The dynamic response of an incompressible non-linearly elastic membrane tube subjected to a dynamic extension

The dynamic response of an isotropic hyperelastic membrane tube, subjected to a dynamic extension at its one end, is studied. In the first part of the paper, an asymptotic expansion technique is used to derive a non-linear membrane theory for finite axially symmetric dynamic deformations of incompressible non-linearly elastic circular cylindrical tubes by starting from the three-dimensional elasticity theory. The equations governing dynamic axially symmetric deformations of the membrane tube are obtained for an arbitrary form of the strain-energy function. In the second part of the paper, finite amplitude wave propagation in an incompressible hyperelastic membrane tube is considered when one end is fixed and the other is subjected to a suddenly applied dynamic extension. A Godunov-type finite volume method is used to solve numerically the corresponding problem. Numerical results are given for the Mooney-Rivlin incompressible material. The question how the present numerical results are related to those obtained in the literature is discussed.     

Laser generated and recorded transient bending waves in composite tubes

Propagating bending waves are studied in three different composite tubes by holographic interferometry. A conical mirror is placed axially inside the tubes. Axial illumination and observation directions make it possible to view the circumference of the tube, with a high sensitivity to radial deformation. It is shown how the deformation field can be numerically evaluated using a phase stepping and unwrapping technique. Transient bending waves in the tubes are both generated and recorded by the same pulsed laser, which makes the experiments easy to perform. Finite element simulations of the impacted tubes are compared to corresponding experiments. Both the geometry and the material properties of the tubes affect the wave propagation. For unidirectional composite tubes, the 0-deg and 90-deg directions have different dynamic behavior. The proposed method could be used in nondestructive testing of tubes.     

Non-planar responses of cantilevered pipes conveying fluid with intermediate motion constraints

In this paper, the nonlinear responses of a loosely constrained cantilevered pipe conveying fluid in the context of three-dimensional (3-D) dynamics are investigated. The pipe is allowed to oscillate in two perpendicular principal planes, and hence its 3-D motions are possible. Two types of motion constraints are considered. One type of constraints is the tube support plate (TSP) which comprises a plate with drilled holes for the pipe to pass through. A second type of constraints consists of two parallel bars (TPBs). The restraining force between the pipe and motion constraints is modeled by a smoothened-trilinear spring. In the theoretical analysis, the 3-D version of nonlinear equations is discretized via Galerkin’s method, and the resulting set of equations is solved using a fourth-order Runge–Kutta integration algorithm. The dynamical behaviors of the pipe system for varying flow velocities are presented in the form of bifurcation diagrams, time traces, power spectra diagrams and phase plots. Results show that both types of motion constraints have a significant influence on the dynamic responses of the cantilevered pipe. Compared to previous work dealing with the loosely constrained pipe with motions restricted to a plane, both planar and non-planar oscillations are explored in this 3-D version of pipe system. With increasing flow velocity, it is shown that both periodic and quasi-periodic motions can occur in the system of a cantilever with TPBs constraints. For a cantilevered pipe with TSP constraints, periodic, chaotic, quasi-periodic and sticking behaviors are detected. Of particular interest of this work is that quasi-periodic motions may be induced in the pipe system with either TPBs or TSP constraints, which have not been observed in the 2-D version of the same system. The results obtained in this work highlight the importance of consideration of the non-planar oscillations in cantilevered pipes subjected to loose constraints.     

聚乙烯泡沫单填充纸瓦楞管的轴向跌落冲击缓冲吸能特性

利用聚乙烯闭孔泡沫单填充纸瓦楞管开展轴向跌落冲击试验,对比分析了结构参数和冲击参数对其缓冲吸能特性参数（比吸能、行程利用率、压缩力效率、比总体效率）的影响。结果表明,X向单填充管的动态缓冲吸能特性优于Y向单填充管,而静态缓冲吸能特性差于Y向单填充管。正四边形单填充管的动态缓冲吸能特性优于正五、六边形单填充管,X向正四边形单填充管的比吸能相较于正五、六边形管分别提高了114.4%和182.3%。对于跌落冲击压缩,单填充管的比吸能、行程利用率、比总体效率随着管长比的增大而减小,管长比为1.4的X向单填充管的比吸能相较于管长比为2.2和3.0的单填充管分别增加了45.8%和117.9%,而压缩力效率随着管长比的增大而增大。随着跌落冲击质量或冲击能量的增加,比吸能、行程利用率、压缩力效率和比总体效率皆呈增大趋势,冲击质量对X向单填充管的影响较大,而冲击速度则对Y向单填充管的影响较大。     

