FLOW-INDUCED VIBRATION OF FREE EDGES OF THIN FILMS

During manufacturing processes of thin materials such as paper, photographic film, and magnetic film, which are handled as continuous sheets and subjected to drying air-flows, the interaction of the air with the web can cause the free edges to vibrate violently. This phenomenon is related to the waving motion of a flag in the wind, except that the thin films under consideration are under tension in the direction of the air-flow or at right angles to it. A travelling-wave analysis was done based on incompressible potential-flow theory; the critical flow speed, wave speed, wavelength, and flutter frequency were predicted. A closed-form solution of the critical flow speed is suggested. Experiments were carried out with stationary thin films mounted in a wind tunnel where the direction of tension was perpendicular to the flow direction. It was shown that the analysis, which assumes that the film is infinitely long in the flow direction, could successfully predict the critical flow speed above which violent edge vibrations occur.     

Stability Analysis of Maxwell Viscoelastic Pipes Conveying Fluid with Both Ends Simply Supported

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高速小展弦比机翼颤振的微分求积法分析

引入微分求积法,分析高速小展弦比机翼的气动弹性问题。将小展弦比机翼等效为悬臂板,基于一阶活塞气动力理论建立机翼颤振偏微分方程,采用微分求积法将偏微分方程转化为常微分方程,根据频率重合理论对颤振问题进行求解。分析了机翼的固有频率及颤振速度,并与有限元软件计算结果进行比较,误差在2％以内,很好的验证了微分求积法求解小展弦比机翼颤振问题的有效性。分析了机翼面积、展弦比及厚度对颤振速度的影响,结果表明,小展弦比机翼的颤振速度受结构尺寸的影响较大,颤振速度随面积和展弦比的增大而减小,随机翼厚度的增大而增大。     

Stability analysis of viscoelastic curved pipes conveying fluid

Based on the Hamilton' s principle for elastic systems of changing mass, a differential equation of motion for viscoelastic curved pipes conveying fluid was derived using variational method, and the complex characteristic equation for the viscoelastic circular pipe conveying fluid was obtained by normalized power series method. The effects of dimensionless delay time on the variation relationship between dimensionless complex frequency of the clamped-clamped viscoelastic circular pipe conveying fluid with the Kelvin-Voigt model and dimensionless flow velocity were analyzed. For greater dimensionless delay time, the behavior of the viscoelastic pipe is that the first, second and third mode does not couple, while the pipe behaves divergent instability in the first and second order mode, then single-mode flutter takes place in the first order mode.     

Effect of multiple engine placement on aeroelastic trim and stability of flying wing aircraft

Effects of multiple engine placement on flutter characteristics of a backswept flying wing resembling the HORTEN IV are investigated using the code NATASHA (Nonlinear Aeroelastic Trim And Stability of HALE Aircraft). Four identical engines with defined mass, inertia, and angular momentum are placed in different locations along the span with different offsets from the elastic axis while fixing the location of the aircraft c.g. The aircraft experiences body freedom flutter along with non-oscillatory instabilities that originate from flight dynamics. Multiple engine placement increases flutter speed particularly when the engines are placed in the outboard portion of the wing (60–70% span), forward of the elastic axis, while the lift to drag ratio is affected negligibly. The behavior of the sub- and supercritical eigenvalues is studied for two cases of engine placement. NATASHA captures a hump body-freedom flutter with low frequency for the clean wing case, which disappears as the engines are placed on the wings. In neither case is there any apparent coalescence between the unstable modes. NATASHA captures other non-oscillatory unstable roots with very small amplitude, apparently originating with flight dynamics. For the clean-wing case, in the absence of aerodynamic and gravitational forces, the regions of minimum kinetic energy density for the first and third bending modes are located around 60% span. For the second mode, this kinetic energy density has local minima around the 20% and 80% span. The regions of minimum kinetic energy of these modes are in agreement with calculations that show a noticeable increase in flutter speed if engines are placed forward of the elastic axis at these regions.     

A note on flow and heat transfer of a viscoelastic fluid over a stretching sheet

This paper presents a study of the flow and heat transfer of an incompressible homogeneous second grade fluid past a stretching sheet. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation. The effects of viscous dissipation and work due to deformation are considered in the energy equation and the variations of dimensionless surface temperature and dimensionless surface temperature gradient with various parameters are graphed and tabulated. Two cases are studied, namely, (i) the sheet with constant surface temperature (CST case) and (ii) the sheet with prescribed surface temperature (PST case).     

