弹性支承输流管道的动力学特性

研究两端弹性支承输流管道横向振动的动力学特性。根据梁模型横向弯曲振动模态函数,由两端弹性支承的边界条件得到其模态函数的一般表达式。根据特征方程具体分析弹性支承刚度、质量比、流体压力和流速、管截面轴向力等主要参数对管道固有特性及失稳临界流速的影响。数值计算结果表明,管道固有频率随弹性支承刚度、管截面轴向拉力的增加而增大,随流体流速、流体压强和管截面轴向压力的增加而下降;静态失稳临界流速则随弹性支承刚度、流体压强、管截面轴向压力的增加而下降,随管截面轴向拉力的增加而上升。     

结构梁损伤的频响函数幅值变化特征分析

为了识别振动筛下横梁的损伤特征,探寻结构梁损伤在线监测的有效途径,通过理论计算与实验模态分析,从两方面系统地研究了结构损伤对其局部刚度的影响,得到了弯曲振动梁的频响函数特征变化与其弯曲刚度下降及梁的损伤程度之间的关系,并分别给出了梁在自由状态与约束状态下的结构损伤程度与频响函数幅值变化之间的定量关系,这种定量关系可以用来进行结构梁损伤的在线监测。     

黏弹性梁弯曲振动的复模态分析

发展复模态分析研究黏弹性梁的弯曲振动。将梁的控制方程写作状态变量的形式，然后利用复模态的正交性可解耦为无穷多个彼此独立的常微分方程组。基于固有频率和模态函数，可以得到黏弹性梁对于任意初始条件和外激励的响应。在固支梁的边界条件下确定黏弹性梁的固有频率、衰减系数和模态函数，并计算梁受两种典型的外激励时的响应。     

两端支承输流管道的稳定性和临界流速分析

推导两端支承梁弯曲振动的频率方程和振型函数的解析表达式。利用频率方程讨论两端扭转弹簧刚度变化对梁的前两阶弯曲振动特征值的影响。以两端支承梁的振型函数为假设振型导出两端支承输流管道在定常流作用下临界速度的解析表达式,为今后分析这类系统的动态响应提供理论依据。利用临界流速公式系统地分析和讨论扭转刚度、重力系数和轴向预紧力对管道临界流速的影响特性。研究结果表明,量纲一扭转弹簧刚度在0到50区间内变化时对临界流速的影响较大,但大于50时影响明显减弱。当重力系数和轴向预紧力增大时,临界流速也随着增大。一般而言,两端扭转弹簧刚度越大也会增大相应的临界流速值。     

带弹性支承的角接触球轴承动态特性分析

针对航空发动机中的轴承支承模型,在有限元分析和轴承动力学的基础上,采用修正的Craig-Bampton固定界面模态综合法,建立了弹性支承结构与刚性的轴承外圈、轴承座之间的耦合连接,开发了带弹性支承的角接触球轴承动力学分析模型,分析并讨论了不同工况下,弹性支承体对轴承振动特性的影响。结果表明:与刚性支承相比,弹性支承能够降低系统固有频率下的振动幅值。轴承在轴向力作用下,力较小时,增大支承体的刚度能够降低振动幅值,力较大时,采用适当刚度的弹性支承有利于减小振动幅值;轴承在径向力作用下,存在一个合理的弹性支承刚度,使径向振动幅值达到最小。     

一种分析旋转梁振动的梁柱有限元

针对旋转柔性梁的弯曲振动问题,提出了一种高精度的有限元——梁柱元。根据旋转梁弯曲时与梁柱相同的受力特点,推导了梁柱元弯曲变形的形状函数,采用传递矩阵方法导出了单元的刚度矩阵及相应的一致质量阵。证明了梁柱元刚度矩阵中各元素的泰勒展开式前两项正好是采用常规弯曲梁元形状函数得到的弹性刚度矩阵和几何刚度矩阵对应的元素的和,因而采用梁柱元分析旋转梁元弯曲振动问题具有很好的精度。对铰支和固支旋转梁振动分析的数值算例也证明了这个结论。     

弹性支承的汽车悬架轴承单元振动故障研究与试验验证

针对弹性支承下的悬架轴承振动噪声问题,基于ABAQUS建立悬架轴承和弹性支承单元模型,并结合Hertz弹性理论对不同刚度支承下轴承的载荷和应力分布进行了有限元分析。结果表明:弹性支承刚度过低时,轴承发生较大弯曲变形,部分钢球会脱离正常运行沟道引起异常接触,导致轴承力矩增加和波动,从而引起故障;而随着支承刚度的增加,轴承变形逐渐减小,与支承刚度呈线性关系,运行状态得到改善;并对不同刚度的支承进行试验,验证了有限元法的正确性。     

