功能梯度压电压磁圆柱轴对称的静力学响应

针对无限长功能梯度压电压磁空心圆柱,研究轴对称空心圆柱电磁弹耦合静力学问题。在柱坐标系下,假定材料参数沿径向为幂函数分布,推导出在外激励作用下空心圆柱体中位移、应力、电势以及磁势等物理场的解析解。数值讨论中,针对BaTiO₃-CoFeO₄复合材料空心柱体,在不同边界条件下得到了不同梯度参数及不同厚度下空心圆柱应力、电势和磁势的分布规律。结果表明,对于功能梯度压电压磁空心圆柱,材料的失效主要是由于环向应力引起的,且圆柱厚度对环向应力有着显著影响。此外,梯度参数强烈影响功能梯度压电压磁传感器/制动器的电/磁输出和力学性能。结果对压电压磁圆柱型传感器/制动器的设计和分析具有一定的指导作用。     

Acoustical multipole source in a hollow fluid-filled cylinder

The propagation of elastic waves generated by an impulse multipole source in a hollow fluid-filled cylinder was studied. The general solution of the problem is illustrated by calculations for monopole and dipole sources applied in geophysical and geoecological measurement practice. The analysis of the outer boundary influence on the waveforms registered by receivers located in the fluid was performed. The estimation has been carried out to determine a cylinder wall thickness under which its influence on cinematic parameters of the waveforms can be neglected.     

Wave propagation in a piezoelectric bone with a cylindrical cavity of arbitrary shape

This paper is concerned with the vibration of a piezoelectic cylinder of arbitrary cross section with a cylindrical cavity of arbitrary shape belonging to class 6. The boundary conditions for the inner and the outer arbitrary surfaces are satisfied by using the Fourier expansion collocation method. The frequency equations for the symmetric and the antisymmetric cases are obtained for the cylinder of general cross section of the inner and the outer boundaries. The analysis of the frequency equations are carried out for the material bone. The longitudinal and flexural vibrations are considered and the numerical results are tabulated. The frequency spectra are also presented.     

Flexural vibration of a pyrocomposite hollow cylinder

Flexural vibration of an infinite pyrocomposite circular hollow cylinder composed of an inner and outer pyroelectric layer of class 6 bonded together by a linear elastic material with voids (LEMV) is studied. The exact frequency equation is obtained for traction-free surfaces with continuity conditions at the interfaces. Numerical results in the form of data and dispersion curves for the first and second modes of the flexural vibration of the cylinder ceramic-1/Adhesive/ceramic-2 by taking the adherents as BaTio₃ and the adhesive as an existing carbon fibre-reinforced polymer (CFRP) or as a hypothetical LEMV layer with and without voids are compared with that of a single-layered pyroelectric hollow cylinder. The damping is analyzed through the imaginary parts of the complex frequencies.     

玻璃纤维增强树脂复合材料管-钢筋/混凝土空心构件抗弯性能

为研究玻璃纤维增强树脂复合材料(GFRP)管-钢筋/混凝土空心构件的抗弯性能,编制了受弯构件的非线性分析程序,系统地分析了空心率、配筋率、GFRP管管壁厚度及混凝土强度等级等主要参数对其抗弯性能的影响,并通过试验对所编制的程序进行验证,最后建立适用于GFRP管-钢筋/混凝土空心构件的抗弯承载力计算公式。结果表明:利用编制的受弯构件非线性分析程序与建立的抗弯承载力公式,计算结果与试验结果均吻合较好,抗弯承载力随空心率的减小、配筋率的提高、GFRP管管壁厚度的增加及混凝土强度的增大而增加,空心率对构件抗弯承载力影响最大,其次是配筋率和GFRP管管壁厚度,最后是混凝土强度等级,空心部分半径比在0.25~0.5为宜,可以适当提高配筋率、GFRP管管壁厚度或混凝土强度等级来弥补该空心构件抗弯承载力,研究结论可为该结构在实际应用中提供参考依据。      

Thermoelastic state of a two-component hollow cylinder with edge radial cracks

Stationary two-dimensional axisymmetric problems of thermal conductivity and thermoelasticity for a hollow two-component cylinder with cracks are studied by the method of singular integral equations. The cross section of the cylinder has the form of a circular concentric ring with a layer of another material that also has the form of a concentric ring and contains edge radial cracks. The surfaces of the cylinder are free of stresses. Thermal processes on these surfaces are characterized by temperature conditions of the third kind. Conditions of ideal thermal and mechanical contact are satisfied on the interface of the two media. A numerical solution is obtained for the case where the inner and outer cylindrical surfaces are kept at different constant temperatures. Stress intensity factors near the tip of one or two edge cracks were found for various values of thermal and mechanical characteristics of the cylinder.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 30, No. 4, pp. 76–80, July – August, 1994.     

