确定性载荷作用下Timoshenko薄壁梁的弯扭耦合动力响应

建立了一种普遍的解析理论用于求解确定性载荷作用下Timoshenko薄壁梁的弯扭耦合动力响应。首先通过直接求解单对称均匀Timoshenko薄壁梁单元弯扭耦合振动的运动偏微分方程，给出了计算其自由振动的精确方法，并导出了Timoshenko弯扭耦合薄壁梁自由振动主模态的正交条件。然后利用简正模态法研究了确定性载荷作用下单对称Timoshenko薄壁梁的弯扭耦合动力响应，该弯扭耦合梁所受到的荷载可以是集中载荷或沿着梁长度分布的分布载荷。最后假定确定性载荷是谐波变化的，得到了各种激励下封闭形式的解，并对动力弯曲位移和扭转位移的数值结果进行了讨论。     

三参数粘弹性地基上层合板的自由和强迫振动

基于三参数粘弹性地基模型及Reddy高阶剪切变形板理论,用双重Fourier级数形式解求得粘弹性地基上四边简支对称正交及反对称斜交层合板的各模态自由振动频率的解析解,以及这两种层合板在任意横向动荷载作用下动力响应的半解析解。通过参数分析讨论了粘弹性地基参数、边厚比等因素对自振频率及动力响应的影响。结果表明,地基的剪切刚度和压缩刚度提高了板的自振频率而降低了板的振动幅值,地基的粘性作用不可忽略。     

轴向受载的Timoshenko薄壁梁的弯扭耦合动力响应

利用简正模态法研究各种集中载荷和分布载荷作用下单对称轴向受载的Timoshenko薄壁梁的弯扭耦合动力响应。该弯扭耦合梁所受到的载荷可以是集中载荷或沿着梁长度分布的分布载荷。目前研究中采用考虑了轴向载荷、剪切变形和转动惯量影响的Timoshenko薄壁梁理论。首先建立轴向受载的Timoshenko薄壁梁结构的普遍运动微分方程并进行其自由振动的分析。一旦得到轴向受载的Timoshenko薄壁梁的固有频率和模态形状，利用简正模态法计算薄壁梁结构的弯扭耦合动力响应。针对具体算例，提出并讨论了动力弯曲位移和扭转位移的数值结果。     

开闭裂纹转子的弯扭耦合振动研究

以水平放置的Jeffcott裂纹转子为研究对象，建立了开闭裂纹转子弯扭耦合振动的非线性运动微分方程，并用数值方法分析了纯弯曲振动与弯扭耦合振动情况下转子的动力响应。结果表明：弯扭耦合振动是由转子质量的偏心和转子自重的共同作用而产生的，当质量偏心很小时可以不考虑扭转振动的影响，当偏心较大时，扭转对弯曲振动的影响主要体现在高转速部分，且由于裂纹开闭的作用，使扭转的耦合作用存在一个范围，随裂纹深度的增加，扭振影响的转速下限就会越低，但当裂纹较深、转速较快时，扭转对弯曲振动在作用范围内有明显的影响，使频谱图和轴心轨迹都发生较大的变化，且对转速的变化极为敏感，因此在故障诊断时必须对扭转的耦合作用高度重视。     

弹性撞击作用下弯扭耦合梁的动力响应

对于质量块以一定初速度撞击悬臂梁端部问题,基于弯扭耦合Timoshenko梁模型,把质量块与悬臂梁作为一个整体振动,动力响应以Duhamel积分表示,使用模态叠加法给出动力响应与撞击力的结果.对于悬臂梁受质量块撞击的算例,分别分析了弯扭耦合梁、弯扭耦合系数很小的梁和各向同性Timoshenko梁,对比讨论了撞击力结果.     

端承粘弹性桩纵向振动的轴对称解析解

将桩和土体视为粘弹性介质,在频率域求得了桩轴对称纵向振动时动力响应的解析解,进而得到桩头复刚度的解析表达式.通过数值计算,给出了桩头动刚度因子和等效阻尼随激励频率的响应,考察了土层粘性、桩长径比、桩土模量比、桩泊松比和粘性等参数对桩头刚度因子和等效阻尼的影响.研究表明:由于考虑了桩的径向变形效应以及土层对桩的径向力作用...     

弯扭耦合振动对次同步谐振响应的影响

建立了考虑弯扭耦合作用时 ,大型气轮发电机组转子轴系与电网耦合次同步谐振 ( SSR)的 1 9维非线性模型。运用数值方法 ,确定系统平衡位置稳定性的转变点 ,着重分析了在不同偏心条件下 ,弯曲振动与扭转振动之间的相互影响 ,同时给出了轴系弯曲刚度对系统稳定性的影响 ,证明在正常情况下 ,由偏心引起的弯扭耦合作用是非常弱的 ,可以不予考虑     

平面偏心结构的三维能力谱方法

基于单自由度模型的性态评估方法,无法考虑偏心结构平扭耦联效应且不便于考虑双向地震动输入,存在很大的局限性.本文在对水平偏心结构模态分析的基础上,利用OpenSees构建等效三自由度模型(ETDOF),将该模型用于双向地震动作用下偏心结构平扭耦联简化计算和性态评估.在对ETDOF模型进行振动特性分析的基础上,基于等位移原...     