The photoelastic determination of the stresses in vibrating cantilevered beams

A method of determining the dynamic stresses in vibrating cantilevered beams using photoelasticity is presented. The method uses the basic principles of photomechanics and the optic-stress laws. A high-intensity strobe light is timed with the frequency of vibration so that the beam image appears to be stationary. Data are recorded with a camera and analyzed to provide an experimental solution. The theoretical solution is derived from the Bernoulli-Euler equation of motion. Two basic types of beams were investigated, an aluminum beam coated with a birefringent material to simulate an actual structural member and a birefringent model that was dynamically similar to the aluminum beam. The feasibility of extending the technique to more complicated shapes is suggested by this investigation. The experimental results and feasibility of the concept are verified by close correlation with the analytical solution.     

横向爆炸载荷下薄壁圆管的动态响应

采用实验研究、理论分析和有限元模拟相结合的方法,研究了横向爆炸载荷作用下薄壁圆管的动态响应。利用弹道冲击摆锤系统,对圆管在爆炸载荷下的动力响应进行了实验研究,分析了薄壁圆管的变形模式;基于地基梁模型,建立了横向爆炸载荷作用下圆管跨中挠度的理论模型,并进行了无量纲化;通过有限元模拟,分析了圆管的几何参数对其变形模式和跨中挠度的影响,并与理论结果进行了对比。研究结果表明:随着TNT药量增加圆管的变形区域和跨中挠度增大;圆管的长径比、厚度及爆炸载荷参数对圆管的变形模式有较大影响;理论预测、有限元模拟结果与实验结果吻合较好。     

横向冲击载荷下不同约束泡沫铝夹芯圆管的动态响应

以泡沫铝夹芯圆管为研究对象,采用数值模拟研究了横向冲击载荷作用下4种不同约束夹芯圆管的动态响应。研究了夹芯圆管的几何参数、冲击速度和芯层泡沫铝相对密度对夹芯圆管力学行为的影响,对比分析了不同约束条件对泡沫铝夹芯圆管变形模式和吸能性能的影响。结果表明:随着内管直径的减小、冲击速度的增大和芯层泡沫铝相对密度的增大,泡沫铝夹芯圆管的比吸能增大;内管壁厚的增加使无约束和倾斜约束下夹芯圆管的比吸能增大,对侧壁约束和组合约束下夹芯圆管的吸能影响不明显;采用一定的外部约束条件是提高泡沫铝夹芯圆管吸能性能的一种可行的方法。     

Flow and thermodynamic characteristics of energy separation in a double-circuit vortex tube - An experimental investigation

Experimental investigations were made into the vortex energy separation effect of gas flux in tubes known as the Ranque effect. Technical applications of the results are considered. Unlike traditional energy separation tubes, so-called double-circuit vortex tubes were chosen that allowed the creation of a refrigeration device with high thermodynamic efficiency. Different thermodynamic and gas dynamical aspects of the processes taking place in the scheme developed are discussed taking into account the modern vortex interaction hypothesis. The possibility of constructing a double-circuit vortex tube refrigeration machine as efficient as a gas expansion system is demonstrated.     

Performance and optimum dimensions of flat fins for tube-and-fin heat exchangers: A generalized analysis

The performance of flat fins for tube-fin heat exchangers has been analyzed for both inline and staggered arrangement of tubes. In earlier published studies, regular square and equilateral triangular array tube layouts were considered. No such restriction is put in the present study. The analysis has been done by a semi-analytical technique where the boundary condition at the fin edge is discretely satisfied at a large number of points by a method of collocation. It has also been demonstrated that the approximate results obtained by the sector method closely agree with the prediction of semi-analytical technique. Finally, a generalized scheme of optimization based on Lagrange multiplier technique has been suggested which shows that irrespective of the volume and thickness of the fins, square and equilateral triangular array of tubes are the optimum layout for inline and staggered arrangements, respectively. This result was known so far only intuitively. The optimum dimensions for flat fins for other layout of tubes have also been obtained specifying the ratio of longitudinal to transverse tube pitch.     

