Guided wave propagation in an elastic hollow cylinder coated with a viscoelastic material

The propagation of ultrasonic guided waves in an elastic hollow cylinder with a viscoelastic coating is studied. The principle motivation is to provide tools for performing a guided wave, nondestructive inspection of piping and tubing with viscoelastic coatings. The theoretical boundary value problem is solved that describes the guided wave propagation in these structures for the purpose of finding the guided wave modes that propagate with little or no attenuation. The model uses the global matrix technique to generate the dispersion equation for the longitudinal modes of a system of an arbitrary number of perfectly bonded hollow cylinders with traction-free outer surfaces. A numerical solution of the dispersion equation produces the phase velocity and attenuation dispersion curves that describe the nature of the guided wave propagation. The attenuation dispersion curves show some guided wave modes that propagate with little or no attenuation in the coated structures of interest. The wave structure is examined for two of the modes to verify that the boundary conditions are satisfied and to explain their attenuation behavior. Experimental results are produced using an array of transducers positioned circumferentially around the pipe to evaluate the accuracy of the numerical solution.     

Torsional Wave Propagation in the Finitely Pre-Stretched Hollow Bi-Material Compound Circular Cylinder

This paper studies the torsional wave dispersion in the hollow bi-material compounded cylinder with finite initial strains. The investigations are carried out within the scope of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies. The mechanical relations of the materials of the cylinders are described through the harmonic potential. The numerical results on the influence of the initial stretching or compression of the cylinders along the torsional wave propagation direction are presented and discussed     

粘弹正交各向异性空心圆柱体周向SH波

基于Kelvin-Voight模型,推导了粘弹正交各向异性空心圆柱体周向SH波控制方程,得出了SH波特性受两个弹性常数与粘性系数的影响。通过第一类和第二类Bessel函数,求出频散方程。计算了四种不同径厚比下的相速度频散曲线和衰减曲线,分析了径厚比的变化对频散和衰减曲线的影响。为了与正交各向异性相比较,计算了粘弹各向同性空心圆柱体中周向SH波,并讨论了两个弹性常数和粘性系数对频散曲线和衰减曲线的影响。     

声子晶体弹性波带隙理论计算及实验研究

声子晶体是一种具有弹性波带隙的新型结构功能材料。本文在详细介绍声子晶体弹性波带隙计算方法——平面波展开法的基础上,采用该方法计算了一维金属／丁腈橡胶杆状结构声子晶体及二维空气中正方形排列的钢管阵列声子晶体的弹性波带隙并进行了实验验证。实验结果同理论计算结果吻合较好。     

Analysis of elastic wave propagation in a functionally graded thick hollow cylinder using a hybrid mesh-free method

In this paper, a hybrid mesh-free method based on generalized finite difference (GFD) and Newmark finite difference (NFD) methods is presented to calculate the velocity of elastic wave propagation in functionally graded materials (FGMs). The physical domain to be considered is a thick hollow cylinder made of functionally graded material in which mechanical properties are graded in the radial direction only. A power-law variation of the volume fractions of the two constituents is assumed for mechanical property variation. The cylinder is excited by shock loading to obtain the time history of the radial displacement. The velocity of elastic wave propagation in functionally graded cylinder is calculated from periodic behavior of the radial displacement in time domain. The effects of various grading patterns and various constitutive mechanical properties on the velocity of elastic wave propagation in functionally graded cylinders are studied in detail. Numerical results demonstrate the efficiency of the proposed method in simulating the wave propagation in FGMs.     

