Laser-induced circumferential waves on hollow cylinder and their interaction with defects by finite element method

A three dimensional (3-D) finite element model for simulating laser induced circumferential wave on a hollow cylinder is developed based on the thermoelastical mechanism, which can take any laser source into account and simulate the interactions between circumferential wave and defects in the hollow cylinder. The model is verified by a control calculation. The results show that the waveforms of circumferential wave are in very good agreement with those available in literature, not only on the arrival time and shape but also on the amplitudes of A ₀, S ₀ and A₁ modes. Using the model, circumferential waves on the surfaces of two series hollow cylinders are simulated, one with same thickness but different outer radius, and the other with the same outer radius but different thickness. The results show that a new mode appears in circumferential wave, compared with Lamb wave in plate. With increase of thickness or radius, the amplitude of the new mode reduces. Another conclusion is that with increase of the thickness of the hollow cylinder, the circumferential wave evolves gradually to the cylindrical Rayleigh waveform, which results from the attenuation of the coupling effect between the outer and inner surface. Moreover, the circumferential waves generated on a hollow cylinder with a surface defect are also simulated, and the results indicate that in the circumferential waves obtained at the point beyond the defect, the amplitude of A ₀ mode decreases and its dispersion enhances. More importantly, a new bipolar waveform corresponding to the interaction of S ₀ mode with the defect appears, its amplitude is larger than three times of that of S ₀ mode. As a result, we consider that the new bipolar waveform will be the optimal feature to nondestructively detect the surface defect on the hollow cylinder.     

激光在管道中激发周向导波的有限元模拟

以超声的热弹激发机理为基础，建立了模拟激光在管道中激发周向导波的有限元模型.为了验证模型的正确性，根据Gao等人报道的实验条件［J. Appl. Phys. 91, 6114 (2002)］进行了模拟，理论模拟结果与Gao等人的实验结果符合很好，说明本数值模型的正确性.在此基础上，模拟激光在不同厚度、不同曲率半径的管道内激发的周向导波波形，同时分析了激光在管道中激发的周向导波波形与平板中激发Lamb波的差异，以及管道厚度和曲率半径对激光激发周向导波的影响.     

Natural beam focusing of non-axisymmetric guided waves in large-diameter pipes

The propagation of non-axisymmetric guided waves in larger diameter pipes is studied in this paper by treating the guided waves as corresponding Lamb waves in an unwrapped plate. This approximation leads to a simpler method for calculating the phase velocities of hollow cylinder guided waves, which reveals a beam focusing nature of non-axisymmetric guided waves generated by a partial source loading. The acoustic fields in a pipe generated by a partial-loading source includes axisymmetric longitudinal modes as well as non-axisymmetric flexural modes. The circumferential distribution of the total acoustic field, also referred as an angular profile, diverges circumferentially while guided waves propagate with dependence on such factors as mode, frequency, cylinder size, propagation distance, etc. Exact prediction of the angular profile of the total field can only be realized by numerical calculations. In particular cases, however, when the wall thickness is far less than the cylinder diameter and the wavelength is smaller than or comparable to the pipe wall thickness, the acoustic field can be analyzed based on the characteristics of Lamb waves that travel along a periodic unwrapped plate. Based on this assumption, a simplified model is derived to calculate the phase velocities of non-axisymmetric flexural mode guided waves. The model is then applied to discussions on some particular characteristics of guided-wave angular profiles generated by a source loading. Some features of flexural modes, such as cutoff frequency values are predicted with the simpler model. The relationship between the angular profiles and other factors such as frequency, propagation distance, and cylinder size is obtained and presented in simple equations. The angular profile rate of change with respect to propagation distance is investigated. In particular, our simplified model for non-axisymmetric guided waves predicts that the wave beam will converge to its original circumferential shape after the wave propagates for a certain distance. A concept of "natural focal point" is introduced and a simple equation is derived to compute the 1st natural focal distance of non-axisymmetric guided waves. The applicable range of the simplified equation is provided. Industrial pipes meet the requirement of wall thickness being far less than the pipe diameter. The approximate analytical algorithms presented in this paper provides a convenient method enabling quick acoustic field analysis on large-diameter industrial pipes for NDE applications.     

