Vibration tailoring of inhomogeneous rod that possesses a trigonometric fundamental mode shape

In this study, a special class of closed-form solutions for inhomogeneous rod is investigated. Namely, the following problem is considered: determine the distribution axial rigidity when the material density is given of an inhomogeneous rod so that the postulated fundamental trigonometric mode shape serves as an exact vibration mode. In this study, the associated semi-inverse problem is solved that results in the distributions of axial rigidity that together with a specified law of material density satisfy the governing eigenvalue problem. For comparison, the obtained closed-form solutions are contrasted with approximate solutions based on an appropriate polynomial shapes, serving as trial functions in an energy method. The obtained results are utilized for vibration tailoring, i.e. construction of the rod with a given natural frequency.     

Coupled flexural-torsional vibration of beams in the presence of static axial loads and end moments

The problem of coupled flexural-torsional vibration of a deep rectangular beam in the presence of a static axial load and an end moment is studied. Closed form analytical solutions are obtained for simply supported boundary conditions. Numerical results are obtained for the coupled frequencies and mode shapes (in terms of the location of axes of rotation of the cross-section) for different values of the load and the geometry parameters. The results show that the predominantly flexural frequencies of coupled flexural-torsional vibration can be obtained as uncoupled flexural frequencies of an equivalent beam-column by defining an effective axial load, and that by defining an equivalent moment parameter the presentation of the results for the predominantly flexural mode can be made in a form independent of the slenderness of the beam in the depth direction.     

非光滑叶片对轴流风扇气动性能的影响

在低速轴流风扇实验台上,通过对比测量光滑转子叶片、两种表面具有流向沟槽的非光滑转子叶片风扇的气动性能,研究了叶片沟槽面对风扇气动性能的影响.结果表明:(1)在设计状态和小流量状态,采用微槽型非光滑叶片能提高该风扇的流量、降低总压损失和提高风扇总压升;(2)在近失速状态,非光滑叶片使风扇性能下降;(3)非光滑叶片对风扇性能的影响在很大程度上取决于非光滑叶片的沟槽尺寸.     

尾缘凹陷轴流风轮内流特性分析与降噪研究

为减少空调室外机用低压轴流风轮叶片的颤振,改善音质,降低噪音和电机功率。本文设计了尾缘凹陷新型三叶轴流风轮,同时除对前缘局部加厚处理外,对叶片其他区域整体减薄。文中采用Navier-Stokes方程对新风轮和原风轮的内流及气动特性进行了三维数值模拟,同时对两者的流量压力曲线和噪音频谱进行了实验研究。研究表明:对轴流风轮叶片尾缘进行凹陷设计,对前缘以外的区域减薄设计,能够减轻风轮重量,降低电机负荷同时减弱转子尾迹;对叶轮前缘进行局部加厚处理可以减小叶尖颤振,降低叶片旋转频率峰值噪音,从整体上降低噪音,改善音质。     

Fundamental frequency evolution in slender beams subjected to imposed axial displacements

The influence of applied axial loads on the fundamental vibration frequency is strictly connected with the stability analysis of elastic slender beams. For this reason, the correct evaluation of the fundamental frequency is of primary importance in designing new structures and components, as well as in monitoring existing ones. At the same time, if an internal axial load arises in a slender element as the consequence of an imposed (static) axial end displacement, then a different dynamic structural response is encountered respect to the case in which a beam end is free to slide, during transverse vibration, and a (constant) axial load is applied externally. This difference is due to the change in the axial boundary condition. Moreover, the presence of an initial curvature of the beam axis may significantly affect the aforesaid response. The experimental study proposed in the present paper investigates the dependence of the fundamental frequency on the axial load in slender beams subjected to imposed axial end displacements. The considered specimens presented different geometrical imperfections (initial curvatures), and were tested in two different constraint conditions (hinged–hinged and hinged–clamped). In addition, the behaviors observed during the experiments were reproduced by numerical simulations offering a valid confirmation for test results and contributing to understand the evolution of the fundamental frequency in the analyzed slender elements subjected to imposed axial end displacements.     