车体垂弯振型节点位置对其弹性振动的影响

根据车体的结构属性和质量分布将其考虑为多段变截面欧拉梁，建立包含车体一阶垂弯模态的车辆垂向动力学模型，研究车体一阶垂弯振型的节点位置对高速列车振动舒适度的影响，提出改善车体弹性振动的措施。基于变截面欧拉梁模型分析车体各截面的质量和抗弯刚度分布对模态振型的影响，发现不同截面之间的抗弯刚度和质量分布对整体模态振型影响显著，提高车体中部结构的抗弯刚度并减小其质量，可以增大节点间距和提高模态频率，而传统均直等截面梁模型则不能准确描述振型的幅值和节点位置。采用频域分析方法计算车辆在轨道随机激励下的振动响应，将车体垂弯振型节点调整到转向架二系上方附近时，车体的弹性振动水平显著降低，在车速为300 km/h时车辆舒适度指标可降低50%。     

粘弹性支承柔性转子的动力学分析

运用有限元方法,对一端带粘弹性支承、另一端弹性支承的柔性转子进行动力学分析。基于Timoshenko梁单元模型建立系统的有限元模型和运动方程,以考虑转子的柔性和轮盘的陀螺效应。对系统进行自由振动和受迫振动分析,计算转子在不同支承条件下的临界转速与不平衡响应等,探究粘弹性支承的弹性刚度、损耗因子对系统动力学特性的影响。结果表明,粘弹性支承的弹性刚度能显著影响系统的临界转速和不平衡响应。较大的损耗因子能降低不平衡响应,但降低的程度会受到弹性刚度的影响。     

求解任意梁的普遍化方法

介绍了一种求解任意弹性梁的新方法。该方法利用奇异函数与拉普拉斯变换相结合的方法导出弹性梁弯曲变形的普遍表达式,并利用边界条件和约束处的变形协调条件确定约束反力和变形常数(左端面的挠度和转角),对由固定和活动铰链支座、径向和角度弹性支承以及固定端等支承形式任意组合而成的,具有任意支承沉降的,承受任意载荷(集中力、集中力偶和均布力)的,具有任意阶梯形状的静定或超静定弹性梁具有普遍的适用性。该方法可以方便、准确地确定任意梁在支座处的约束反力以及任一截面的挠度和转角等参数,可用于复杂梁的计算机分析、优化设计和计算机辅助设计。     

Free vibration analysis of beams with non-ideal clamped boundary conditions

A non-ideal boundary condition is modeled as a linear combination of the ideal simply supported and the ideal clamped boundary conditions with the weighting factors k and 1-k, respectively. The proposed non-ideal boundary model is applied to the free vibration analyses of Euler-Bernoulli beam and Timoshenko beam. The free vibration analysis of the Euler-Bernoulli beam is carried out analytically, and the pseudospectral method is employed to accommodate the non-ideal boundary conditions in the analysis of the free vibration of Timoshenko beam. For the free vibration with the non-ideal boundary condition at one end and the free boundary condition at the other end, the natural frequencies of the beam decrease as k increases. The free vibration where both the ends of a beam are restrained by the non-ideal boundary conditions is also considered. It is found that when the non-ideal boundary conditions are close to the ideal clamped boundary conditions the natural frequencies are reduced noticeably as k increases. When the non-ideal boundary conditions are close to the ideal simply supported boundary conditions, however, the natural frequencies hardly change as k varies, which indicate that the proposed boundary condition model is more suitable to the non-ideal boundary condition close to the ideal clamped boundary condition.     

Creative approach for the deflection formula according to relative length of supporting edge in a partially supported circular plate

The purpose of this investigation is to derive the maximum deflection formula of the circular plate with nonaxisymmetric boundary condition, such as chalk valves for vessel and artificial heart valves, with respect to the length ratio of supporting edge using elastic beam theory. To evaluate the deflection characteristics of this plate, we assumed the circular plate to have a cross-section that varies in the longitudinal direction, and derived the maximum deflection formula of this circular plate with a radius of ‘r’ in four boundary conditions. Then to verify the deflection formula that is derived from elastic beam theory, five different relative lengths of the supporting edge were adopted as the design parameter, and finite element analysis was carried out for each model.     

Experimental behaviour of a fixed ended beam under simulated uniformly distributed load

The behaviour of an aluminium beam of constant rectangular cross section which is fully restrained against translation and rotation and subjected to a simulated uniformly distributed load is investigated. It is shown experimentally and supported analytically that the axial end restraint has a significant stiffening effect on the post-elastic behaviour when the central plastic zone spreads towards the beam ends. The engineering bending theory which includes axial force effects gives an accurate prediction of the pre-yield behaviour and the rigid-plastic theories are shown to give a close approximation to the load/central deflection response for a real fixed ended beam in the plastic range.     