A liquid level sensor using the absorption of guided acoustic waves

This liquid level sensor consists of a vertically movable 10-cm-long hollow cylinder with an impedance matching conic section suspended at one end of a few-meters-long magnetorestrictive wire. The wire is automatically wound up or unwound such that the cylindrical sensor element at the bottom of the wire is immersed by just a small and measurable distance into the liquid whose level is sought. Acoustic waves are launched in the wire by a pulse of current in a coil and are transmitted to the hollow cylinder through the cylindrical horn. The carrier frequency of the wave trains and the thickness of the tube are chosen so that the elastic waves strongly leak into the liquid when the hollow cylinder is immersed. The level is then determined by measuring the time-of-flight of the echo reflected at the junction between the wire and the horn, followed by taking into account a small correction term computed from the attenuation of the end echo.     

Compound piezoelectric cylindrical resonators as sensors of the rheological parameters of viscoelastic media

The electro-elastic behavior of a viscoelastically loaded layered cylindrical resonator (sensor) comprising two coupled hollow cylinders is presented. The inner cylinder is a piezoelectric ceramic tube. The outer cylinder is a non-piezoelectric (passive) metallic cylinder. An analytical formula for the electrical admittance of a compound layered cylindrical resonator loaded with a viscoelastic liquid is established. Admittance (conductance) diagrams were obtained using a continuum electromechanical model. The established analytical formulas enable the determination of the influence of the liquid viscosity, material, and geometrical parameters of a compound cylindrical resonator on the response characteristics of the compound sensor. In the paper, the sensor implications resulting from the performed analysis are described. Moreover, the algorithm of the method developed by the authors to evaluate the rheological parameters of a viscoelastic liquid is presented. Good agreement between the theoretical results and experimental data is shown. The analysis presented in this paper can be utilized for the design and construction of cylindrical piezoelectric viscosity sensors, annular accelerometers, filters, transducers, and multilayer resonators.     

Fracture life prediction and sensitivity analysis for hollow extrusion dies

It has been reported in literature that extrusion dies most often fail by fatigue fracture. Experimental studies have shown that cracks pre‐exist in dies because of various factors including machining, heat treatment and surface hardening. High levels of repeated mechanical and thermal loads result in crack propagation leading to ultimate fracture failure. In an earlier work by the authors, a simplified approach of plate‐with‐edge‐crack was used to develop a fracture mechanics based fatigue life prediction model for tube dies. In the current work, extrusion die is modeled as a pressurized‐cylinder‐with‐internal‐crack, a more realistic approach for a hollow (tube) die. Stochastic nature of various fatigue‐related die parameters has been used to reflect their variability. Monte Carlo simulation has been performed to forecast fracture failure of extrusion dies under a given set of operating conditions and mechanical properties. Predicted mean‐time‐to‐failure is quite close to actual average extrusion die life data from the industry. Using tube die as a basis, fracture life of other hollow profiles can be estimated through their shape complexity values. Analysis has also been carried out to evaluate how sensitive fracture life of hollow extrusion dies is to material and process parameters. Major findings are that die life is highly sensitive to initial crack size, wall thickness, profile outer diameter and billet length; moderately sensitive to Paris constant and extrusion ratio; and only slightly sensitive to fracture toughness and ram speed. These results can contribute to a deeper understanding of the factors responsible for fracture failure of an extrusion die exposed to thermo‐mechanical fatigue environment.     

Analysis of flexural properties of hollow-particle filled composites

This paper studies flexural properties of vinyl ester–glass hollow-particle filled composites, which are used in marine applications. Sixteen compositions of composite materials are studied under three-point bending conditions to assess the effect of wall thickness and volume fraction of hollow inclusions. The results show that the flexural modulus of several composites is higher as compared to the neat resin. Moreover, the specific modulus of all composites is higher than the neat resin providing the possibility of appreciable weight saving in marine structures. Nevertheless, the flexural strength of the composites is lower than that of the neat resin. In addition, it is found that the flexural strength decreases as the inclusion volume fraction increases and is independent of the inclusion wall thickness. An analytical framework is presented to interpret the experimental findings and generate predictive capabilities for hollow-particle filled composites. Tractable formulas are used for computing the flexural modulus and strength from the mechanical and geometrical properties of the constituents. Analytical and experimental results are found to be in close agreement.     