正交各向异性空心圆柱体中的纵向导波

基于三维线弹性理论,采用勒让德正交多项式展开法,推导了正交各向异性材料中纵向导波的耦合波动方程,并对耦合波动方程进行了数值求解。首先,为确定方法的适用性和准确性,利用Disperse软件求解各向同性空心圆柱体中纵向导波的频散曲线,并将其与勒让德正交多项式展开法求解结果相对比,二者结果完全一致。然后,讨论了勒让德正交多项式截止值对轴对称导波频散曲线收敛性的影响,并从数值计算的角度分析了产生影响的原因。最后,针对碳纤维缠绕的复合材料空心圆柱体,分别求解纵向、扭转和弯曲三种不同模态纵向导波的相速度频散曲线。计算了不同径厚比下的弯曲模态相速度频散曲线,分析径厚比的变化对频散曲线的影响。     

压电空心圆柱体中的周向SH波

基于三维线性压电弹性理论,采用一种正交多项式级数方法研究了轴向极化、电开路时正交各向异性压电空心圆柱中的周向SH波。把位移和电势展开成勒让德多项式级数,引入点确定的材料常数以解决边界条件,最后把问题的解简化为一个特征值问题。计算了不同径厚比下FZT-4管道周向SH的波频散曲线和电势分布。讨论了压电的影响。     

Magnetoelastodynamic stress and perturbation of magnetic field vector in an orthotropic laminated hollow cylinder

An analytical method is presented to solve magneto-elastic wave propagation and perturbation of the magnetic field vector in an orthotropic laminated hollow cylinder with arbitrary thickness. The magnetoelastodynamic equation for each separate orthotropic hollow cylinder is solved by making use of finite Hankel transforms and Laplace transforms. The unknown constants involved in the solution for each separate layer are determined by using the interface continuity conditions between layers and the boundary conditions at the internal and external boundaries of the laminated hollow cylinders. Thus, an exact solution for magnetoelastodynamic stresses and perturbation response of an axial magnetic field vector in laminated hollow cylinder is obtained. From sample numerical calculations, it is seen that the present method is suitable to solve magnetoelastodynamic problems of laminated hollow cylinders subjected to a radial shock load and an axial magnetic field.     

On Axisymmetric Longitudinal Wave Propagation in Double-Walled Carbon Nanotubes

An attempt is made into the investigation of longitudinal axisymmetric wave propagation in the DWCNT with the use of the exact equations of motion of the linear theory of elastodynamics. The DWCNT is modeled as concentricallynested two circular hollow cylinders between which there is free space. The difference in the radial displacements of these cylinders is coupled with the van der Waals forces and it is assumed that full slipping conditions occur on the inner surface of the outer tube and on the outer surface of the inner tube. Numerical results on the influence of the problem parameters such as the thickness/radius ratio, the distance between the tubes of the DWCNT and the van der Waals forces on the dispersion curves are presented and discussed. In particular, it is established that new types of modes arise under propagation of axisymmetric longitudinal waves as a result of the van der Waals interaction between the tubes of the DWCNT. The limit values of the wave propagation velocity are also analyzed.     

Wave propagation in coated cylinders with reference to fretting fatigue

Fretting fatigue is the phenomenon of crack initiation due to dynamic contact loading, a situation which is commonly encountered in mechanical couplings subjected to vibration. The study of fretting fatigue in high frequency regime has gained importance in recent years. However the stress wave effects at high frequency loading is scanty in the literature. The objective of present investigation is to study stress wave propagation in cylinders with reference to high frequency fretting. The case of a coated cylinder is considered since coating is often provided to improve tribological properties of the component. Rule of mixtures is proposed to understand the dispersion phenomenon in coated or layered cylinder knowing the dispersion relation for the cases of homogeneous cylinders made of coating and substrate materials separately. The possibility of stress wave propagation at the interface with a particular phase velocity without dispersion is also discussed. Results are given for two different thicknesses of coating.     

Multi-modal wave propagation in smart structures with shunted piezoelectric patches

The propagation of wave modes in elastic structures with shunted piezoelectric patches is dealt with in this work. The wave finite element approach, which is based on the finite element method and periodical structure theory, is firstly developed as a prediction tool for wave propagation characteristics in beam like structures, and subsequently extended to consider shunted piezoelectric elements through the diffusion matrix model (DMM). With these numerical techniques, reflection and transmission coefficients of propagating waves in structures with shunted piezoelectric patches can be calculated. The performance of shunted piezoelectric patches on the control of wave propagation is investigated numerically with the DMM. Forced response of the smart structure can also be calculated, and based on which the time response of the structure can be obtained via an inverse discrete fourier transform approach. These general formulations can be applied to all types of slender structures. All these numerical tools can facilitate design modifications and systematic investigations of geometric and electric parameters of smart structures with shunted piezoelectric elements.     

