Wave-based defect detection and interwire friction modeling for overhead transmission lines

In this study, the feasibility of continuous, online monitoring of power lines using ultrasonic waves is considered. Local and global wave-based approaches for wire break detection in overhead transmission lines are presented. Both methods use a sending/receiving transducer to generate an ultrasonic, longitudinal, elastic wave in the cable. Defects in the cable cause a portion of the incident ultrasonic wave to be reflected back to the transducer, which when received, can be used to identify the presence of the defect. Although the transducers can only be attached to the surface of the cable, subsurface wires can also be interrogated since elastic energy spreads to these wires through friction contact. This study also explores how the elastic energy of a propagating wave becomes distributed among contacting rods via friction contact. This work focuses specifically on a two-rod system in which the wave energy from an excited “active” rod is transmitted to a neighboring “passive” rod through friction contact. An energy-based model is used to approximate the time average elastic wave power in the two rods as a function of propagation distance. Power predictions from the energy-based model compare well with experimental measurements and finite element simulations.     

梯形应力脉冲在弹性杆中的传播过程和几何弥散

在应力波传播过程中,几何弥散效应往往难以避免.对应力波在弹性杆中传播的几何弥散效应进行解析分析,对于基础波动问题研究以及材料动态力学行为表征等课题,显得至关重要.本文简单说明了弹性杆中考虑横向惯性修正的一维 Rayleigh-Love应力波理论,概述了其波动控制方程的变分法推导过程;针对 Hopkinson杆实验中常用的梯形应力加载脉冲,建立了相应的偏微分方程初边值问题的求解模型,并运用 Laplace变换方法研究了脉冲在杆中传播的几何弥散现象;根据留数定理进行 Laplace反变换,给出了杆中不同位置和时刻的应力波的级数形式解析解,分析了计算项数对结果收敛性的影响;将解析计算结果与采用三维有限元数值模拟的计算结果进行对比,两者吻合程度良好,从而证明 Rayleigh-Love横向惯性修正理论可以有效地表征典型 Hopkinson杆实验中的几何弥散效应.在此基础上围绕梯形加载脉冲的弥散效应进行参数研究,定量描述了传播距离、泊松比、脉冲斜率等参数的影响.本文给出的 Rayleigh-Love杆在梯形加载条件下的解析解,揭示了几何弥散效应的本质规律,可以用于实际实验的弥散修正过程.      

Vibration modelling of structural networks using a hybrid finite element/wave and finite element approach

The vibration modelling of waveguide structures is considered. These structures comprise waveguides connected via joints. Traditionally, analytical models of the wave behaviour of such structures can be developed if they are simple (beams or rods connected at point joints, etc.). However, if the waveguides are of complicated constructions (truss-like, layered media, etc.) or the joints are complicated (e.g. of significant physical dimensions), obtaining the wave characteristics might be a formidable task. In this paper, such structures are modelled using a hybrid finite element/wave and finite element (FE/WFE) approach. The waveguides are modelled using the WFE method and thus their wave characteristics are obtained regardless of the complexity of their cross-section. The joints are modelled using standard FE, and the WFE and FE models are coupled to yield the scattering properties of the joints. The propagation and scattering models are assembled to describe the behaviour of the structure using relatively small models, while also providing information for other applications such as structure-borne sound, statistical energy analysis, etc. Numerical examples are presented to illustrate the approach.     

Homogenization of acoustic waves in strongly heterogeneous porous structures

We consider acoustic waves in fluid-saturated periodic media with dual porosity. At the mesoscopic level, the fluid motion is governed by the Darcy flow model extended by inertia terms and by the mass conservation equation. In this study, assuming the porous skeleton is rigid, the aim is to distinguish the effects of the strong heterogeneity in the permeability coefficients. Using the asymptotic homogenization method we derive macroscopic equations and obtain the dispersion relationship for harmonic waves. The double porosity gives rise to an extra homogenized coefficient of dynamic compressibility which is not obtained in the upscaled single porosity model. Both the single and double porosity models are compared using an example illustrating wave propagation in layered media.     

Propagation of elastic waves in circular rods homogeneous over the cross section

Propagation of elastic waves in circular rods and in rods with a cylindrical cavity is numerically studied. The influence of the rod size on the wave propagation velocity is analyzed. A phenomenon of repeated rebound in short homogeneous rods is described.     

