The influence of Murnaghan constants on the propagation of a torsional wave in pre-stretched compound circular cylinders

The propagation of torsional waves in prestressed compound circular cylinders is investigated modeling them by a piecewise-homogeneous body and using the three-dimensional linearized theory of elastic waves in prestressed body. It is assumed that the elastic relations for the components of the cylinders include the Murnaghan potential. The numerical investigations are performed for bronze (Br) or brass (Pr) (for the solid cylinder) and steel (St) (for the hollow cylinder). The effect of the variation of the geometric (the ratio of the thickness of the outer cylinder to the radius of the inner cylinder) and mechanical parameters on the dispersion curves are analyzed using the numerical results obtained     

Dynamic analysis of thick short length FGM cylinders

In this paper a thick short length hollow cylinder made of functionally graded materials (FGMs) under internal impact loading is considered. The inner surface of the cylinder is pure ceramic, the outer surface is pure metal, and the material composition varies continuously along its thickness. Finite Element Method based on Rayleigh-Ritz energy formulation has been applied to study the propagation of elastic waves in FG thick hollow cylinders. The Newmark direct integration method is applied to solve the time dependent equations. The time histories of displacements, stresses, wave propagation in two directions and velocities of radial stress wave propagation for various values of volume fraction exponent have been investigated. Also by using fast Fourier transform, the first natural frequencies for FG cylinders with simply-simply and clamped-clamped ends conditions are illustrated. The model has been compared with result of a plane strain FG thick hollow cylinder which is subjected to an internal impact loading, and it shows very good agreement.     

45钢柱壳爆炸膨胀断裂的SPH模拟分析

金属柱壳爆炸膨胀断裂存在拉伸、剪切及拉剪混合等多种断裂模式,目前其物理机制及影响因素还不清晰。本文中采用光滑粒子流体动力学方法（smoothed particle hydrodynamics, SPH）对45钢柱壳在JOB-9003及RHT-901不同装药条件下的外爆实验进行了数值模拟,探讨柱壳在不同装药条件下发生的剪切断裂、拉剪混合断裂模式及其演化过程,模拟结果与实验结果一致。SPH数值模拟结果表明:在爆炸加载阶段,随着冲击波在柱壳内、外壁间来回反射形成二次塑性区,沿柱壳壁厚等效塑性应变演化呈凸形分布,壁厚中部区域等效塑性应变较内、外壁大;在较高爆炸压力（JOB-9003）作用下,柱壳断裂发生在爆轰波加载阶段,损伤裂纹从塑性应变积累较大的壁厚中部开始沿剪切方向向内、外壁扩展,形成剪切型断裂模式;而在RHT-901空心炸药加载下,虽然裂纹仍从壁厚中部开始沿剪切方向扩展,但随后柱壳进入自由膨胀阶段,未断区域处于拉伸应力状态,柱壳局部发生结构失稳,形成类似“颈缩”现象,裂纹从剪切方向转向沿颈缩区向外扩展,呈现拉剪混合断裂模式。拉伸裂纹占截面的比例与柱壳结构失稳时刻相关。可见,柱壳断裂演化是一个爆炸冲击波与柱壳结构相互作用的过程,不能简单将其作为一系列膨胀拉伸环处理。     

Hydroelastic analysis of surface wave interaction with concentric porous and flexible cylinder systems

The present study deals with the hydroelastic analysis of gravity wave interaction with concentric porous and flexible cylinder systems, in which the inner cylinder is rigid and the outer cylinder is porous and flexible. The problems are analyzed in finite water depth under the assumption of small amplitude water wave theory and structural response. The cylinder configurations in the present study are namely (a) surface-piercing truncated cylinders, (b) bottom-touching truncated cylinders and (c) complete submerged cylinders extended from free surface to bottom. As special cases of the concentric cylinder system, wave diffraction by (i) porous flexible cylinder and (ii) flexible floating cage with rigid bottom are analyzed. The scattering potentials are evaluated using Fourier–Bessel series expansion method and the least square approximation method. The convergence of the double series is tested numerically to determine the number of terms in the Fourier–Bessel series expansion. The effects of porosity and flexibility of the outer cylinder, in attenuating the hydrodynamic forces and dynamic overturning moments, are analyzed for various cylinder configurations and wave characteristics. A parametric study with respect to wave frequency, ratios of inner-to-outer cylinder radii, annular spacing between the two cylinders and porosities is done. In order to understand the flow distribution around the cylinders, contour plots are provided. The findings of the present study are likely to be of immense help in the design of various types of marine structures which can withstand the wave loads of varied nature in the marine environment. The theory can be easily extended to deal with a large class of problems associated with acoustic wave interaction with flexible porous structures.     