Transient wave propagation in a semi-infinite,transversely isotropic rod

In this study the response in a transversely isotropic, semi-infinite elastic rod is found to an input on its end that is time dependent. The solution follows closely the method developed by Skalak for isotropic rods which uses integral transforms to solve the governing equations. The solution differs from that of Skalak, apart from material properties, in that in this study mixed-mixed conditions are assumed for the end of the rod. The responses are found at a “distant” station and are expressed in terms of the axial and tangential strains.     

Longitudinal vibration and stability analysis of carbon nanotubes conveying viscous fluid

Nowadays, carbon nanotubes (CNT) play an important role in practical applications in fluidic devices. To this end, researchers have studied various aspects of vibration analysis of a behavior of CNT conveying fluid. In this paper, based on nonlocal elasticity theory, single-walled carbon nanotube (SWCNT) is simulated. To investigate and analyze the effect of internal fluid flow on the longitudinal vibration and stability of SWCNT, the equation of motion for longitudinal vibration is obtained by using Navier-Stokes equations. In the governing equation of motion, the interaction of fluid-structure, dynamic and fluid flow velocity along the axial coordinate of the nanotube and the nano-scale effect of the structure are considered. To solve the nonlocal longitudinal vibration equation, the approximate Galerkin method is employed and appropriate simply supported boundary conditions are applied. The results show that the axial vibrations of the nanotubesstrongly depend on the small-size effect. In addition, the fluid flowing in nanotube causes a decrease in the natural frequency of the system. It is obvious that the system natural frequencies reach zero at lower critical flow velocities as the wave number increases. Moreover, the critical flow velocity decreases as the nonlocal parameter increases.     

Investigation on the Flow Field Entropy Structure of Non-Synchronous Blade Vibration in an Axial Turbocompressor

In order to explore the inducing factors and mechanism of the non-synchronous vibration, the flow field structure and its formation mechanism in the non-synchronous vibration state of a high speed turbocompressor are discussed in this paper, based on the fluid–structure interaction method. The predicted frequencies f_BV (4.4EO), f_AR (9.6EO) in the field have a good correspondence with the experimental data, which verify the reliability and accuracy of the numerical method. The results indicate that, under a deviation in the adjustment of inlet guide vane (IGV), the disturbances of pressure in the tip diffuse upstream and downstream, and maintain the corresponding relationship with the non-synchronous vibration frequency of the blade. An instability flow that developed at the tip region of 90% span emerged due to interactions among the incoming main flow, the axial separation backflow, and the tip leakage vortices. The separation vortices in the blade passage mixed up with the tip leakage flow reverse at the trailing edge of blade tip, presenting a spiral vortex structure which flows upstream to the leading edge of the adjacent blade. The disturbances of the spiral vortexes emerge to rotate at 54.5% of the rotor speed in the same rotating direction as a modal oscillation. The blade vibration in the turbocompressor is found to be related to the unsteadiness of the tip flow. The large pressure oscillation caused by the movement of the spiral vortex is regarded as the one of the main drivers for the non-synchronous vibration for the present turbocompressor, besides the deviation in the adjustment of IGV.     

出气边形状对叶栅中凝结流动影响机理的数值研究

湿蒸汽两相凝结流中凝结过程对流场参数的变化敏感。本文对一个叶型五种出气边形状对应的凝结流动进行了比较,以初步揭示几何参数影响凝结流动的机理。结果显示,出气边形状的改变影响凝结流中水滴状态、熵增、湿度、出口气流角的分布。在本文计算条件下,当出气边为平行于切向的平面时,流动中熵增最小,叶栅出口处湿度也最小,其原因在于这种出气边形状造成的流场参数改变使叶栅中蒸汽凝结过程受到抑制,叶栅出口蒸汽仍然维持了较高的非平衡程度。     

