ＋Ｃ（ｔ）（ｍ≥２，ｍ∈Ｎ）其中，Ａ（ｔ）、Ｂ（ｔ）和Ｃ（ｔ）均是以ω为周期的连续函数，ω〉０解的振动性渐近性，不仅得以了方程（＊＊）的非振动解与其ω周期解之间的渐近关系，而且得到了方程（＊＊）存在振动解的必要条件和充分条件。     

非线性转子——轴承系统油膜失稳新机理研究

本言语以采用短轴承模型的具有不平衡质量单圆盘刚性转子－－轴承系统类 直角座标系中建立了该系统的非线性振动方程对油膜失稳机理进行了研究。在其临界点处利用中心流形定理对系统进行简化处理后，求得了中心流形上流的方程对于１２亚谐共振情况通过平均法得到其平均方程根据奇异性理论对之进行了普适开折，并得到了１０种分岔模式。该理论表明，如果系统的参数位于图４的（４）和（５）内，则可得到减低油膜振动的良好效果。这是     

等效线性化方法的最优性

等效线性化方法的最优性陈立群（鞍山钢铁学院理论力学教研室鞍山１１４００２）对于弱非线性单自由度自由振动系统的第一次近似用能量平衡原理或谐波平衡原理都可以导出等效线性化系统ｌ‘］其中而且可以证明方程（３）是精确到Ｏ（。）的方程．这里将进一步证明以等效线...     

流固耦合振动问题的普遍方程与解法

本文研究了在一般正交曲线坐标下，分别就理想不可压缩流体与粘性流体两种不同情况时的流固耦合振动。综合运动了混合座标法（动－－静坐标法）及曲面映射方法，考虑了原来难以描 流体自由表面和流固耦合面的运动情况，并保持了方程中的非线性项，从而获得了一组较为切合实际的方程，以描写流固耦合振动的性态。讨论了由Ｍ个弹性 本（或弹性板）组成的容器与流体耦合振动的方程的解法，并举例说明这类问题的方程的具体形式与解当，     

结构力学教材中δ_(ij(i≠j))=0的主振型问题

本文对振动方程副系数δｉｊ（ｉ≠ｊ）不等于零的振动体系从线性代数矩阵秩的判断，并结合实例分析，给出解并绘振型图     

按广义坐标建立具有移动质量的箱梁振动方程

在文献（５）讨论移动荷载作用于箱梁的基础上，进一步考虑了移动质量对梁的动力作用；推导，建立了与前者性质，形式完全不同的变系数振动方程，并用数值方法救是解答，算例验证了本文建立了振动方程是正确的。     

叶轮机中振动叶片非定常气动力的研究

采用“单一叶片振动方法”代替传统的“全部叶片振动方法”，用线性化的方法推导出计算振动叶片非定常气动力（引起叶片弯曲振动）及力矩（引起叶片扭转振动）方程。通过输入叶型及气流参数，它可以方便有效地估计出作用在振动叶片上的非定常气动力和力矩，以及振动叶片不稳定工况发生的条件和范围。并在氟里昂超音速风洞上进行了实验测量，结果表明，理论计算结果与实验测试结果符合较好。     

弹性力学混合状态方程的弱形式及其边值问题

导出了弹性力学混合状态方程和边界条件弱形式的统一方程，此法使函数的选择无需事先完全满足边界条件，对于各种不同的边值问题可以用统一形式处理，这使得求解弹性力学问题的形式得以扩大和统一     

Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials

We consider the equations of linear homogeneous anisotropic elasticity admitting the possibility that the material is internally constrained, and formulate a simple necessary and sufficient condition for the fundamental boundary value problems to be well-posed. For materials fulfilling the condition, we establish continuous dependence of the displacement and stress on the elastic moduli and ellipticity of the elasticity system. As an application we determine the orthotropic materials for which the fundamental problems are well-posed in terms of their Young's moduli, shear moduli, and Poisson ratios. Finally, we derive a reformulation of the elasticity system that is valid for both constrained and unconstrained materials and involves only one scalar unknown in addition to the displacements. For a two-dimensional constrained material a further reduction to a single scalar equation is outlined.This paper is dedicated to Professor Joachim Nitsche on the occasion of his sixtieth birthday     

Verifying consistency of boundary conditions with integral characteristics of mass conservation for particulates in flow

The mass conservation equation of the particulate phase, in the form of Euler-type transport equation for particle-number density, is integrated to investigate issues related to its boundary condition consistency. For each of the effects of convection, diffusion and particle settling, the provided boundary conditions need to meet the requirement for well-posed problems physically and mathematically for particulate phase simulation. The integration of the conservative form of the transport equation yields the relations between the rate of change of the total particle number and the boundary conditions. Results of these relations are compared with numerical solutions using a finite-volume solver, of which the numerical formulation is also based on the conservative form of the transport equation. Cases for particulate flow in a room-scale chamber with various combinations of convection, diffusion and settling processes are used as examples for boundary-condition consistency verification.     