Stability of flow between two rotating cylinders in the presence of a constant heat flux at the outer cylinder and radial temperature gradient – wide gap problem

The stability of Couette flow of a viscous incompressible fluid between two concentric rotating cylinders in the presence of a radial temperature gradient due to a constant heat flux at the outer cylinder is studied. The critical values of `a' (the wave number) and Ta (the Taylor number) are listed in a table and some critical Taylor numbers are shown graphically. It is shown that as the heat flux is increased the flow becomes more unstable for all values of μ calculated, where μ is the ratio of the angular velocity of the outer cylinder to that of the inner cylinder. Received on 04 March 1997     

Water surface wave radiation generated by multiple cylinders oscillating with identical frequency

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Features of flow-induced forces deduced from wavelet analysis

In the present study, the effect of Reynolds number (Re) on flow interference between two side-by-side stationary cylinders and the associated flow-induced forces are investigated using finite element method and wavelet analysis. The pitch ratio chosen is T/D=1.7, where T is the separation distance measured between cylinder centers and D is the diameter, and Re, based on the free-stream velocity and the diameter of the cylinder, is varied within the laminar flow regime, i.e., 60<Re<200. The method of continuous wavelet transform is used to analyze time-variant features of flow-induced forces in the time–frequency domain. Flow patterns in the form of vorticity plots are presented to demonstrate the underlying physics. It is found that flow interference initially occurs in the inner vortices shed from the two cylinders, and extends to the outer vortices with increasing Re. The flow behind two cylinders undergoes three regimes: Regime I—unbiased gap flow, Regime II—stable biased gap flow, and Regime III—unstable gap flow. Flow-induced forces show significant variations when the flow transits from one regime to another. In particular, during the transition from Regimes II to III, the forces not only increase by amplitude, but also change their nature from deterministic to random, and show some nonstationary features. This is shown to be caused by the amalgamation of inner and outer vortices behind the two cylinders when the flow interference extends from inner vortices to outer vortices. Whenever possible, the present results are compared with experimental measurements and theoretical predictions. The numerical simulations are consistent with these other results.     

Determination of the thermal stress wave propagation in orthotropic hollow cylinder based on classical theory of thermoelasticity

The thermoelasticity problem in a thick-walled orthotropic hollow cylinder is solved analytically using finite Hankel transform and Laplace transform. Time-dependent thermal and mechanical boundary conditions are applied on the inner and the outer surfaces of the cylinder. For solving the energy equation, the temperature itself is considered as boundary condition to be applied on both the inner and the outer surfaces of the orthotropic cylinder. Two different cases are assumed for solving the equation of motion: traction–traction problem (tractions are prescribed on both the inner and the outer surfaces) and traction–displacement (traction is prescribed on the inner surface and displacement is prescribed on the outer surface of the hollow orthotropic cylinder). Due to considering uncoupled theory, after obtaining temperature distribution, the dynamical structural problem is solved and closed-form relations are derived for radial displacement, radial and hoop stress. As a case study, exponentially decaying temperature with respect to time is prescribed on the inner surface of the cylinder and the temperature of the outer surface is considered to be zero. Owing to solving dynamical problem, the stress wave propagation and its reflections were observed after plotting the results in both cases.     