Wave propagation in non-homogeneous magneto-electro-elastic hollow cylinders

A dynamic solution is presented for the propagation of harmonic waves in imhomogeneous (functionally graded) magneto-electro-elastic hollow cylinders composed of piezoelectric BaTiO₃ and magnetostrictive CoFe₂O₄. The materials properties are assumed to vary in the direction of the thickness according to a known variation law. The Legendre orthogonal polynomial series expansion approach is employed to determine the wave propagating characteristics in the hollow cylinders. The dispersion curves of the imhomogeneous piezoelectric-piezomagnetic hollow cylinder and the corresponding non-piezoelectric and non-piezomagnetic hollow cylinders are calculated to show the influence of the piezoelectricity and piezomagnetism. Electric potential and magnetic potential distributions are obtained to illustrate the different influences of the piezoelectricity and piezomagnetism and the different influences of the piezoelectric effect and piezomagnetic effect on longitudinal modes and torsional modes. For the radial polarizing piezoelectric-piezomagnetic hollow cylinder, the piezoelectric effect and piezomagnetic effect take mostly on the longitudinal mode. Finally, a hollow cylinder at different ratio of radius to thickness is calculated to show the influence of the ratio on the piezoelectric effect and piezomagnetic effect.     

Guided circumferential waves in orthotropic cylindrical curved plate and the mode conversion by the end-reflection

In ultrasonic nondestructive inspection of large-diameter pipes and curved plate, longitudinal cracks are detected more efficiently by using guided circumferential waves. In the present, the study of guided circumferential waves and their application in detecting longitudinal defect were relative adequate when pipe material is isotropic. Based on linear three-dimensional elasticity, an orthogonal polynomial series expansions approach is used for determining the guided circumferential waves dispersion curves in homogeneous infinitely long orthotropic hollow cylinders. Results are compared with those published earlier and with the finite element simulation to check up the accuracy and range of applicability of this polynomial approach. Through the analysis of the displacements distributions and finite element simulation, the mode conversion of guided circumferential waves by end-reflection in cylindrical curved plate is discovered.     

Excitation and propagation of non-axisymmetric guided waves in a hollow cylinder

Excitation and propagation of non-axisymmetric guided waves in a hollow cylinder is studied by using the normal mode expansion method (NME). Different sources such as angle beam, tube end excitation with normal beam, and comb transducer possibilities are discussed based on the derivations of the NME method. Numerical calculations are focused on the case of angle beam partial loading. Based on the NME method, the amplitude coefficients for all of the harmonic modes are obtained. Due to the difference of phase velocities for different modes, the superimposed total field varies with propagating distances and hence makes particle displacement distribution patterns (angular profile) change with distance. This varying non-axisymmetric angular profile of guided waves represents a nonuniform energy distribution around the hollow cylinder and thus has an impact on the inspection ability of guided waves. The angular profiles of an angle beam source are predicted by theory and then verified by experiments. The predicted angular profiles also provide information for determining the transducer location to find defects in a certain position on the hollow cylinder.     

Radiative absorption in an infinitely long hollow cylinder with Fresnel surfaces

Radiation absorption in an infinitely long hollow cylinder with Fresnel surfaces is studied using the ray tracing method. It is found that the inner boundary can be modeled as a total reflective surface for the infinitely long hollow cylinder. Radiative absorption of hollow cylinders with Fresnel surfaces is compared to diffusive surfaces predicted by the finite volume method. Effects of refractive index, optical thickness and hole size on radiative absorption are studied. Abrupt changes in radiative absorption near τ_r/τ_Ro=1/n are observed for hollow cylinders with Fresnel surfaces. It is because the Fresnel relation predicts a critical angle at . This trend is not observed in diffusive surfaces. Refractive index and optical thickness are two competing factors that govern the radiative absorption. Higher refractive index drives higher absorption close to the inner surface, while higher optical thickness yields higher absorption near the outer surface. The results of this study can also serve as benchmark solutions for modeling radiative heat transfer in hollow cylinders with Fresnel surfaces. It is also found that the directional or hemispherical emittance can be calculated without solving the radiative transfer equation in the media when the temperature variation in the media is small.     