A parametric study on nonlinear flow-induced dynamics of a fluid-conveying cantilevered pipe in post-flutter region from macro to micro scale

A mathematical formulation is proposed to investigate the nonlinear flow-induced dynamic characteristics of a cantilevered pipe conveying fluid from macro to micro scale. The model is developed by using the extended Hamilton's principle in conjunction with the inextensibility condition and laminar and turbulent flow profiles as well as modified couple stress theory. The current model is capable of recovering the classical model of cantilevered pipe conveying fluid by neglecting the couple stress effect. The governing equation of motion is presented in dimensionless form in a convenient and usable manner. To solve the problem at hand, the integro-partial-differential equation of motion is discretized into a set of ordinary differential equations via Galerkin method. Afterward, a Runge–Kutta's finite difference scheme is employed to evaluate the nonlinear dynamic response of the cantilevered pipe conveying fluid. A parametric study is carried out to examine the influences of mass parameter and dimensionless mean flow velocity on the nonlinear dynamic characteristics of the cantilevered pipe conveying fluid in post-flutter region. The role of size-dependency in the nonlinear behavior of pipe is explored by converting the new set of dimensionless parameters into the conventional one. Eventually, some convergence studies are performed to indicate the reliability of present results.     

径向惯性对薄壁圆管中弹塑性复合应力波传播的影响

弹塑性压扭复合应力波在薄壁管中的传播特性,已得到较为深入的研究,但为得到简单波解,大部分研究忽略了薄壁圆管中与径向惯性有关的周向应力σθ的影响。该文采用便于动态数值方法应用的增量型弹塑性本构关系,应用有限差分数值方法,计算了考虑径向惯性效应的弹塑性薄壁管中复合应力波的演化规律和传播特性,并与无径向惯性效应的计算结果作了对比,结果表明薄壁管中的径向惯性效应对弹塑性复合应力的传播有较大的影响。     

Dynamic neck development in a polymer tube under internal pressure loading

The initiation and growth of necks in polymer tubes subjected to rapidly increasing internal pressure is analyzed numerically. Plane strain conditions are assumed to prevail in the axial direction. The polymer is characterized by a finite strain elastic–viscoplastic constitutive relation and the calculations are carried out using a dynamic finite element program. Numerical results for neck development are illustrated and discussed for tubes of various thicknesses. The sensitivity to the wave number of the thickness imperfections is studied with a focus on comparing a long wave length imperfection and a short wave length imperfection. After some thinning down at the necks, the mode of deformation switches to neck propagation along the circumference of the tube. A case is shown in which the necks have propagated along the entire tube wall, so that network locking in the polymer results in high stiffness against further expansion of the tube. The rate dependence of the necking behavior gives noticeable differences in neck development for slow loading versus fast loading.     

CHAOTIC TRANSIENTS IN A CURVED FLUID CONVEYING TUBE

I. INTRODUCTIONChaotic motion is a kind of reciprocal non-periodic motion caused by a deterministic system. Itis very sensitive to the initial conditions, apparently random and incapable of long-term prediction.Chaotic transient is such a motion that the system will undergo a final steady state, which is one ofseveral or much more possible steady motions of the system. But this final steady state is very sensitiveto the initial conditions of the system. As it is e?ected by many uncertain…     

Development of the Bicone Mandrel Ring Expansion Test to Evaluate the Hoop Stress in Extruded Aluminum Tubes

Experimental Mechanics - The burst testing technique is used to determine the failure hoop stress of tubes that are subjected to internal pressure. In that technique, the tube is subjected to...     

Effect of acoustic resonance on the dynamic lift of tube arrays

The effect of acoustic resonance on the dynamic lift force acting on the central tube in square and normal triangle tube arrays is investigated experimentally. For each array pattern three different tube spacing ratios, corresponding to small, intermediate and large spacing ratios, are tested. The resonant sound field in the tube array is found to cause two main effects. First, it generates a “sound-induced” dynamic lift due to the resonant acoustic pressure distribution on the surface of the tube, and secondly, it synchronizes vorticity shedding from the tubes and thereby enhances the hydrodynamic lift force due to vortex shedding. The combined effect of these two unsteady lift forces depends on the phase shift between them, which is dictated by the frequency ratio of the acoustic mode to the natural vortex shedding frequencies. When the flow velocity is increased during the coincidence resonance range, the phase shift increases rapidly and therefore the effects of the two lift components change from reinforcing to counteracting each other. For the pre-coincidence lock-on range, the frequency ratio remains larger than unity and the two lift components always reinforce each other. Numerical simulations are also performed to compute the sound-induced lift force, and sound-enhancement coefficients are developed to estimate the effect of sound on the vortex shedding forces. The simulation and experimental results are implemented in a simplified design guide, which can be used to evaluate the dynamic lift forces acting on the tubes during acoustic resonances.     