多层电磁弹性圆柱壳内波的轴向传播

对多层电磁弹性圆柱壳内波的轴向传播进行了分析。根据柱坐标系下电磁弹性多层结构的几何方程、平衡方程和本构方程,推导出了两个层间变量所满足的状态方程。通过状态方程的解和层间变量连续性条件,得到了多层圆柱体内外表面层间变量的传递关系。最后利用边界条件,导出了波在传播时所满足的频散方程,并求得该结构的模态参数。以一个三层的压电/压磁材料组成的柱壳结构作为数值算例,计算出波在其中轴向传播时的频散关系和模态参数,并对计算结果进行了分析。     

Purely tangential flow of a PTT-viscoelastic fluid within a concentric annulus

An analytical solution is presented for the steady state, purely tangential flow of a viscoelastic fluid obeying the Phan-Thien–Tanner (PTT) constitutive equation in a concentric annulus with relative rotation of the inner and outer cylinders. The influence on the velocity distribution within the annulus and on fRe of the Weissenberg number, aspect ratio and an elongational parameter are investigated. The results show that the differences between the radial location of the minimum velocity and of the critical angular velocity compared with their Newtonian counterparts increase as the fluid elasticity increases. The results also show that fRe decreases with increasing Weissenberg number, radius ratio and the elongational parameter in the case of inner-cylinder rotation. In contrast, fRe increases with increasing radius ratio when the outer cylinder is rotating while the inner cylinder is at rest.     

Direct numerical simulation of Taylor–Couette turbulent flow controlled by a traveling wave-like blowing and suction

In wall turbulence, a traveling wave-like control is known to decrease the skin-friction drag and induce the relaminarization phenomenon. Because it is noteworthy to investigate the control effect in other canonical flows, direct numerical simulations of fully developed turbulent Taylor–Couette flows are performed. The Reynolds number, based on the wall velocity of a rotating inner cylinder and the radius of a centerline between cylinders, is set to 84,000. The traveling wave-like blowing and suction is imposed on the inner or outer cylinder wall, and the control effect is parametrically investigated. In the inner cylinder control, the torque reduction is obtained when the wave travels in the co-rotating direction with the inner cylinder, and its wavespeed is faster than the rotation. In the outer cylinder control, in contrast, the torque reduction is obtained when the wave propagates in the opposite direction. While the control is imposed on one side wall (i.e., inner or outer cylinder), the control affects the entire flow region. The Taylor vortex remains, while the traveling wave affects its strength. The three-component decomposition analysis shows that the traveling wave creates the coherent contribution on the torque, while the random contribution on it is reduced. Accordingly, a major factor of the torque reduction in the Taylor–Couette flow is the reduction of the random contribution. In addition, for the faster wavespeed cases with the small wavenumber (i.e., the long wavelength), the drag reduction larger than 60% is obtained and the relaminarization occurs in these cases.     

Effect of acceleration on the wavy Taylor vortex flow

In this paper, we use a laser optical technique to investigate the characteristics of a wavy Taylor vortex flow between two concentric cylinders, with the inner cylinder subjected to a wide range of predetermined acceleration and the outer one at rest. We focus on the inner/outer radius ratio of 0.894, with an acceleration (dRe/dt*) from 0.1123 to 2,247, and Reynolds number from Re/Re _c =1.0 to 36. The results show that, with increasing Reynolds number, there is an initial increase in the wavelength of the wavy vortex flow (λ), and a decrease in the wave speed (c) before they asymptote to a constant value, which is a function of the acceleration. As for the wave amplitude (A), it is found that the effect of acceleration is significant only in a very narrow range of Reynolds numbers. Received: 21 August 2001 / Accepted: 22 November 2001     

压电空心圆柱中波的传播

应用三维压电弹性体轴对称模型对压电空心圆柱中波的传播进行了研究. 发现在 圆柱中是否具有压电性质会对波的传播带来显著的差异. 当波长趋向于零时，在压电圆柱中 拟P波的波速渐进趋向于横观各向同性弹性体的准P波波速，而非压电圆柱中拟P波的波速 渐进趋向于一维杆模型中的P波波速；在压电圆柱中拟SV波存在驻波现象. 圆柱中的SH波 同电场无关，所以在压电圆柱和非压电圆柱中SH波具有相同的频散曲线. 应用积分变 换方法将圆柱的控制方程同其侧边界条件相结合，得到了一组动力学方程. 针对具体的侧边 界条件，得到相对应的波导条件和频散方程. 在此基础上通过数值计算模拟了圆柱受到端部 应力脉冲激励后的瞬态响应. 同时讨论了空心圆柱的半径比对轴向波传播的影响.     