带缺陷二维光子晶体的透射谱研究

在一维线缺陷的研究基础上进一步应用转移矩阵方法数值研究带其它缺陷的二维正方晶格圆柱光子晶体的透射谱,缺陷的引入使得原来不透电磁波的禁带中,出现了缺陷模,即某一波长的电磁波可以透过,计算结果表明禁带位置、宽度,缺陷模的位置与透过率随着缺陷的种类、介质、程度有关,特别是都受到波源的入射角调制.     

Circumferential waves for a cylindrical shell in smooth contact with a continuum

Dispersion relations are determined for circumferential waves propagating in a layered, circular cylinder by using shell equations to approximate the behavior of the outer layer. These equations include the effects of transverse shear deformation and rotatory inertia. The cylinder consists of an elastic core in smooth contact with a hollow, circular cylinder of distinctly different elastic properties. Two distinct modes exist as the shell thickness reduces to zero. One mode is recognized to be surface waves on the convex cylindrical surface of the core; the second mode is associated with long longitudinal waves in the shell. The approximate dispersion curves for these modes are compared with curves obtained by employing elasticity equations for the layer. As the curvature increases, the agreement of the two theories becomes progressively poorer whether or not any disagreement exists for the case of no curvature. The agreement of the two theories is better when the layer is relatively stiff than when the layer is relatively soft. The shell equations simplify the calculations necessary to produce the dispersion curves.     

Point defect states of a hollow cylinder in two-dimensional phononic crystal

Point defect states in two-dimensional phononic crystal of a hollow mercury cylinder in a water host are studied.An improved plane expansion method combined with the supercell technique is used to calculate the band gaps and the pressure distribution at the defect position.The sonic pressure of defect modes shows that the waves are localized at or near the defect.As the filing fraction increases,more defect modes appear in the band gaps.     

Correlation between helical surface waves and guided modes of an infinite immersed elastic cylinder

Scattering of obliquely incident plane acoustic waves from immersed infinite solid elastic cylinders is a complex phenomenon that involves generation of various types of surface waves on the body of the cylinder. Mitri [F.G. Mitri, Acoustic backscattering enhancement resulting from the interaction of an obliquely incident plane wave with an infinite cylinder, Ultrasonics 50 (2010) 675-682] recently showed that for a solid aluminum cylinder, there exist acoustic backscattering enhancements at a normalized frequency of ka?0.1. The incidence angle α_c at which these enhancements are observed lies between the first (longitudinal) and second (shear) coupling angles of the cylinder. He also confirmed the observations previously reported by the authors that there exist backscattering enhancements of the dipole mode at large angles of incidence where no wave penetration into the cylinder is expected. In this paper, physical explanations are provided for the aforementioned observations by establishing a correlation between helical surface waves generated by oblique insonification of an immersed infinite solid elastic cylinder and the longitudinal and flexural guided modes that can propagate along the cylinder. In particular, it is shown that the backscattering enhancement observed at ka?0.1 is due to the excitation of the first longitudinal guided mode travelling at the bar velocity along the cylinder. It is also demonstrated that the dipole resonance mode observed at incidence angles larger than the Rayleigh coupling angle is associated with the first flexural guided mode of the cylinder. The correlation established between the scattering and propagation problems can be used in both numerical and experimental studies of interaction of mechanical waves with cylinders.     