Application of color structured light pattern to measurement of large out-of-plane deformation

Measurement of out-of-plane deformation is significant to understanding of the deflection mechanisms of the plate and tube structures.In this study,a new surface contouring technique with color structured light is applied to measure the out-of-plane deformation of structures with one-shot projection.Through color fringe recognizing,decoding and triangulation processing for the captured images corresponding to each deformation state,the feasibility of the method is testified by the measurement of elastic deflections of a flexible square plate,showing good agreement with those from the calibrated displacement driver.The plastic deformation of two alloy aluminum rectangular tubes is measured to show the technique application to surface topographic evaluation of the buckling structures with large displacements.     

Modal localization in mistuned tube-array structures

An investigation of mode localization in mistuned tube-array structures is studied in this work. The continuous action of hot-cold fluid shock waves in tube-array heat exchangers results in a significant abrasive wear of the tubes, which in turn alters their dynamic behavior and may introduce an undesirable modal localization effect within the tube bundle. This study performs a numerical investigation into the problem of modal localization in mistuned tube-array heat exchangers, with cross-flow. In conducting the investigation, the heat exchanger is modeled as a bundle of periodically-arranged cooling tubes in which the vibrational displacements of the individual tubes are weakly coupled to those of their neighbors via a squeezed water film in the gap between them. In general, the numerical results reveal that damage to even a single tube within the array is sufficient to introduce a severe modal localization effect. Furthermore, due to the weak coupling effect of the fluid, the vibrational energy induced by modal localization is confined to the defected tube and its immediate neighbors, and hence the risk of further wear defected within the tube bundle is increased. The results suggest that the modal localization phenomenon is alleviated at higher values of the cross-flow velocity, but becomes more severe as the tube wall thickness is increased.     

A STUDY ON THE EFFECT OF RADIAL INERTIA ON THE ELASTO-PLASTIC COMBINED STRESS WAVE PROPAGATION IN THIN-WALLED TUBES

An in-depth analysis of propagation characteristics of elasto-plastic combined stress waves in circular thin-walled tubes has been made. In obtaining the simple-wave solution, however, most researches have ignored the influence of the circumferential stress related to the radial inertial effect in the tubes. In this paper the incremental elasto-plastic constitutive relations which are convenient for dynamic numerical analysis are adopted, and the finite-difference method is used to study the evolution and propagation of elasto-plastic combined stress waves in a thin-walled tube with the radial inertial effect of the tube considered. The calculation results are compared with those obtained when the radial inertial effect is not considered. The calculation results show that the radial inertial effect of a tube has a fairly great influence on the propagation of elasto-plastic combined stress waves. Project supported by the National Natural Science Foundation of China (No. 19572064) and the National Defence Preresearch Foundation (No. 96J11. 4. 4. 0102).     

On the radial oscillations of incompressible, isotropic, elastic and limited elastic thick-walled tubes

The finite amplitude, free radial oscillations of a thick-walled circular cylindrical tube are studied for an arbitrary incompressible, isotropic and homogeneous rubber-like material having limiting molecular chain extensibility. First, based on classical results for hyperelastic tubes, some results for thick-walled Mooney-Rivlin tubes are described graphically in the phase plane. Then the periodicity of the finite amplitude, free oscillations of a general limited elastic, thick-walled tube is studied; and some analytical results for the Gent model are illustrated in several numerical examples. Results for thick-walled Gent tubes are compared with those for corresponding Mooney-Rivlin tubes; and the motion of thin-walled Gent tubes is illustrated in the phase plane. Physical conclusions are presented. The period of small amplitude oscillations of an arbitrary elastic or limited elastic tube is derived from relations obtained by a linearization of a general class of equations of which the tube problem is a special case. Classical results of the linear theory are thereby recovered and compared with results for Mooney-Rivlin and Gent tubes.     

Dynamic Stability of a Fluid-Coveying Cantilevered Pipe on an Additional Combined Support

Based on an analytical study, a numerical analysis is made of the dynamic stability of a cantilevered steel pipe conveying a fluid. The pipe is modeled by a beam restrained at the left end and supported by a special device (a rotational elastic restraint plus a Q-apparatus) at the right end. The numerical analysis reveals that the critical velocity of the fluid depends on the governing parameters of the problem such as the ratio of the fluid mass to the pipe mass per unit length and the rotational elastic constant at the right end