正交各向异性空心圆柱体中的周向超声导波

周向导波适于大直径管道纵向缺陷的超声无损检测。基于三维弹性理论,采用一种正交多项式法研究正交各向异性无限长管道中的周向导波。为验证方法的正确性与适用性,首先计算了各向同性和横观各向同性管道中的周向导波并与已有数据相比较。其次,计算了单向复合材料中不同纤维增强强度下的频散曲线,论证了纤维增强强度变化对于频散曲线的影响。最后,求解了不同径厚比下正交各向异性管道的周向导波的频散曲线,论述了径厚比的变化对频散曲线的影响。     

Investigation of Absolute Photonic Band Gaps in Two-dimensional Dielectric Structures

Abstract

We examine the photonic band structure of two-dimensional (2D) arrays of dielectric holes using the coherent microwave transient spectroscopy (COMITS) technique. Such 2D hole arrays are constructed by embedding low-index rods (air) in a dielectric background of higher-index Stycast material (n = 3·60). The dispersion relation for electromagnetic wave propagation in these photonic crystals is directly determined using the phase sensitivity of COMITS. We find that both the square and triangular lattice structures exhibit photonic band gaps that are common to both polarizations for all wave-vectors along major symmetry axes. In addition, the connectivity of the high-index dielectric and the opening of a large gap for propagation with E field perpendicular to the hole cylinders are found to be important criteria for generating a large absolute photonic band gap.     

基于波有限元法的流固耦合结构波传导问题

本文采用波有限元方法研究流固耦合结构中的波传导问题。该方法以有限元法为基础,首先建立研究对象的有限元法模型,得到模型的动态刚度矩阵。通过对动态刚度矩阵的重新排列组合得到研究对象的传递矩阵,求解传递矩阵的特征值问题可以得到分别代表自由波传递的波数和波模。本研究首先分析独立流体结构和固体结构中的振动问题,并比较了采用波有限元法和理论方法求解得到的固体结构中波数分布情况,验证了模型的正确性。随后采用波有限元法分析流固耦合结构中的波传导问题。波有限元法的应用并不局限于本文所给出的均匀或周期性结构,还可将其应用于缓慢变化的非均匀结构。     

A finite element analysis of the time-delay periodic ring arrays for guided wave generation and reception in hollow cylinders

A new guided wave transducer model, time-delay periodic ring arrays (TDPRAs), is proposed and investigated in this paper for guided cylindrical wave generation and reception in hollow cylinders with application interests focusing on non-destructive testing (NDT) of piping/tubing. A finite element simulation has been performed for axisymmetric guided-mode excitation and reception with TDPRAs. By arranging a proper configuration of the time-delay profile and the electric-connection pattern of a ring array, unidirectional excitation and reception of guided waves can be achieved. The numerical results are obtained for the first three axisymmetrical modes and are compared with respect to generation efficiency and mode selectivity. Parametric influences on the performance of TDPRAs are discussed, combining a 2-D phase velocity-frequency spectrum approach with the mode dispersion and displacement structure analyses. The identification of converted modes in guided cylindrical wave reflections with a flexible TDPRA receiver has also been studied through sample notch reflection.     