一种微开关悬臂梁的静力变形分析模型及其应用

建立一种微开关悬臂梁的静力变形分析模型,该模型将微开关悬臂梁的受力变形分为三个阶段,受电场力作用的悬臂梁阶段,受电场力作用的一端固支、另一端铰支的单跨梁阶段以及受电场力和集中力联合作用而保持自由端有指定的位移和零转角阶段。第二阶段中铰支端支反力的大小以及第三阶段中集中力的大小和作用位置均与电场力的驱动电压有关;同时文中将求解微开关悬臂梁挠度的高阶微分方程问题转化为含有未知初始条件的一阶微分方程组问题。在实例中,设计一种求解未知初始条件的迭代方法,并给出部分计算结果,从中可得出一些有益的结论。     

弹性地基上转动功能梯度材料Timoshenko梁自由振动的微分变换法求解

基于Timoshenko梁理论研究弹性地基上转动功能梯度材料（FGM）梁的自由振动。首先确定功能梯度材料Timoshenko梁的物理中面,利用广义Hamilton原理推导出该梁在弹性地基上转动时横向自由振动的两个控制微分方程。其次采用微分变换法（DTM）对控制微分方程及其边界条件进行变换,计算了弹性地基上转动功能梯度材料Timoshenko梁在夹紧-夹紧、夹紧-简支和夹紧-自由三种不同边界条件下横向自由振动的量纲一固有频率,与已有文献的计算结果进行比较,退化后结果一致。最后讨论了不同边界条件、转速、弹性地基模量和梯度指数对功能梯度材料Timoshenko梁自振频率的影响。结果表明：功能梯度材料Timoshenko梁的量纲一固有频率随量纲一转速和量纲一弹性地基模量的增大而增大;在量纲一转速和量纲一弹性地基模量一定的情况下,梁的量纲一固有频率随着功能梯度材料梯度指数的增大而减小。     

Influence of in-plane displacements at the boundaries of rigid-plastic beams and plates

An approximate theoretical rigid-plastic study has been undertaken into the influence of small in-plane displacements at the boundaries of various laterally loaded beams. The most interesting feature of these theoretical predictions is the remarkably small in-plane displacements at the supports which can change the response from that of an axially restrained beam, with considerable reserve strengthening beyond the limit load for moderate lateral deflections, to that of a freely supported beam with no concomitant increase in strength beyond the limit load. A comparison has also been made between some theoretical predictions for a laterally loaded square plate and the corresponding experimental results obtained by Clarkson on rotationally fixed plates with edges free to slide inwards.     

Exact analysis of resonance frequency and mode shapes of isotropic and laminated composite cylindrical shells; Part I: analytical studies

In order to study the free vibration of simply supported circular cylindrical shells, an exact analytical procedure is developed and discussed in detail. Part I presents a general approach for exact analysis of natural frequencies and mode shapes of circular cylindrical shells. The validity of the exact technique is verified using four different shell theories 1) Soedel, 2) Flugge, 3) Morley-Koiter and 4) Donnell. The exact procedure is compared favorably with experimental results and those obtained using a numerical finite element method. A literature review reveals that beam functions are used extensively as an approximation for simply supported boundary conditions. The accuracy of the resonance frequencies obtained using the approximate method are also investigated by comparing results with those of the exact analysis. Part II presents effects of different parameters on mode shapes and natural frequencies of circular cylindrical shells.     

纤维增强FGM梁的自由振动和临界屈曲载荷分析

基于经典梁理论（CBT）研究轴向力作用下纤维增强功能梯度材料（FGM）梁的横向自由振动和临界屈曲载荷问题。首先考虑由混合律模型来表征纤维增强FGM梁的材料属性,其次利用Hamilton原理推导轴向力作用下纤维增强FGM梁横向自由振动和临界屈曲载荷的控制微分方程,并应用微分变换法（DTM）对控制微分方程及边界条件进行变换,计算了纤维增强FGM梁在固定-固定（C-C）、固定-简支（C-S）和简支-简支（S-S）3种边界条件下横向自由振动的无量纲固有频率和无量纲临界屈曲载荷。退化为各向同性梁和FGM梁,并与已有文献结果进行对比,验证了本文方法的有效性。最后讨论在不同边界条件下纤维增强FGM梁的刚度比、纤维体积分数和无量纲压载荷对无量纲固有频率的影响以及各参数对无量纲临界屈曲载荷的影响。     

Plates in uniaxial compression with various support conditions at the unloaded boundaries

A theoretical investigation is presented for the behaviour after buckling of plates loaded in compression with the unloaded edges subject to various support boundary conditions. The loaded ends are uniformly compressed and simply supported and the unloaded edges are considered to be either elastically restrained against rotation to an equal or unequal degree on both edges, or to be rotationally restrained on one edge and free on the other.