层间接触对沥青路面粘弹性动力响应影响研究

为分析沥青面层材料粘弹特性及路面各层间接触条件对沥青路面动力响应的影响,基于解析的方法,开展了层间非完全连续沥青路面粘弹性动力响应的求解工作．采用修正的Burgers模型定义沥青面层材料的粘弹性本构关系,考虑沥青路面层间接触条件,在车辆荷载作用下,建立沥青路面的理论计算模型;通过Laplace-Hankel积分变换将偏微分方程组转化为常微分方程组并对问题进行求解;采用转换矩阵表征层间接触条件,求得层间非完全连续沥青路面粘弹性动力响应的解析表达式．从沥青路面实例计算结果发现：修正的Burgers模型中的瞬时弹性模量参数是对弯沉计算结果影响最大的因素之一,路表弯沉随的增大呈下降趋势,特别是当较小时,这种趋势尤为明显;沥青混合料本构模型中的粘弹性修正系数B和黏性参数是影响路面路表弯沉计算结果的另两个重要因素,并且B和对弯沉峰值出现时间的影响具有相反的趋势;层间的非完全连续条件对沥青路面动态弯沉计算结果影响较大,并以面层与基层间的非完全连续对弯沉计算结果影响最为显著．     

考虑粘弹性材料频变特性的复合结构频率响应分析

论文采用基于Layerwise离散层理论的有限元板单元建模粘弹性阻尼复合结构,发展了一种考虑粘弹性材料的频变特性的复合结构频率响应计算方法.该方法首先计算结构的质量矩阵和各个频率点下的结构复刚度矩阵,然后求解运动方程的若干阶复特征对并由此计算各阶模态的传递函数,最后将各模态传函线性叠加得到近似的总传函.为了提高计算效率,论文采用了一种高效的数值方法,即只计算若干频率点下的特征向量与特征值,并计算这些点处特征向量关于频率的高阶导数,通过泰勒系数展开逼近和Rayleigh商式,可求得附近若干频率点处的特征向量和特征值,从而避免了在各个频率点下求解大自由度结构特征方程的问题,可以极大地提高计算效率.对一端简支的三层约束阻尼梁算例进行了分析,并与文献中的结果作对比,结果验证了方法的有效性和计算效率.     

大学物理《力学》中的自由度分析

对《力学》中的物体自由度进行多方面分析,以深化教学、提高学生正 确分析物理问题的能力.使用实际教学分析的研究方法,在《力学》范围内讨论自由度与坐标、 自由与约束的关系并得以下结论: (1) 同一物体的自由度随其所在的``空间'不同而不同, 不因坐标系的选取不同而 异, 在同类参考系中不因参考系的动静而有别;(2)自由度遵循叠加原理. 讨论了质点系的总自由度及相关计算问题,并指出研究《力学》中自由度的意义.     

Development and design of new methods of measurement of state of strain of structures

The present paper deals with development and design of new methods utilizing Wiedemann's effect for determination of state of strain in building structures. Wiedemann's effect and some features of torsional strain of magnetic field are the basis of new experimental method. Especially the point electromagnetic strain gages using the effect of pure torsion of electromagnetic field to enable universal examination. For strain-gage measurements, almost all physical quantities are used which can be related to the variation in length of the structures. From the electric strain measurements, the most commonly used methods are the measurements by resonance-wire strain gages or by electric-resistance strain gages. In this paper, electromagnetic strain gages are discussed using the Wiedemann effect, and the author describes some new measuring equipment and his own suggestions and methods based on an application of this effect.     

Calculation of aerodynamic characteristics of arrays of profiles of arbitrary shape

It is well known that the problem on nonseparating potential flow of an incompressible fluid about an array of profiles reduces to an integral equation for a certain real function, determined on the contours of the profiles of the array. As such a function one can take, as was done, for instance, in [1–5], the relative velocity of the fluid on the profiles of the array. For arrays of profiles of arbitrary shape it is necessary to solve the corresponding integral equation numerically. In the particular examples of the calculation of aerodynamic arrays that are available [1–3] the numerical methods used were based on the approximate evaluation of contour integrals by rectangle formulas. As investigations showed, sizeable errors arose thereby in the approximate solution obtained, these being especially significant in the case of curved profiles of relatively small bulk. In the present paper a method for the numerical solution of the integral equation obtained in [5] is proposed. The method is based on the replacement of a profile of the array with an inscribed N polygon, the length of whose sides is of the order N^–1 and whose internal angles are close to . Convergence with increasing N of the numerical solution to an exact solution of the integral equations at the reference points is demonstrated. Examples of the calculation are given.Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 105–112, March–April, 1972.     

Method of constructing estimates of the solution of equations of filtration of an aerated liquid

The exact solutions of the nonlinear equations of filtration of an aerated liquid have been obtained in [1–3]. In [4] the system of equations of an aerated liquid have been reduced to the heat-conduction equation under certain assumptions. An approximate method of computing the nonsteady flow of an aerated liquid is given in [5], where the real flow pattern is replaced by a computational scheme of successive change of stationary states. In [6] the same problem is solved by the method of averaging. In the present article estimates of the solution of the equations for nonstationary filtration of an aerated liquid in one-dimensional layer are constructed under certain conditions imposed on the desired functions. These estimates can be used as approximate solutions with known error or for the verification of the accuracy of different approximate methods. We note that the use of comparison theorem for the estimate of solutions of equations of nonlinear filtration is discussed in [7–9]. The methods of constructing estimates of solutions of various problems of heat conduction are given in [10, 11]