On the Some Particularities of the Torsional Wave Dispersion in a Finitely Pre-Deformed Hollow Sandwich Cylinder

This paper develops the investigations started in a work by Akbarov, Kepceler and Mert Egilmez (2011) and studies the some particularities of the torsional wave dispersion in a finitely pre-deformed sandwich hollow cylinder. The mentioned particularities relate to the influence of the stiffness ratio of the core and face layers' materials and the influence of the thickness ratio of these layers on the dispersion character of the wave under consideration. Moreover, the mentioned influences are studied for the various values of the parameter which characterizes the initial strains in the cylinder's layers. The mechanical relations of the materials of the cylinders are described through the harmonic potential. The analytical expression is presented for the low wave number limit values of the torsional wave propagation velocity. The numerical results on the foregoing influences are presented and discussed.     

Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method

In this paper, dynamic analysis of nanocomposite cylinders reinforced by single-walled carbon nanotubes (SWCNTs) subjected to an impact load was carried out by a mesh-free method. Free vibration and stress wave propagation analysis of carbon nanotube reinforced composite (CNTRC) cylinders are presented. In this simulation, an axisymmetric model is used. Four types of distributions of the aligned carbon nanotubes (CNTs) are considered; uniform and three kinds of functionally graded (FG) distributions along the radial direction of cylinder. Material properties are estimated by a micro mechanical model. In the mesh-free analysis, moving least squares (MLSs) shape functions are used for approximation of displacement field in the weak form of motion equation and the transformation method was used for the imposition of essential boundary conditions. Effects of the kind of distribution and volume fractions of carbon nanotubes and cylinder thickness on the natural frequencies and stress wave propagation of CNTRC cylinders are investigated. Results obtained for this analysis were compared with FEM and previous published work and good agreement was seen between them.     

Laplace‐domain,high‐order homogenization for transient dynamic response of viscoelastic composites

This paper presents a high‐order homogenization model for wave propagation in viscoelastic composite structures. Asymptotic expansions with multiple spatial scales are employed to formulate the homogenization model. The proposed multiscale model operates in the Laplace domain allowing the representation of linear viscoelastic constitutive relationship using a proportionality law. The high‐order terms in the asymptotic expansion of response fields are included to reproduce micro‐heterogeneity‐induced wave dispersion and formation of bandgaps. The first and second‐order influence functions and the macroscopic deformation are evaluated using the finite element method with complex coefficients in the Laplace domain. The performance of the proposed model is assessed by investigating wave propagation characteristics in layered and particulate composites and verified against direct numerical simulations and analytical solutions. The analysis of dissipated energy revealed that material dispersion may contribute significantly to wave attenuation in dissipative composite materials. The wave dispersion characteristics are shown to be sensitive to microstructure morphology. Copyright © 2015 John Wiley & Sons, Ltd.     

全局矩阵法及其在层状各向异性复合板中Lamb波传播特性研究中的应用

纤维增强复合材料中兰姆波的传播因其在无损评价中的应用而成为广泛研究的课题。一般采用传递矩阵法对各向异性多层媒质进行建模。虽然这种方法较为方便,但在大频厚积时会出现数值不稳定。本文作者对Nafeh的传递矩阵方法进行改进,所得到的全局矩阵方法具有较好的稳定性,其程序能有效地产生兰姆波的频散曲线。纤维增强复合材料中兰姆波的传播受多种因素的影响,层数的影响是其中之一。给出了不同层数复合板中兰姆波的相速度频散曲线以及两个基本模式a₀和s₀沿板厚方向的应力分布。这些数值示例为层状各向异性复合材料板的无损评价提供了理论依据。      

Influences of initial stresses on guided waves in functionally graded hollow cylinders

Limitations of the manufacturing technology result in the existence of initial stresses in functionally graded material (FGM) structures. In the context of the theory of “Mechanics of Incremental Deformations,” the guided wave characteristics in FGM hollow cylinders under initial stresses in the radial and axial directions are investigated. The Legendre polynomial series method is used to solve the coupled wave equations with variable coefficients. The convergence of the method is discussed through numerical examples. It is found that the influences of initial stresses on the longitudinal waves and on the torsional waves are quite distinct, and that the influences of initial stresses in the axial direction are very different from those in the radial direction, both on the dispersion curves and on the displacement and stress distributions.