汽轮机调节阀内流动特性的试验研究

介绍了最常用的G-I型调节阀内的动态压力测量方法及其各关键部位的流动特性,尤其是引起不稳定流动的主要因素即气流的压力脉动特性。测试结果表明,调节阀处于不稳定工作状态即阀杆振动工况取决于脉动压力与阀杆固频率是否同频,并非其脉动压力值大小;调整阀杆固有频率是消除调节阀振动最简便和有效的方法。     

Active control of low-frequency sound radiation by cylindrical shell with piezoelectric stack force actuators

A novel active control method of sound radiation from a cylindrical shell under axial excitations is proposed and theoretically analyzed. This control method is based on a pair of piezoelectric stack force actuators which are installed on the shell and parallel to the axial direction. The actuators are driven in phase and generate the same forces to control the vibration and the sound radiation of the cylindrical shell. The model considered is a fluid-loaded finite stiffened cylindrical shell with rigid end-caps and only low-frequency axial vibration modes are involved. Numerical simulations are performed to explore the required control forces and the optimal mounting positions of actuators under different cost functions. The results show that the proposed force actuators can reduce the radiated sound pressure of low-frequency axial modes in all directions.     

Dynamic strain of a longitudinally vibrating viscoelastic rod with an end mass

The dynamic strain of a viscoelastic rod excited into longitudinal simple harmonic vibration, a constant amplitude displacement being maintained by a shaker at one end and a mass terminating the other end, is theoretically investigated in this paper. The general equation of the strain distribution in the rod is derived by solving the one-dimensional wave equation. It is shown that the strain in the rod is the largest at the excited end, at the antiresonant frequencies. Simplified approximate equations are derived for the low loss case to calculate the largest strain in the rod with knowledge of the loss factor.     

激光二极管阵列端面抽运复合棒状激光器热效应的有限元法分析

建立了激光二极管阵列(LDA)端面抽运棒状激光介质的数值模型.考虑到介质与空气的对流换热和介质的热力学参数随温度的变化,根据经典热传导方程和热弹性方程,运用有限元法得出了复合棒状介质和未复合棒状介质内瞬态温度、热应力和应变的时空分布,分析了温度、热应力和应变随抽运功率、换热系数和时间的变化规律.结果表明,复合棒的最高温度、最大张应力和最大轴向应变的位置与未复合棒不同,并且数值分别为未复合棒的73%,60%和33%.由此可知,利用复合棒可极大地减小热效应的影响.理论分析结果可为LDA抽运固体激光器的结构优化设计和实验研究提供理论参考.     

The influence of the wake on the stability of cantilevered flexible plates in axial flow

Cantilevered flexible plates in axial flow lose stability through flutter. Using the inextensibility condition for the cantilevered nonlinear plate equation of motion and the unsteady lumped-vortex model to calculate the fluid loads, a flutter boundary has been obtained. In the time-domain analysis performed to this end, the wake behind the oscillating cantilevered plate is assumed to issue tangentially from the free trailing edge and extend downstream with an undulating form. The influence of the wake on system stability may be characterized in terms of the non-dimensional mass ratio, reduced flow velocity and flutter frequency. For large values of the mass ratio, the plate vibrates with high frequency and high-order mode content. It is shown that the wake has less influence on system stability for long plates than it does for short ones.     

端面受到空气阻力的弹性杆的振动

研究了一端固定、一端受到空气阻力的弹性杆的振动.建立了受阻力端的近似边界条件.本征振动模式含有阻尼振动特有的指数衰减因子,但不具有分离变量的形式.因为边界条件不属于斯特姆-刘维型,所以关于本征函数的完备性和正交性的一般定理不适用于本问题.用拉普拉斯变换法求解了任意给定初始条件下的振动.     