Investigation of the flopping regime with two-, three- and four-cylinder arrays

The variation of the base pressure coefficient (Cp), and the characteristics of the velocity power spectra for arrays of two-, three- and four-cylinders aligned normal to the flow are presented. For the two-cylinder array with s/d=0.750 (where s is the spacing between the top and bottom surfaces of adjacent cylinders and d is the diameter of the cylinder) and Re=2.5×10³, peaks in the power spectra of 145 and 45?Hz which correspond to Strouhal numbers of 0.35 and 0.11 have been observed. For the three-cylinder array with Re=2.5×10³, at 0.338?s/d?0.730, three quasi-stable modes are observed. For 0.730?s/d?0.850, flopping and one quasi-stable mode are observed. For 0.850?s/d?1.202, only one mode is observed. The hot-wire power spectra measured downstream of the cylinder array on the center plane between the top and center cylinder and, also on the plane at s/2 above the top cylinder has three relative peaks that correspond to a wake structure, i.e. a pattern of vortices. For the four-cylinder array, when 0.338?s/d?0.750, four quasi-stable modes are observed. First, a mode can be observed in which the average Cp value of the top cylinder is relatively high, the average Cp value of the bottom cylinder is relatively low, and the average Cp values of the two center cylinders are nearly equal. A second mode is sometimes observed that is similar to the first except that the relatively high and low average Cp values of the outer cylinders are interchanged. A third mode is observed in which the average Cp value of the upper–inner cylinder is relatively high, the average Cp value of the lower–inner cylinder is relatively low, and the average Cp values of the outer cylinders are nearly equal. A fourth mode can be observed that is similar to the third mode except that the relative high and low average Cp values of the two inner cylinders are interchanged. For 0.750?s/d?1.202, only two of these modes are observed.     

Spiral and Wavy Vortex Flows in Short Counter-Rotating Taylor–Couette Cells

Differentially rotating cylinders result in a rich variety of vortical flows for cylindrical Couette flow. In this study we investigate the case of a short, finite-length cavity with counter-rotating cylinders via direct numerical simulation using a three-dimensional spectral method. We consider aspect ratios ranging from 5 to 6. Two complex flow regimes, wavy vortices and interpenetrating spirals, occur with similar appearance to those found experimentally for much larger aspect ratios. For wavy vortices the wave speed is similar to that found for counter-rotating systems and systems in which the outer cylinder is stationary. For the interpenetrating spiral structure, the vortices are largely confined to the unstable region near the inner cylinder. The endwalls appear to damp and stabilize the flow as the aspect ratio is reduced to the point that in some cases the vortical flow is suppressed. At higher inner cylinder speeds, the interpenetrating spirals acquire a waviness and the vortices, while generally near the inner cylinder, can extend all of the way to the outer cylinder. Received 5 November 2001 and accepted 29 March 2002 Published online 2 October 2002 Communicated by H.J.S. Fernando     

Rotating cylinder drag balance with application to riblets

Experimental results are reported and discussed for a rotating cylinder drag balance designed to predict drag reduction by surfaces like riblets. The apparatus functions by measuring the torque applied to the inner cylinder by a fluid, such as water, that is set in motion by the controlled rotation of the outer cylinder. The instrument was validated by calibration for laminar flow and comparison of turbulent flow results to the those of G. I. Taylor. The ability to predict drag reduction was demonstrated by testing 114 m symmetric sawtooth riblets, which gave a maximum reduction of about 5% and an overall drag reduction range of 5<S ⁺<20, both of which are in excellent comparison to results reported in literature. The most suitable conditions for testing riblets are to apply the riblets only to the inner cylinder surface and to use cylinders for which the curvature of the flow is minimized. Received: 2 February 1999/Accepted: 1 October 1999     