A THEORETICAL STUDY OF PAPER FLUTTER

Two different methods of analysis were developed in order to clarify the phenomenon of paper flutter. One of these is a flutter simulation using a Navier–Stokes code (N–S simulation). N–S simulation was used to determine the unsteady lift force, the amplitude of flutter, and the air-flow around a paper sheet, by means of a time-marching scheme. The other form of analysis is based on a potential-flow analysis of an oscillating thin airfoil via an eigenvalue analysis for determining stability. The flutter speeds and flutter modes obtained by each method are consistent. Aspects of the behavior of paper flutter that had not been clarified in the experimental analysis were clarified by potential flow analysis. From the results of this study, it was shown that potential flow analysis is very convenient and adequate for a parametric study of this problem.     

采用分布式压电驱动器升力面的颤振主动抑制

对采用分布式压电驱动器升力面的颤振主动抑制进行了理论与试验研究.应用 LQG最优控制法设计了主动控制律,在控制律降阶时提出了平衡实现与LK法结合使用的新途径,在对不定常气动力进行有理函数拟合时对LS法进行了改进.试验中利用激光测速仪非接触测量模型的速度响应并在地面共振试验中用压电驱动器激振模型.颤振风洞试验结果表明,理论计算合理并与试验结果吻合良好.     

Mechanics of slitting and cutting webs

The quality of edges formed during cutting and slitting of thin polymer webs is important for many industrial applications. To control the edge quality of the separated material, it is necessary to understand cutting. A model is proposed, and the mechanics of cutting are described. Experiments were conducted on polyethylene terephthalate. Photoelastic micrographs were used for qualitative and quantitative observations of the two-dimensional stress distributions. The results of this analysis supported the model for cutting of thin polymer webs. An apparatus was constructed to instrument, monitor and control the web-slitting process. The slitting speed, tension in the web and angle of cut were varied during tests. This allowed a quantitative understanding of the cutting mechanisms to be established. The results of the experiments showed that the in-plane cutting forces were minimally affected by changes in rate or web tension. The angle of cut had a pronounced effect on the in-plane cutting forces and the stability of the cut. The results are a beginning of a mechanistic understanding of deformation taking place during slitting and cutting. The experimentation emphasized an instability in slitting. An understanding of this instability will allow quality web edges with minimal deformation and straight stable cuts to be achieved.     

Dimensionless modeling and nonlinear analysis of a coupled pitch–plunge–leadlag airfoil-based piezoaeroelastic energy harvesting system

In this paper, an airfoil-based piezoaeroelastic energy harvesting system is proposed with an additional supporting device to harvest the mechanical energy from the leadlag motion. A dimensionless dynamic model is built considering the large-effective-angle-of-attack vibrations causing (1) the nonlinear coupling between the pitch–plunge–leadlag motions, (2) the inertia nonlinearity, and (3) the aerodynamic nonlinearity modeled by the ONERA dynamic stall model. Cubic hardening stiffness is introduced in the pitch degree of freedom for persistent vibrations with acceptable amplitude beyond the flutter boundary. The nonlinear aeroelastic response and the average power output are numerically studied. Limit cycle oscillations are observed and, as the flow velocity exceeds a secondary critical speed, the system experiences complex vibrations. The power output from the leadlag motion is smaller than that from the plunge motion, whereas the gap is narrowed with increasing flow velocity. Case studies are performed toward the effects of several dimensionless system parameters, including the nonlinear torsional stiffness, airfoil mass eccentricity, airfoil radius of gyration, mass of the supporting devices, and load resistances in the external circuits. The optimal parameter values for the power outputs from the plunge and leadlag motions are, respectively, obtained. Beyond the secondary critical speed, it is shown that the variations of the power outputs with those parameters become irregular with fluctuations and multiple local maximums. The bifurcation analysis shows the mutual transitions between the limit cycle oscillations, multi-periodic vibrations, and possible chaos. The influences of these complex vibrations on the power outputs are discussed.     