菱形HSLDS隔振器负刚度机构质量及摩擦力影响分析

以菱形负刚度机构HSLDS(high static low dynamic stiffness)隔振器(简称菱形HSLDS隔振器)为研究目标,采用虚功法建立负刚度机构等效摩擦力模型,并以拉格朗日方法建立包含负刚度机构质量及摩擦力因素的动力学方程;利用谐波平衡法(HBM)求解动力学方程,分析了负刚度机构质量及摩擦力对隔振...     

圆截面弹性螺旋杆的稳定性与振动

基于Kirchhoff理论讨论圆截面弹性螺旋杆的动力学问题.以杆中心线的Frenet坐标系为参考系，建立用欧拉角描述的弹性杆动力学方程.讨论其在端部轴向力和扭矩作用下保持的无扭转螺旋线平衡状态.在静力学和动力学领域内讨论其平衡稳定性问题.还讨论了弹性杆平衡的Lyapunov稳定性和欧拉稳定性两种不同稳定性概念之间的区别和联系.在一次近似意义下证明了螺旋杆在空间域内的欧拉稳定性条件是时域内Lyapunov稳定性的必要条件.导出了解析形式螺旋杆三维弯曲振动的固有频率，为螺旋线倾角和受扰挠性线波数的函数. 关键词： 弹性螺旋杆 Kirchhoff动力学比拟 Lyapunov稳定性 欧拉稳定性     

非定常尾迹控制叶栅分离研究

本文采用大涡模拟对某大转角叶栅的非定常分离流动及其在非定常尾迹作用下的分离控制机理进行了数值分析。主要捕捉了两个特征频率:分离泡不稳定频率f_shear和尾缘脱落涡频率f_shed,研究了不同的激励频率、尾迹移动方向、随机脉动等激励特征控制流动分离的效果。结果显示:特定外部频率强化了分离剪切层中的K-H展向涡结构,f_shed能同时影响分离区域和尾涡区域,f_shear只能作用于分离区域;尾迹从吸力面向压力面移动时,分离结构表现出对来流周期性更明显的响应;进口随机脉动对破坏K-H展向涡结构非常有效。     

Numerical flow visualization of a Single Expansion Ramp Nozzle with hypersonic external flow

Numerical simulation of scramjet asymmetric nozzle flow is carried out to visualize and investigate the effects of interaction between engine exhaust and hypersonic external flow. The Single Expansion Ramp Nozzle (SERN) configuration studied here consists of flat ramp and a cowl with different combinations of ramp angle and cowl geometry. UsingPARAS 3D, simulations are performed for a free stream Mach number of 6.5 that constitutes the external flow around the vehicle. Appropriate specific heats ratio has been simulated for the jet and free stream flow. External shock wave due to jet plume interaction with free stream flow, the internal barrel shock wave and the shear layer emanating from the cowl trailing edge and sidewalls are well captured. Wall static pressure distribution on the nozzle ramp for different nozzle expansion angles has been computed for both with and without side fence. Axial thrust and normal force have been evaluated by integrating the wall static pressure. Effect of cowl length variation and side fence on the SERN performance has also been studied and found to be quite significant. Based on this study, an optimum ramp angle at which the SERN generates maximum axial thrust is obtained. SERN angle of 20° was found to be optimum when the flight axis coincides with nozzle axis.     

On dynamics of elastic rod based on exact Cosserat model

The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical equations of a rod with arbitrary initial shape are established in general form. The dynamics of a straight rod under axial tension and torsion is discussed as an example. In discussion of static stability in the space domain the Greenhill criteria of stability and the Euler load are corrected by the influence of tension and shear strain. In analysis of dynamical stability in the time domain it is shown that the Lyapunov and Euler stability conditions of the rod in space domain are the necessary conditions of Lyapunov's stability in the time domain. The longitudinal, torsional and lateral vibrations of a straight rod based on exact model are discussed, and an exact formula of free frequency of lateral vibration is obtained. The free frequency formulas of various simplified models, such as the Rayleigh beam, the Kirchhoff rod, and the Timoshenko beam, can be seen as special cases of the exact formula under different conditions of simplification.