充水圆柱壳声散射的环绕波分析

研究了内部充水圆柱壳散射声场的构成。采用弹性薄壳理论和Sommerfeld-Watson变换(SWT)方法导出散射声场的解析解。数值搜索环绕波的复波数极点,比较圆柱壳体内部真空和内部充水两种情况下表面环绕波的相速度、衰减等性质。用镜反射波和环绕波的叠加合成反向散射形态函数,与简正级数解符合良好。计算流体附加环绕波的回波时序并与实验数据对照。结果表明,流体附加环绕波的再辐射是内部充水圆柱壳的形态函数出现更加丰富的共振峰和回波结构形成的重要原因。      

Mechanism of the excitation of single pure mode L（0, 2） and its interaction with the defect in a hollow cylinder

Guided elastic waves have a great potential in pipe inspection as an efficient and low-cost nondestructive evaluation （NDE） technique, among which the wave of mode L（0, 2） receives a lot of attention because this mode is the fastest mode in a weakly dispersive region of frequency to minimize dispersion effects over a long distance and sensitive to the defects distributed circumferentially. Though many experimental and numerical researches have already been carried out about the excitation of L（0, 2） and its interaction with the defect in a hollow cylinder, its excitation mechanism has not been clarified yet. In this paper based on the transient response solution of the hollow cylinder, derived by the method of eigenfunction expansion, the theory about the exciting mechanism of mode L（0, 2） is advanced and the effects of the spatial distribution, vibration frequency and direction of the external force on the excitation are discussed. And the pure mode L（0, 2） is excited successfully under the parameters obtained through theoretical analysis. Furthermore, its interactions with some kinds of defects in hollow cylinders are simulated with the method of finite element analysis （FEA） and the results agree well with those obtained by other researchers.     

Axial acoustic radiation force of progressive cylindrical diverging waves on a rigid and a soft cylinder immersed in an ideal compressible fluid

Background and motivation

Previous works investigating the radiation force of diverging spherical progressive waves incident upon spherical particles have demonstrated the direction of reversal of the force when the particle is subjected to a curved wave-front. In this communication, the analysis is extended to the case of diverging cylindrical progressive waves incident upon a rigid or a soft cylinder in a non-viscous fluid with explicit calculations for the radiation force function (which is the radiation force per unit energy density and unit cross-sectional surface) not shown in [F.G. Mitri, Ultrasonics 50 (2010) 620-627].

Method

A closed-form solution presented previously in [F.G. Mitri, Ultrasonics 50 (2010) 620-627] is used to plot the radiation force function with particular emphasis on the difference from the results of incident plane progressive waves versus the size parameter ka (k is the wave number and a is the cylinder’s radius) and the distance of the cylinder from the acoustic source r₀.

Results

Radiation force function calculations for the rigid cylinder unexpectedly reveal that under specific conditions determined by the frequency of the acoustic field, the radius of the cylinder, as well as the distance to the acoustic source, the force becomes attractive (negative force). In addition, the numerical results show that the radiation force on a rigid cylinder does not generally obey the inverse-distance law with respect to the distance from the source.

Conclusion and potential applications

These results suggest that it may be possible, under specific conditions, to pull a cylindrical structure back toward the acoustic source using progressive cylindrical diverging waves. They may also provide a means to predict the radiation force required to manipulate non-destructively a single cylindrical structure. Potential applications include the design of a new generation of acoustic tweezers operating using a single beam of progressive waves (in contrast to the traditional version of acoustical tweezers in which an acoustic standing wave field is produced using two counter-propagating acoustic fields) for investigations in the field of flow cytometry, particle manipulation and entrapment.     

Analysis of circumferential waves on a water-filled cylindrical shell

The formation of scattering field from a water-filled cylindrical shell was studied. The analytic solutions of scattering field are derived using elastic thin shell theory and Sommerfeld-Watson Transformation(SWT) method.Complex wave-number poles of circumferential waves are found numerically,the phase speed and attenuation of circumferential waves between the situation of a hollow cylindrical shell and a water-filled cylindrical shell are compared. The synthesis of backscattering form functions which are sum of specular reflection component and circumferential waves is consistent with normal mode result.The calculated echo sequences of additional fluid circumferential waves are compared with experimental results. The results show that richer resonance peaks appeared in the backscattering form functions of a water-filled cylindrical shell and the formation of echo’s structure are due to re-radiation effects of additional fluid circumferential waves.     