联接刚度对机翼／外挂系统颤振边界特性的影响

本文对带外挂物二元机翼的颤振特性进行了理论和实验研究,主要分析机翼与外挂物之间俯仰联接刚度对颤振边界的影响。在大量算例的分析基础上,给出了颤振频率及颤振边界变化的一般规律及对颤振边界类型的一般判别方法,颤振模型的风洞实验验证了理论分析结果的正确性。     

A first assessment of the NEPTUNE_CFD code: Instabilities in a stratified flow comparison between the VOF method and a two-field approach

This paper presents some results concerning a first benchmark for the new European research code for thermal hydraulics computations: NEPTUNE_CFD. This benchmark relies on the Thorpe experiment to model the occurrence of instabilities in a stratified two-phase flow. The first part of this work is to create a numerical trial case with the VOF approach. The results, in terms of time of onset of the instability, critical wave-number or wave phase speed, are rather good compared to linear inviscid theory and experimental data. Additional numerical tests showed the effect of the surface tension and density ratio on the growing dynamics of the instability and the structure of the waves. In the second part, a code to code (VOF/multi-field) comparison is performed for a case with zero surface tension. The results showed some discrepancies in terms of wave amplitudes, growing rates and a time shifting in the global dynamics. Afterward, two surface tension formulations are proposed in the multi-field approach. Both formulations provided similar results. The time for onset of the instability, the most amplified wave-number and its amplitude were in rather good agreement with the linear analysis and VOF results. However, the time-shifted dynamics was still observed.     

动态多稳态压电风能俘能结构设计与实验验证

传统的线性颤振式风能俘能结构在变风速环境下转换效率不高。针对此问题,本文提出了一种动态多稳态颤振式压电俘能结构,可在较宽的风速范围内保持较高的电压输出。该结构由矩形平板、压电悬臂梁与3块永磁体组成,并通过磁吸力实现结构的多稳态。通过在不同风速下开展的能量转换特性实验研究,发现当风速较小时,该结构具有双稳态特性;而当风速较大时,会出现新的稳定位置,结构变为三稳态系统。这样的动态稳定位置,可以保证结构在很宽的风速范围内出现阱间跳跃,进而保持大的电能输出。实验结果表明,这种动态多稳态结构,风速在2.0m/s—7.5m/s区间变化时,能够激发并保持阱间跳跃,甚至相干共振,产生较大的电能输出。     

线弹簧和转动弹簧支承粘弹性圆柱体的动力特性

对线、转动弹簧支承三参量模型粘弹性圆柱体轴向流动中的特征方程进行了推导,运用Matlab软件求解了其在轴向流动中的前三阶复频率.给出了当质量比β、量纲为一的延滞时间α和弹性系数比λ一定时,改变量纲为一的弹簧刚度a和转动弹簧b的情况下,三参量模型粘弹性圆柱体的前三阶模态量纲为一的复频率的实部及虚部与流速ν之间的关系曲线图;并分析了量纲为一的弹簧刚度对圆柱体动力特性的影响.研究结果表明:三参量模型粘弹性圆柱体分别处于两端固定和两端自由状态的两种特殊情况:两种情况下,第一阶模态的临界发散速度几乎相同,但当圆柱体两端自由时,第三阶模态发散的无量纲临界流速明显小于两端固定的圆柱体.且当ν=0时,两种情况下的前三阶复频率的虚部都相等.     

Numerical investigation of the influence of gravity on flutter of cantilevered pipes conveying fluid

We have carried out a numerical investigation of the three dimensional nonlinear dynamics of a cantilevered pipe conveying fluid in the presence of gravity. The pipe may be misaligned at the clamped end with respect to gravity, and the effects of this misalignment are the main objects of the present investigation. The problem has been formulated using the Cosserat rod model. First, we have computed the equilibrium solutions and used them to experimentally validate both the Cosserat model and the constitutive law. Then, we have analyzed the occurrence of flutter, via Hopf bifurcation, for critical values of the relevant parameters of the problem, such as fluid to total mass ratio, dimensionless flow rate, dimensionless gravity and misalignment angle. The influence of the equilibrium solution on flutter has been explored, and the results of the linear stability analysis show that the stabilizing or destabilizing effect of fluid flow, either in or out of the plane of the pipe, depend crucially on the misalignment. We have also computed the non-linear periodic behavior after flutter instability by two different methods: the first one is by solving the full nonlinear equations by direct integration in time and space, while the second one is by assuming the time dependence given by an appropriate ansatz. Circular periodic orbits have then been studied and found that its loss of stability via Hopf bifurcation gives rise to stable planar periodic orbits. Finally, we have also computed the multiply periodic and chaotic behaviors which take place for sufficiently large values of the flow rate.     