Dirichlet and Neumann boundary conditions for the pressure poisson equation of incompressible flow

In a recent paper Gresho and Sani showed that Dirichlet and Neumann boundary conditions for the pressure Poisson equation give the same solution. The purpose of this paper is to confirm this (for one case at least) by numerically solving the pressure equation with Dirichlet and Neumann boundary conditions for the inviscid stagnation point flow problem. The Dirichlet boundary condition is obtained by integrating the tangential component of the momentum equation along the boundary. The Neumann boundary condition is obtained by applying the normal component of the momentum equation at the boundary. In this work solutions for the Neumann problem exist only if a compatibility condition is satisfied. A consistent finite difference procedure which satisfies this condition on non-staggered grids is used for the solution of the pressure equation with Neumann conditions. Two test cases are computed. In the first case the velocity field is given from the analytical solution and the pressure is recovered from the solution of the associated Poisson equation. The computed results are identical for both Dirichlet and Neumann boundary conditions. However, the Dirichlet problem converges faster than the Neumann case. In the second test case the velocity field is computed from the momentum equations, which are solved iteratively with the pressure Poisson equation. In this case the Neumann problem converges faster than the Dirichlet problem.     

埋在土中的输液管道的耦联振动

本文对平面应变情况下,管道、流体与外土壤介质三者间的耦联振动进行了精确分析。在严格满足所有耦合边界条件的情况下,导出了系统自由振动的频率方程,并给出了各参数对最低阶固有频率影响的数值结果。当对更复杂水一管一土耦合系统进行数值解时,本文结果可作为检验其精度的一个依据。     

车轨系统随机响应周期性拟稳态分析

提出用于三维车轨耦合系统随机动力响应高效求解的周期性拟稳态分析方法. 车辆采用三维刚体动力学模型,轨道结构利用三维轨道广义单元建模. 假定轨枕间距均匀,则列车在轨道上行驶过程中,车轨耦合系统动力学方程具有典型周期时变特征. 应用虚拟激励方法将轨道随机不平顺转化为虚拟简谐不平顺,在状态空间下运用周期系数微分方程的性质和Schur分解技巧将上述问题的求解转化为周期性拟稳态响应分析,只需通过求解系数矩阵为上三角的线性方程组即可代替以往时变系统虚拟响应求解过程中的逐步积分过程,计算效率获得较大提高. 采用该方法进行了三维车轨耦合系统的随机动力响应分析,并进行了不平顺随机载荷在车体、转向架、轮对和轨道等部件中传递机理分析,获得了一些有价值结论.      

The semi-discrete method for solving high-dimension wave equation

The article gives a semi-discrete method for solving high-dimension wave equation. By the method, high-dimension wave equation is converted by means of discretization into I-D wave equation system which is well-posed. The convergence of the semidiscrete method is given. The numerical calculating results show that the speed of convergence is high.     

ON THE NONHOLONOMIC CONSTRAINTS AND MOTION CONTROL OF WHEELED MOBILE STRUCTURES1)

当质点沿光滑曲线运动时,必须满足横向速度为零的条件.同样地,不同轮式移动结构在平面上做光滑曲线运动时都需要满足该非完整约束条件.本文结合轮子转速和它们运动速度的完整约束关系,理清各轮式移动结构的完整和非完整约束,然后利用 Euler-Lagrange 方程方便地推导出相应的动力学方程.另外,通过该非完整约束,将目标轨迹曲线转化为速度目标的形式,然后引入目标轨迹曲线的相对曲率设计合适的动态跟踪目标.进一步,通过采用该动态跟踪目标可以将轮式移动结构的运动规律和动力学方程有机结合起来,并将原运动任务简化为一般的 轨迹 控制问题.基于该动态跟踪目标可以为轮式移动结构设计合适的鲁棒跟踪控制器,通过跟踪目标轨迹曲线的相对曲率来实现对目标曲线的精确跟踪.最后,理论分析和仿真结果显示,采用动态目标跟踪方法能够从根本上解决初始速度误差过大和位置误差不断被累积的问题,即使前向速度误差系统不稳定的,实际运动轨迹也几乎能和目标轨迹曲线重合.     

THE SEMI-DISCREIXTE METHOD FOR SOLVING HIGH-DIMENSION WAVE EQUATION

1.IntroductionWaveequationiswidelyusedinsuchsubjectsasgeophysics,elasticmechanics,andsoon.Therefore,how'tosolvewaveequationbecomesaveryimportantproblem.Althoughpeoplehaveachievedalotinthetheoryandcalculationofwaveequationl']'121,newproblemsandsolutionskeep.comingoutl3]'141.Oneofthemethodsgiveninpaper[5]istoreducetwodimensionequationtoone-dimensionequationsystem.However,itisdifficulttoextendhighdimensionwave'equationandwaveequationwithvariablecoefficient.Bythesemi-discrete'methoddiscussedinthi…     

论轮式移动结构的非完整约束及其运动控制

当质点沿光滑曲线运动时,必须满足横向速度为零的条件.同样地,不同轮式移动结构在平面上做光滑曲线运动时都需要满足该非完整约束条件.本文结合轮子转速和它们运动速度的完整约束关系,理清各轮式移动结构的完整和非完整约束,然后利用 Euler-Lagrange 方程方便地推导出相应的动力学方程.另外,通过该非完整约束,将目标轨迹曲线转化为速度目标的形式,然后引入目标轨迹曲线的相对曲率设计合适的动态跟踪目标.进一步,通过采用该动态跟踪目标可以将轮式移动结构的运动规律和动力学方程有机结合起来,并将原运动任务简化为一般的 轨迹 控制问题.基于该动态跟踪目标可以为轮式移动结构设计合适的鲁棒跟踪控制器,通过跟踪目标轨迹曲线的相对曲率来实现对目标曲线的精确跟踪.最后,理论分析和仿真结果显示,采用动态目标跟踪方法能够从根本上解决初始速度误差过大和位置误差不断被累积的问题,即使前向速度误差系统不稳定的,实际运动轨迹也几乎能和目标轨迹曲线重合.