Transient thermoelastic waves in an anisotropic hollow cylinder due to localized heating

This paper presents a theoretical study of transient ultrasonic guided waves generated by concentrated heating of the outer surface of an infinite anisotropic hollow circular cylinder. Generalized thermoelastic theory proposed by Lord and Shulman is adopted to model the dynamic thermoelastic behavior of the cylinder. The concentrated heat source model used is to represent heating due to a pulsed laser beam, which is focused on the outer surface of the cylinder. A semi-analytical finite element (SAFE) method is employed to evaluate guided wave modes in the cylinder. Using integral transform techniques, the modal wave forms are obtained in frequency and wave number domains. Time histories of the propagating modes are then calculated by applying inverse Fourier transformation in the time domain. Numerical results showing the dispersion curves for the group velocities of the propagating modes and transient radial displacements are presented. For this purpose it is assumed that the cylinder is made of transversely isotropic silicon nitride (Si₃N₄). Attention is focused on the propagation characteristics of longitudinal and flexural modes separately.     

Hydrodynamic forces and moments due to interaction of linear water waves with truncated partial-porous cylinders in finite depth

An exact analytical method is employed for studying the diffraction problems in an ocean due to the presence of a specific type of cylinders. In this current work, two models are studied: (i) a floating surface-piercing truncated partial-porous cylinder, (ii) a surface-piercing truncated partial-porous cylinder placed at the bottom. In both cases, the configuration of the composite cylinder is such that it consists of an impermeable inner cylinder rising above the free surface and a coaxial truncated porous cylinder around the lower part of the inner cylinder with the top of the porous cylinder being impermeable. By using linear water wave theory, a three-dimensional representation of the problem is developed based on eigenfunction expansion method. The condition on the porous boundary is defined by applying Darcy’s law. Pressure and velocity satisfy continuity conditions across the linear interface between the adjacent fluid domains. Hydrodynamic force, moment and wave run-up are calculated by using the velocity potentials. Comparisons are carried out with results of wave diffraction by a floating and bottom-mounted compound cylinder, i.e., when the whole cylinder is non-porous. Handy agreements are observed from these comparisons. Through numerical tests, various experiments are carried out to investigate the impact of various parameters, such as porous coefficients, draft ratio, the ratio of inner and outer radii, the water depth etc., on hydrodynamic force, moment and wave run-up. The results clearly indicate that an appropriate optimal ratio for various parameters may be considered in designing practical ocean structures with minimum adverse hydrodynamic effect. The appearance of resonance in the results and role of porosity in mitigating resonance effect are explained. Proposal to select various appropriate parameters for the best possible effect is put forward.     

侧柱对串列双柱脉动压力的干扰

研究了串列双圆柱旁加上一个等直径的圆柱，组成一个等边三角形排列的三圆柱的脉动压力分布．着重研究侧柱对串列双圆柱脉动压力分布的影响．研究的结果表明，绕流等边三角形排列的三圆柱，受影响最严重的是后柱．脉动压力分布出现了严重的不对称，外侧的压力脉动极其强烈，内侧的压力脉动较弱，与时均压力分布，很好的对应关系．另外，侧柱对于串列双圆柱是否达到超过临界间距的绕流流态，有很大的影响     

An experimental study of diabatic spiral vortex flow

In spiral vortex flow, between concentric cylinders with the inner cylinder rotating and the outer stationary, the addition of a thermal gradient across the gap is a known complicating factor. The present diabatic study for narrow and wide gaps (radius ratios N=0.955 and N=0.8), with a heated outer and adiabatic inner cylinder, was undertaken to investigate this problem. The heat transfer characteristics and the modes of transition have been investigated together with the relationship between them. Using standard on-line digital computer techniques, the onset of vortex flow and its higher transitions have been shown to cause a sharp increase in Nusselt number. At higher Taylor numbers, of the order of 10⁶, a marked change in the Nusselt number occurs with the onset of the transition to periodic turbulent vortex flow. Outer wall heating is seen to affect the modes of transition. Diabatic critical Taylor numbers are much higher than those for adiabatic conditions and are found to depend on the close approach of the vortices to the outer wall