热塑性树脂LDPE长圆形中空体口模流道优化设计

目的 探索特殊的进料方式和分流流道,以满足长圆形分流均衡的特殊性需求。方法 运用流体力学对LDPE树脂流动进行力学分析,研究长圆形中空体成型质量与口模流道分流区数量、缝隙的关系,确定最佳的口模流道分流区数量、缝隙,并通过试制结果来验证分析数据的准确性。结果 采用1个衣架流道和6个区域的狭缝流道,衣架流道采用2个进口,并且狭缝流道的6个区域缝隙分别为4、3、3.5、1、5和1 mm时,长圆形中空体成型质量可以达到最佳效果:壁厚均匀性好,偏差小于0.15 mm;外表光滑无带褶皱竖纹;竖直度好,偏斜度小于3 mm。结论 文中设计方案先进、有效,可以用于包装用LDPE塑料瓶生产过程中的长圆形中空体成型过程。     

钢质圆柱壳在侧向局部冲击荷载下的变形及失效破坏

基于动力有限元程序LS-DYNA及随动塑性Cowper-Symonds模型,对两端固支钢质薄壁圆柱壳经受半球头弹体侧向局部冲击的非线性动力响应问题进行数值模拟,获得了不同冲击条件下圆柱壳的变形及破坏模态,并研究了弹体在不同周向冲击倾角时壳壁产生穿透性破裂的最小速度（临界破裂速度）。研究表明,圆柱壳破坏模式与弹体冲击倾角θ0、冲击速度V等因素密切相关,将发生局部凹陷、碟形变形及穿透现象,且临界破裂速度随冲击倾角的增大而增大。研究结果可应用于圆柱壳在侧向局部冲击作用下的毁伤预测,从而为圆柱壳结构的安全防护设计提供理论依据。     

Wave propagation in a hollow pyroelectric circular cylinder of crystal class 6

Summary Flexural and longitudinal wave propagation in a hollow pyroelectric cylinder of crystal class 6 are considered. The frequency equation has been derived for two different cases. Case (i) is for a hollow cylinder whose inner and outer surfaces are traction free, completely coated with electrode which are shorted and thermally insulated. Case (ii) is for a hollow cylinder whose inner surface is clamped, completely coated with electrode which are shorted and thermally insulated while the outer surface is same as in case (i). The frequency equation has been analyzed numerically for Barium titanate ceramic. The results are tabulated and the dispersion curves are presented.     

Vibration and buckling analysis of two-layered functionally graded cylindrical shell,considering the effects of transverse shear and rotary inertia

This research investigates the free vibration and buckling of a two-layered cylindrical shell made of inner functionally graded (FG) and outer isotropic elastic layer, subjected to combined static and periodic axial forces. Material properties of functionally graded cylindrical shell are considered as temperature dependent and graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. Theoretical formulations are presented based on two different methods of first-order shear deformation theory (FSDT) considering the transverse shear strains and the rotary inertias and the classical shell theory (CST). The results obtained show that the transverse shear and rotary inertias have considerable effect on the fundamental frequency of the FG cylindrical shell. The results for nondimensional natural frequency are in a close agreement with those in literature. It is inferred from the results that the geometry parameters and material composition of the shell have significant effect on the critical axial force, so that the minimum critical load is obtained for fully metal shell. Good agreement between theoretical and finite element results validates the approach. It is concluded that the presence of an additional elastic layer significantly increases the nondimensional natural frequency, the buckling resistance and hence the elastic stability in axial compression with respect to a FG hollow cylinder.     

Spectral strip analysis for composite cylinders subjected to lateral impact

An efficient computational method, combining the spectral element and the finite-strip method (spectral-strip) is developed in order to obtain numerical results to time dependent problems of cylindrical composite structures subjected to lateral impact, within moderate CPU times. The finite strip method is applied to cylindrical structures uses global interpolation in the circumferential direction, and spectral emenents in the meridional cross section. A term superposition solution is obtained, where every iteration refines the solution and is independent of former iterations. In this manner, a full three-dimensional solution to the problem of the dynamic response of cross-ply cylindrical composite shells subjected to a lateral impact, is obtained. The stability and the accuracy of the method are examined. The main goal is to predict the damage caused by a high velocity non penetrating impact of microparticles. Two types of shells are studied—thin and thick cross-ply laminates. The effect of curvature on a high velocity impact is studied. Also, the stress field obtained by the finite element code is investigated and damage evaluation is discussed. The present work focuses on moderate and high velocity impacts and therefore the force duration is of the order of the through-the-thickness propagation time, causing the imapct region to be in tension due to the reflected stress wave. The results demonstrate the dilatational compression wave traverses the shell thickness as a result of the impact and the dilatational tension wave reflected from the interior free surface as well as the propagation of shear waves in different directions. Using failure criteria, one can find that the compressive stress wave causes matrix cracking and the tensile stress wave causes both delamination and matrix cracking. It is shown that for a thin cylinder, the impact phenomenon is concentrated near the striking region while for a thick-walled cylinder the results of the impact are visible in points far from the striking point as well. The interference of the stress waves that circumevent the cylinder create other points of local maxima for the equivalent stresses. The code written for the finite element solution embloys the object oriented programming through the C++ language. A special matrix class is developed to perform various linear algebra operations. Dedicated to the memory of Professor Joab J. Blech (1934–1996)     

