Pasternak地基上输流管道固有频率计算分析

分别使用复模态法和Galerkin模态截断方法计算Pasternak地基上两端铰支输流管道的固有频率,并通过与复模态法计算得到的精确解的比较,以说明Galerkin法模态截断对固有频率计算结果的影响,然后研究Pasternak地基剪切刚度和弹簧刚度以及质量参数对截断误差的影响。研究结果表明:在固定的流速范围内,地基剪切刚度和弹簧刚度的增大均可以减小Galerkin法的截断误差,但与前者相比,后者的作用可以忽略不计;同时伴随质量参数的增大,截断误差也将迅速的增加。     

Timoshenko模型轴向运动梁的横向振动特性分析

通过对梁微单元体的受力分析,导出Timoshenko模型的轴向运动梁横向振动的运动方程, 并利用复模态分析方法及半解析半数值方法, 研究两端铰支条件下轴向运动梁横向振动的振动模态及固有频率.文中还讨论运动梁前两阶固有频率随轴向运动速度变化的情况.最后利用数值算例对Timoshenko梁、Euler梁、Rayleigh梁及剪切梁的固有频率进行比较, 分析转动惯量及剪切变形的影响.     

一种提高管道临界流速计算效率的方法

使用复模态法和Galerkin模态截断法分别计算了Pasternak地基上两端铰支输流管道的临界流速,并通过与复模态法计算得到的精确解的比较,证明了Galerkin模态截断法对临界流速计算结果具有一定的影响。研究了Pasternak地基剪切刚度和弹簧刚度对截断误差的影响。计算结果表明:地基剪切刚度对管道系统临界流速的影响比弹簧刚度要大,且前者的增加可以减小Galerkin法的截断误差,但后者的增加则会增大这一误差。在此基础上,提出了分区域系数确定方法,并针对不同管道地基刚度,通过合理选取Galerkin法阶数,提高了输流管道临界流速计算效率。     

Winkler地基上输流管道的临界流速分析

应用Galerkin法和复模态法研究Winkler弹性地基上两端铰支输流管道的临界流速问题。将系统偏微分控制方程进行Galerkin离散后,根据系统静态失稳条件求得临界流速,并利用复模态法对偏微分控制方程直接求解加以验证。结果表明:较低阶Galerkin法只适用于弱刚性地基情况,而当地基刚性比较强时,采用较高阶Galerkin法才能得到精确的结果。研究同时发现,临界流速只与地基刚度及管道轴向预紧力有关,而管道黏弹性系数及质量比等参数不会影响临界流速。     

轴向运动简支-固支梁的横向振动和稳定性

研究一端简支一端固支轴向运动梁的横向振动和稳定性。提出在给定边界条件下确定一匀速运动梁固有频率和模态函数的方法。当轴向运动速度在其常平均值附近作简谐波动时,应用多尺度法给出轴向变速运动梁参数共振时的不稳定条件。用数值仿真说明相关参数对固有频率和不稳定边界的影响。     

关于EBZ160型掘进机减速器振动过程的分析与研究

以EBZ160掘进机减速器为研究对象,介绍了有限元计算模态的基本理论,并基于有限元分析模态分析方法,对该型掘进机的一级与二级行星减速器模态进行分析.分析结果表明,一级行星齿轮最低固有频率为97.57 Hz,二级行星齿轮的最低固有频率为96.35 Hz,其均有沿轴向方向的窜动,所以减速器的结构设计应考虑限制轴向位移,以避免设备产生比较剧烈的振动.同时在设备的使用中,应避开前几阶固有频率,对掘进机减速器模态分析研究.该研究结论可为减速器的结构设计、整机性能的提高奠定理论基础.     

非线性轴向运动黏弹性Rayleigh梁受迫振动的微分求积法

研究了轴向运动黏弹性Rayleigh梁的非线性受迫振动。运用广义Hamilton原理推导出梁和边界条件的非线性控制方程。通过复模态法计算固有频率和模态函数。运用多尺度法获得主共振的稳态响应,根据Routh-Hurwitz分析稳态响应的稳定性,同时得到粘性阻尼,力和非线性系数的影响曲线。如果存在不稳定区域,通过增加粘性阻尼或减小力可使稳态响应的稳定。运用微分求积法对轴向黏弹性梁的受迫振动进行数值分析,并与多尺度分析进行对比,以此来证明了多尺度法的结果的正确性。     

旋转柔性悬臂梁的固有频率分析

在精确描述柔性梁非线性变形基础上,利用Lagrange方程推导出考虑动力刚化项的一次近似刚柔耦合动力学方程。忽略柔性梁纵向变形的影响,给出一次近似简化模型,引入无量纲变量,对简化模型作无量纲化处理,首先分析模态截断数对固有频率的影响,其次研究一次近似简化模型和零次近似简化模型的振动特性。研究发现,梁固有频率与模态截断数有关,合理的模态截断数应随无量纲角速度的增大而适当增加;一次近似简化模型的固有频率随无量纲角速度和系统径长比的增大而增大,零次近似简化模型的固有频率随无量纲角速度增大而减小;一次近似简化模型下梁横向弯曲振动不存在物理意义上的共振失稳现象。现有典型文献的相关结论值得商榷。     