HEAT TRANSFER TO TWO-PHASE AIR–VISCOELASTIC FLUID FLOWS OVER A HOT CYLINDER

Over a range of 70 < Re _a < 9,600, 7 < Pr _a < 130, 0 < β < 0.12, and 0.7 < n < 1, circumferential wall temperatures for air–water and air–aqueous polymer (viscoelastic) solution flows over a horizontal cylinder were measured experimentally. The 2.5-cm-diameter and 7.5-cm-long cylinder was heated by passing direct electric current through it. The peripherally averaged heat transfer coefficient for relatively dilute viscoelastic–air solutions, at any fixed flow rate of liquid phase, increases with β. Such increase is more pronounced at lower flow rates of liquid phase. For relatively more elastic solutions, the two-phase heat transfer decreases with increasing β. Such reduction is more pronounced at higher flow rates of liquid phase. A new correlation is proposed for predicting the Nusselt number for air–viscoelastic fluid flows over a heated cylinder in cross flow.     

Dynamic stability of liquid-filled cylindrical shells under horizontal excitation,part I: Experiment

Experimental studies have been carried out on the dynamic stability of a cantilever cylindrical shell partially filled with liquid, under horizontal excitation. The test cylinder was harmonically excited with constant acceleration or displacement amplitude. It was found that a combination instability resonance of sum type could occur, involving two natural vibrations with the same axial mode of vibration number but with the circumferential wave numbers differing by one. By varying the dimensionless water height from 0 to 1·0 stepwise by 0·25 increments, the instability regions and vibration modes were determined for two polyester test cylinders. The response waves, axial and circumferential vibration modes, and behavior of the free liquid surface were also observed.     

Guided wave propagation and mode differentiation in hollow cylinders with viscoelastic coatings

Guided wave propagation theories have been widely explored for about one century. Earlier theories on single-layer elastic hollow cylinders have been very beneficial for practical nondestructive testing on piping and tubing systems. Guided wave flexural (nonaxisymmetric) modes in cylinders can be generated by a partial source loading or any nonaxisymmetric discontinuity. They are especially important for guided wave mode control and defect analysis. Previous investigations on guided wave propagation in multilayered hollow cylindrical structures mostly concentrate on the axisymmetric wave mode characteristics. In this paper, the problem of guided wave propagation in free hollow cylinders with viscoelastic coatings is solved by a semianalytical finite element (SAFE) method. Guided wave dispersion curves and attenuation characteristics for both axisymmetric and flexural modes are presented. Due to the fact that dispersion curve modes obtained from SAFE calculations are difficult to differentiate from each other, a mode sorting method is established to distinguish modes by their orthogonality. Theoretical proof of the orthogonality between guided wave modes in a viscoelastic coated hollow cylinder is provided. Wave structures are also calculated and discussed in view of wave mechanics in multilayered cylindrical structures containing viscoelastic materials.     

Natural frequencies of free finite-length circular cylinders

Sets of tables are given for the natural frequencies of the first five symmetric and first five antisymmetric modes of a hollow or solid cylinder for circumferential wave numbers n = 0, 1, 2. Contour graphs are given for the lowest frequencies as functions of (length)/(mean radius) and (thickness)/(mean radius).     

Electromagnetic wave modulation in hollow vanadium dioxide microcrystals

The optical properties of vanadium dioxide (VO₂) single crystals with a hollow rectangular inner channel are numerically simulated. In such microstructures, electromagnetic waves are shown to propagate in the form of waveguide modes, and the semiconductor-metal phase transition in VO₂ results in substantial modulation of the mode propagation constant. The propagation constants are calculated for TE, TM, and EH modes in the spectral range 0.8–1.3 μm.