Thermoelectric effect in hollow superconducting cylinders

The thermoelectric effect in hollow cylindrical specimens (of circular and slit-like shapes) is considered. The detailed analysis of the behavior of the superconducting thin-walled cylinder in presence of normal current, is presented. The ratio of magnetic fluxes through the cylinder in superconducting and normal states is calculated as a function of temperature, wall thickness and other parameters of the superconductors. The gigantic thermoelectric effect is discussed using the concept of quantum transitions between the magnetic levels of cylindrical system. Some experimentally observable predictions are made.     

Transient Response in Cross-Ply Laminated Cylinders and Its Application to Reconstruction of Elastic Constants

An efficient hybrid numerical method is presented for investigating transient response of cross-ply laminated axisymmetric cylinders subjected to an impact load. In this hybrid numerical method, the laminated cylinder is divided into layered cylindrical elements in the thickness direction. The Hamilton principle is used to develop governing equations of the structure. The displacement response is determined by employing the Fourier transformations and the modal analysis. Numerical examples for analyzing transient waves have been provided in axisymmetric laminated cylindrical structures, both for thin cylindrical shells and thick cylinders.
A computational inverse technique is also presented for reconstructing elastic constants of axisymmetric crossply laminated cylinders from the surface displacement response data, using the present hybrid numerical method as the forward solver and neural network as the inverse operator. This technique is utilized to reconstruct the elastic constants of an axisymmetric laminated cylindrical shell.     

Finite axisymmetric deformations of elastic tubes: An approximate method

Finite axisymmetric deformation of a hollow circular cylinder with a finite length, composed of a neo-Hookean material, is studied. The inner surface of the tube is subjected to both normal and tangential tractions, while the outer surface is free of tractions. The cylinder will undergo both radial and axial deformations. An asymptotic-expansion method is used to determine the stress and shape of the deformed tube. The deformed radial and axial coordinates, the stress tensor and the surface tractions are expanded into a power series of an appropriate thickness parameter. A hierarchy of equilibrium equations, boundary conditions and constitutive equation are derived following the usual procedure. The theories corresponding to the lowest two order members in this hierarchy are studied in detail. It is shown that the zeroth-order theory corresponds to the membrane theory. The shape of the deformed tube, up to the second-order in the thickness parameter, is determined in terms of the zeroth-order radial and axial deformations. The zeroth-order radial and axial deformations are governed by a coupled pair of nonlinear ordinary differential equations, both of which are of second order. For illustrative purposes the present approach is then applied to a simple representative problem: simultaneous extension and inflation of a cylindrical elastic tube. Finally, the solutions corresponding to the zeroth and first-order approximations of the present theory and the exact solutions obtained from finite elasticity theory are compared for the above-mentioned problem.     

On The Problem of an Axial Semi-Elliptical Crack in a Hollow Ductile Cylinder

We revisit the problem of an axial crack in a hollow cylinder and attempt to show that the wall thickness is as a governing length scale for the design of such structures. In particular, yield based design should be performed for thin-walled tubes leading to a critical pressure. Large thick-walled tubes should on the other hand, be designed using the fracture mechanics criterion based on a material dependent fracture toughness.     

Improved impact-echo technique by signal processing

An experimental study was performed to modify the conventional impact-echo technique to detect small diameter spherical voids in concrete. High velocity impact of steel balls was used to generate the high frequency waves in concrete necessary for detection of small voids. Elastodynamic wave propagation in concrete, type of impact source, and the size of the flaw that can be detected were studied. These laboratory studies were carried out on a 4 in. (10.2 cm) thick 4 ft. × 4 ft. (1.22 m × 1.22 m) concrete slab that contained a variety of artificial spherical flaws embedded at known locations. Analysis of the frequency spectrum of the response of the slab was used to determine the slab's thickness and presence of voids.Signal processing techniques were applied for a better interpretation of the slab's response. Autocorrelation and cross-correlation algorithms were used to determine the characteristics of the slab at different locations. The problems associated with determination of flaws and voids in concrete have been delineated. Some practical and easy to implement solutions have been proposed and ways of using the impact-echo technique more efficiently for field applications have been discussed.