Anticlastic curvature in draw-bend springback

Draw-bend springback shows a sudden decline as the applied sheet tension approaches the force to yield the strip. This phenomenon coincides with the appearance of persistent anticlastic curvature, which develops during the forming operation and is maintained during unloading under certain test conditions. In order to understand the mechanics of persistent anticlastic curvature and its dependence on forming conditions, aluminum sheet strips of widths ranging from 12 to 50 mm were draw-bend tested with various sheet tensions and tool radii. Finite element simulations were also carried out, and the simulated and measured springback angle and anticlastic curvature were compared. Analytical methods based on large deformation bending theory for elastic plates were employed to understand the occurrence and persistence of the anticlastic curvature. The results showed that the final shape of a specimen cross-section is determined by a dimensionless parameter, which is a function of sheet width, thickness and radius of the primary curvature in the curled region of an unloaded sample. When the normalized sheet tension approaches 1, this parameter rapidly decreases, and significant anticlastic deflection is retained after unloading. The retained anticlastic curvature greatly increases the moment of inertia for bending, and thus reduces springback angle.     

三参量固体模型粘弹性输流管道的动力特性分析

推导了三参量固体模型粘弹性输流管道的振动微分方程 ,计算了在不同无量纲松弛系数和弹性常数比下管道的无量纲临界流速和无量纲自振复频率 ,并给出了前三阶复频率与流速的关系 .计算结果表明 ,质量比、无量纲松弛系数及无量纲弹性常数比对输流管道的动力特性均有影响 .     

Dynamic stability of a pipe conveying fluid with an uncertain computational model

This paper deals with the problem of a pipe conveying fluid of interest in several engineering applications, such as micro-systems or drill-string dynamics. The deterministic stability analysis developed by Paidoussis and Issid (1974) is extended to the case for which there are model uncertainties induced by modeling errors in the computational model. The aim of this work is twofold: (1) to propose a probabilistic model for the fluid–structure interaction considering modeling errors and (2) to analyze the stability and reliability of the stochastic system. The Euler–Bernoulli beam model is used to model the pipe and the plug flow model is used to take into account the internal flow in the pipe. The resulting differential equation is discretized by means of the finite element method and a reduced-order model is constructed from some eigenmodes of the beam. A probabilistic approach is used to model uncertainties in the fluid–structure interaction. The proposed strategy takes into account global uncertainties related to the noninertial coupled fluid forces (related to damping and stiffness). The resulting random eigenvalue problem is used to analyze flutter and divergence unstable modes of the system for different values of the dimensionless flow speed. The numerical results show the random response of the system for different levels of uncertainty, and the reliability of the system for different dimensionless speeds and levels of uncertainty.     

Effects of vertical central stabilizers on nonlinear wind-induced stabilization of a closed-box girder suspension bridge with various aspect ratios

The aerodynamic shape of a closed-box girder plays an important role in the wind-induced stabilization of long-span suspension bridges. The purpose of this study is to investigate the effects of the combination of five aspect ratios and a downward vertical central stabilizer (DVCS) on nonlinear flutter and aerostatic behaviors of a super long-span suspension bridge with closed-box girders. Through conducting a series of wind-tunnel tests and nonlinear finite element analysis, the results show that the nonlinear self-excited forces and the critical wind speed (U_cr) gradually increase as the increase of the aspect ratio (i.e. the width to depth ratios). Furthermore, the application of 20% deck depth DVCS could significantly increase the nonlinear self-excited forces and U_cr for small aspect ratios of 7.9 and 7.1. Particularly, the installation of the DVCS could change the flutter divergence patterns of the bridge from soft flutter to hard flutter, especially for a relatively small aspect ratio. In addition, the aerostatic force coefficients and torsional divergence critical wind speeds of the larger aspect ratio with DVCS are significantly larger than that without DVCS. A relatively small aspect ratio of the bridge has better aerostatic performance than that with a larger aspect ratio.

     

A plane stress anisotropic plastic flow theory for orthotropic sheet metals

A phenomenological theory is presented for describing the anisotropic plastic flow of orthotropic polycrystalline aluminum sheet metals under plane stress. The theory uses a stress exponent, a rate-dependent effective flow strength function, and five anisotropic material functions to specify a flow potential, an associated flow rule of plastic strain rates, a flow rule of plastic spin, and an evolution law of isotropic hardening of a sheet metal. Each of the five anisotropic material functions may be represented by a truncated Fourier series based on the orthotropic symmetry of the sheet metal and their Fourier coefficients can be determined using experimental data obtained from uniaxial tension and equal biaxial tension tests. Depending on the number of uniaxial tension tests conducted, three models with various degrees of planar anisotropy are constructed based on the proposed plasticity theory for power-law strain hardening sheet metals. These models are applied successfully to describe the anisotropic plastic flow behavior of 10 commercial aluminum alloy sheet metals reported in the literature.