人字齿行星传动固有特性及模态突变现象分析

建立了NGW型人字齿行星传动的平移-扭转耦合动力学模型。依托所建模型,推导出系统的运动微分方程,进而通过求解特征值问题获知系统的固有频率和振型。根据传动系统的运动特征,将NGW型人字齿行星传动的自由振动归纳为3种典型振动模式,即:中心构件轴向扭转振动模式、中心构件径向平移振动模式和行星轮振动模式。在模态跃迁、相交原则的基础上,从振动模式和模态能量角度进一步分析了两种固有频率轨迹突变现象对传动特性的影响。结果表明,模态相交现象发生时,固有频率振动模式和模态能量均发生突变式交换;模态跃迁现象发生时,模态能量发生突变但不交换,且突变较平缓,而振动模式不变。最后,通过具体实例仿真验证了所得结论的正确性。论文工作可有效预估人字齿行星传动系统的固有频率及模态、能量突变位置,从而为减噪抑振及参数优化提供基本的理论依据。     

大型分体式磁轴承电动机系统定子模态分析

准确分析定子固有模态对低振动噪声电机系统优化设计和控制有十分重要的意义。针对大型分体式磁轴承电动机系统,采用有限元仿真方法分析轴向磁轴承定子绕组、径向磁轴承定子叠片结构、机座螺栓连接以及底座附加质量对大型分体式磁轴承电动机系统定子模态的影响。结果表明:轴向轴承定子绕组对定子固有频率影响较大,宜采用质量计入铁心的方式处理;径向轴承定子叠片结构对定子固有频率的影响较小,可按各向同性处理;机座螺栓连接刚度对机座固有频率有一定影响,但当连接刚度远大于机座刚度时,影响较小;底座附加质量对整机模态频率有一定的影响,但对不同振型的固有频率的影响效果相差较大。计算了整机的模态频率,并与振动试验结果进行了对比验证。     

轴向运动耦合热弹梁的稳定性分析

研究了轴向运动梁的耦合热弹稳定性.根据轴向运动梁的运动微分方程和考虑变形影响时的热传导方程,得出了温度场和变形场耦合情况下梁的耦合热弹运动微分方程.对两端简支轴向运动梁耦合热弹振动的复频率进行了数值计算,得出了无量纲复频率与无量纲运动速度之间的关系曲线.分析了无量纲热弹耦合因子、无量纲运动速度和梁的长高比对梁的临界速度和稳定性的影响.     

Natural frequencies,modes and critical speeds of axially moving Timoshenko beams with different boundary conditions

In this paper, natural frequencies, modes and critical speeds of axially moving beams on different supports are analyzed based on Timoshenko model. The governing differential equation of motion is derived from Newton's second law. The expressions for various boundary conditions are established based on the balance of forces. The complex mode approach is performed. The transverse vibration modes and the natural frequencies are investigated for the beams on different supports. The effects of some parameters, such as axially moving speed, the moment of inertia, and the shear deformation, are examined, respectively, as other parameters are fixed. Some numerical examples are presented to demonstrate the comparisons of natural frequencies for four beam models, namely, Timoshenko model, Rayleigh model, Shear model and Euler–Bernoulli model. Finally, the critical speeds for different boundary conditions are determined and numerically investigated.     

轴向运动功能梯度梁的横向振动

新型非均匀复合材料,功能梯度材料具有防止脱层和减缓热应力等优良性能,将其应用于功能梯度梁的结构有着非常重要的工程应用价值。基于Euler-Bernoulli梁理论和Hamilton原理,建立轴向运动功能梯度梁横向自由振动的运动微分方程,其中假设功能梯度梁的材料特性沿梁厚度方向按各组分材料体积分数的幂函数连续变化;再对运动微分方程和边界条件进行量纲一处理,采用微分求积法对其进行离散化,导出系统的广义复特征方程,然后计算分析轴向运动功能梯度简支梁横向振动复频率的实部和虚部随量纲一轴向运动速度、梯度指标等参数的变化情况,并讨论量纲一轴向运动速度和梯度指标对功能梯度梁的横向振动特性以及失稳形式的影响。     

Non-linear free vibrations of Kelvin–Voigt visco-elastic beams

A full visco-elastic non-linear beam with cubic non-linearities is considered, and the governing equations of motion of the system for large amplitude vibrations are derived. By using the method of multiple scales, the non-linear mode shapes and natural frequencies of the beam are then analytically formulated. The resulting formulations for amplitude, non-linear natural frequencies and mode shapes can be used for any type of boundary conditions. Next, method of Galerkin is used to separate the time and space variables. The equations of motion show the presence of a non-linear damping term in addition to the ones with non-linear inertia and geometry. As it is known, the presence of non-linear inertia and the geometric terms make the non-linear natural frequencies to be dependent on constant amplitude of vibration. But, when damping non-linearities are present, it is seen that the amplitude is exponentially time-dependent, and so, the non-linear natural frequencies will be logarithmically time-dependent. Additionally, it is shown that the mode shapes will be dependent on the third power of time-dependent amplitude. The analytical results are applied to hinged–hinged and hinged–clamped boundary conditions and the results are compared with numerical simulations. The results match very closely for both cases specially for the case of hinged–hinged beam.     

