微分求积法求解功能梯度材料梁的弯曲问题

基于Reddy三阶剪切变形理论,研究了功能梯度材料梁的线性弯曲问题,假设功能梯度材料性质只沿梁厚度方向变化,且服从幂函数规律,推导了问题的控制方程,考虑固支边界条件,并选用合适的计算结构,用微分求积法对其进行数值求解.利用数值结果考察了材料的梯度性质,载荷条件、细长比等对梁弯曲行为的影响.结果表明:相同条件下,FGM梁的挠度介于纯金属和纯陶瓷之间,并且随着梯度参数的增加,挠度在减小;随着FGM梁的细长比的增大,梁中心挠度迅速减小.     

确定轴向运动梁固有频率的多尺度法

The natural frequencies of an axially moving beam were determined by using the method of multiple scales. The method of second-order multiple scales could be directly applied to the governing equation if the axial motion of the beam is assumed to be small. It can be concluded that the natural frequencies affected by the axial motion are proportional to the square of the velocity of the axially moving beam. The results obtained by the perturbation method were compared with those given with a numerical method and the comparison shows the correctness of the multiple-scale method if the velocity is rather small.     

Galerkin截断方法在轴向运动梁问题中的应用

研究了Galerkin截断方法在不同支承条件下轴向运动梁振动问题中的应用．利用离散化后的微分方程在u-vf平面上的失稳区域随离散维数的变化情况，验证了两端铰支的轴向运动梁取正弦函数做Galerkin截断方法时所得结果的正确性，对于两端固支的轴向运动梁，选取不同的特征函数，分别应用Galerkin截断方法并比较所得结果，最后得到适用于此种支承条件下的离散方法．     

六元函数全微分求积研究

本文介绍六元函数的全微分求积的相关定义、定理,以及定理的证明.     

梁轴向力对弯曲振动频率的影响

本文通过支各种支承下，受轴向力Ｎ作用的平面弯曲梁振动频率的求解，找到了弯曲振动频率与轴向力Ｎ间的关系。     

微分求积法求解不可压二阶粘弹性流体和热迁移模型中的稳态流动

1IntroductionAlthoughthe computation of the fluid mechanics hasgreat development during the last decades,due to themodel in nonlinear fluid mechanics is very complicat-ed,the more efficient techniques for solvingthis prob-lemstill attract the interest of many researchers.Thedifferential quadrature method(DQM)introduced byBell man,et al.[1,2]is an efficient numerical methodfor solving partial differential equations.In recentyears,the DQMhas been widely used for solving theproblems of enginee…     

用非规则节点解偏微分方程的局部微分求积法

In the conventional differential quadrature (DQ) method the functional values along a mesh line are used toapproximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature (LDQ)method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximatedby a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in thenew approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directlyapproximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature isstill kept. Numerical examples are provided to validate the LDQ method.     

不定积分凑微分法教学探析

凑微分法是微积分学中的一个重要的计算技巧,也是不定积分的一个教学难点。如何在教学中改进教学理念与方法,正确引导学生学习和思考,教会学生理解、诊断和表征问题,培养思维的流畅性、变通性和独创性,从而提高学生的数学能力。     

微分法在几何上的应用

本文用二元函数的微分法解决求空间曲线的切线及法平面问题.     

微分法在不等式证明中的应用

介绍了用微分法证明不等式的四种方法,借助这些方法可使各种不等式的证明简便易行.     

Natural Frequency of Full-Prestressed Concrete Beam

Dynamic tests of three bonded and two unbonded full-prestressed concrete beams were carried out.The purpose was to seek the relation between prestressing force and natural frequency.Test results indicate that the frequency of prestressed concrete(PSC)beam increases with the increase in prestressing force approximately.The results are different from the dynamic characteristics of isotropic material beam subjected to compressive axial force which were put forward by Clough et al.The reason is that the beams were considered as isotropic,homogeneous,linear elastic material in the traditional analysis method.However,more accurate results are required in the analysis of frequency of PSC beam.The constitutive mode of PSC member is analyzed based on microstructure of concrete in this paper.The orthotropic linear elastic mode is used to analyze the relation between dynamic frequency and prestressing force of concrete beam,at the same time the equivalent stiffness of prestressed tendon relating to the prestressing force is added to the bending deformation stiffness of the beam.The analytical value agrees well with the test result,indicating that the current analysis method in this paper is feasible to full-prestressed concrete beam.     

简支梁固有频率与固有振型的实验室测量与理论分析

具有连续结构的等截面简支梁是分析振动现象的一种常用工具．应用理论分析和实验测试的方法对等截面简支梁进行动力学分析,可以找出该连续系统振动的固有频率、振幅、临界阻尼．通过分析系统振动的固有频率、振幅和临界阻尼,避免了对机构破坏最大的共振现象的发生,达到主动避振的目的．从等截面简支梁固有频率与固有振型入手,为我们分析复杂机构的振动提供了参考方法．     

带分布质量梁的自振频率分析

通过离散化的质量分布 ,使梁成为一多自由度的力学系统 ,并研究它的自由振动的频率 ,以使外来动载荷的频率避开梁的自振频率 ,或改变梁的刚度 ,来改变梁的频率 ,以避免共振发生 ,达到安全生产的目的     

计算悬空管线固有频率的新方法

长输管线在石油工程中大量使用 .穿河段管线由于河水的冲刷变得悬空 ,如果管线附近的涡泻频率接近管线的固有频率 ,将引起悬空管线的共振 ,并且导致管线的破坏 .本文将悬空管线视为弹性基础上的半无限长梁 ,建立了悬空段管线和埋入土中管线的偏微分振动方程 ,提出了计算管线固有频率的迭代计算方法 ,实例计算结果同现场测试结果基本一致 .     

梁横向振动方程的离散谱估计

考虑梁横向振动方程的离散谱估计，获得了用前n个离散谱来估计第n 1个离散谱的上界的不等式的结果，估计系数与区间的几何度量无关，萁 结果在物理学和力学等领域中应用广泛。     

自然遗产地利益相关者共同治理机制研究——基于泰宁丹霞世界自然遗产地的调查

基于泰宁丹霞世界自然遗产地的调查,应用利益相关者理论为指导,分析了自然遗产地各主体的利益诉求及其与现实的符合度。分析认为,中国现行自然遗产管理实行的是单边治理方式,各主体因角色不同,利益出发点和关注点不同,现实利益符合度与其愿望诉求尚有差距,既是矛盾产生的根源也是合作的基础,进而在分析各主体角色定位的基础上。提出自然遗产地相关者参与共同治理的主张。共同治理机制包括兼容机制、管理机制和保障机制,并分别作为该机制的轴心、驱动和条件等三个基本构成。     

动态法测杨氏模量共振频率的拟合研究

分析讨论了动力学法测杨氏模量基频固有频率的最小二乘法拟合,指出在笔者采用数据的试验条件下,拟合多项式的幂次以3~4次为宜.