Rotary inertia and temperature effects on non-linear vibration, steady-state response and stability of an axially moving beam with time-dependent velocity

Free non-linear transverse vibration of an axially moving beam in which rotary inertia and temperature variation effects have been considered, is investigated. The beam is moving with a harmonic velocity about a constant mean velocity. The governing partial-differential equations are derived from the Hamilton's principle and geometrical relations. Under special assumptions, the two partial-differential equations can be mixed to form one integro-partial-differential equation. The multiple scales method is applied to obtain steady-state response. Elimination of secular terms will give us the amplitude of vibration. Additionally, the stability and bifurcation of trivial and non-trivial steady-state responses are analyzed using Routh-Hurwitz criterion. Eventually, numerical examples are presented to show rotary inertia, non-linear term, temperature gradient and mean velocity variation effects on natural frequencies, critical speeds, bifurcation points and stability of trivial and non-trivial solutions.     

Dynamic Behaviors of Axially Moving Viscoelastic Plate with Varying Thicknessn

Structural components of varying thickness draw increasing attention these days due to economy and light-weight considerations. In view of the absence of research in vibration analysis of viscoelastic plate with varying thickness, this study devotes to investigate the dynamic behaviors of axially moving viscoelastic plate with varying thickness. Based on the thin plate theory and the two-dimensional viscoelastic differential constitutive relation, the differential equation of motion of the axially moving viscoelastic rectangular plate is derived, the plate constituted by Kelvin-Voigt model has linearly varying thickness in the y-direction. The dimensionless complex frequencies of axially moving viscoelastic plate with four edges simply supported are calculated by the differential quadrature method, curves of real parts and imaginary parts of the first three-order dimensionless complex frequencies versus dimensionless moving speed are obtained, the effects of the aspect ratio, thickness ratio, the dimensionless moving speed and delay time on the dynamic behaviors of the axially moving viscoelastic rectangular plate with varying thickness are analyzed. When other parameters keep constant, with the decrease of thickness ratio, the real parts of the first three-order natural frequencies decrease, and the critical divergence speeds of various modes decrease too, moreover, whether the delay time is large or small, the frequencies are all complex numbers.     

Free transverse vibration of an axially loaded non-uniform spinning twisted Timoshenko beam using differential transform

This study investigates the vibration problems of an axially loaded non-uniform spinning twisted Timoshenko beam. First, using the Timoshenko beam theory and Hamilton's principle, we derive the governing equations and boundary conditions of the beam. Secondly, the differential transform method is used to solve these equations with appropriate boundary conditions. Finally, the effects of the twist angle, spinning speed, and axial force on the natural frequencies of a non-uniform Timoshenko beam are investigated and discussed.     

磁场中轴向运动导电板磁弹性主共振分析

给出轴向运动薄板动能、应变能以及电磁力虚功的表达形式。应用哈密顿变分原理,推得横向磁场中轴向运动条形导电薄板的非线性磁弹性振动方程。针对对边简支边界约束条件,通过位移函数的设定并应用伽辽金积分法,得到三阶位移展开形式下轴向运动板的非线性振动微分方程组。利用多尺度法对系统的主共振问题进行求解,分别得到三种频率关系条件下关于稳态解的幅频响应方程。依据李雅普诺夫稳定性理论对解的稳定性进行分析,得到相应的稳定性判别式。通过数值算例,得到轴向速度、磁感应强度、激励力幅值及板厚不同时的振幅变化规律曲线图,分析不同参量对共振幅值和非线性特征的影响,并对不同频率关系进行比较。     

磁场中轴向变速运动载流梁的参强联合共振

研究磁场环境中轴向变速运动载流梁在简谐激励作用下的参强联合共振问题,应用弹性力学理论、电磁场基本理论以及哈密顿变分原理,得到轴向变速运动载流梁的非线性磁弹性耦合振动方程。利用伽辽金积分法对其进行时间变量和空间变量的离散化,进而运用多尺度法以及坐标变换的方法求得系统主共振-主参数共振的幅频响应方程。通过算例,得到了系统随不同参数变化的幅频响应曲线图、时间历程图、相轨迹图、庞加莱映射图和共振系统的动相平面轨迹图,分析了轴向速度、轴向拉力、磁感应强度、电流密度及强迫激励对系统主共振-主参数共振特性的影响,结果表明系统呈现典型的非线性振动特征和复杂的动力学行为。