Wave propagation in circular cylindrical shells with periodic axial curvature

The propagation of longitudinal and flexural waves in axisymmetric circular cylindrical shells with periodic circular axial curvature is studied using a finite element method previously developed by the authors. Of primary interest is the coupling of these wave modes due to the periodic axial curvature which results in the generation of two types of stop bands not present in straight circular cylinders. The first type is related to the periodic spacing and occurs independently for longitudinal and flexural wave modes without coupling. However, the second type is caused by longitudinal and flexural wave mode coupling due to the axial curvature. A parametric study is conducted where the effects of cylinder radius, degree of axial curvature, and periodic spacing on wave propagation characteristics are investigated. It is shown that even a small degree of periodic axial curvature results in significant stop bands associated with wave mode coupling. These stop bands are broad and conceivably could be tuned to a specific frequency range by judicious choice of the shell parameters. Forced harmonic analyses performed on finite periodic structures show that strong attenuation of longitudinal and flexural motion occurs in the frequency ranges associated with the stop bands of the infinite periodic structure.     

Boundary element calculation of shallow water waves

A boundary element method is proposed for studying periodic shallow water problems. The numerical model is based on the shallow water equation. The key feature of this method is that the boundary integral equations are derived using the weighted residual method and the fundamental solutions for shallow water wave problems are obtained by solving the simultaneous singular equations. The accuracy of this method is studied for the wave reflection problem in a rectangular tank. As a result of this test, it has been shown that the number of element divisions and the distribution of nodes are significant to the accuracy. For numerical examples of external problems, the wave diffraction problems due to single cylindrical, double cylindrical and plate obstructions are analysed and compared with the exact and other numerical solutions. Relatively accurate solutions are obtained.     

梁波传播的固有特性

以分布参数的理论为基础，分析了梁波传播的一些固有特性，说明了它们与周期性结构的关系，讨论了支持条件对波传播特性的影响，指出了如果把近似方法应用于波传播分析中，可能引起的一些问题．本文的结果可直接应用于周期性结构的分析中     

Decay of acceleration waves in elastic rods

The problem of the propagation and decay of acceleration waves in nonlinear hyperelastic rods is treated herein. The general growth-decay law governing wave strength is obtained for all waves which can propagate in the rod. An expression for the induced higher order wave is also obtained. The forms taken by the law of growth or decay in a number of special cases are given.     

Frequency-dependent acoustic energy focusing in hexagonal ceramic micro-scaffolds

Acoustic properties of an additive-manufactured SiC scaffold with hexagonal symmetry fabricated by the robocasting method are studied both numerically and experimentally. The numerical analysis is based on the finite element method (FEM) using Bloch boundary conditions. The calculations show both angular and frequency dispersion of the acoustic waves with wavelengths comparable to the spacing between the rods, i.e., on a millimeter scale, indicating interesting acoustic properties in the MHz range. The dispersion character leads to focusing of the energy propagation into the directions of the rods of the hexagonal structure. This is illustrated by modal-based calculations of the propagation of longitudinal and out-of-plane shear wave packets with a dominant wavelength. The experimental analysis consists of two steps, the measurement of the resonant spectrum and shear wave propagation character. The measured resonant spectrum is in good agreement with the one calculated using numerically obtained low-frequency properties of the structure, also showing the quality of the overall manufactured structure. The time-domain measurement shows significant changes in the energy propagation between low and high frequencies, as predicted by FEM calculations.     

WAVE LOCALIZATION IN RANDOMLY DISORDERED PERIODIC PIEZOELECTRIC RODS

The wave propagation in periodic and disordered periodic piezoelectric rods is studied in this paper. The transfer matrix between two consecutive unit cells is obtained according to the continuity conditions. The electromechanical coupling of piezoelectric materials is considered. According to the theory of matrix eigenvalues, the frequency bands in periodic structures are studied. Moreover, by introducing disorder in both the dimensionless length and elastic constants of the piezoelectric ceramics, the wave localization in disordered periodic structures is also studied by using the matrix eigenvalue method and Lyapunov exponent method. It is found that tuned periodic structures have the frequency passbands and stopbands and localization phenomenon can occur in mistuned periodic structures. Furthermore, owing to the effect of piezoelectricity, the frequency regions for waves that cannot propagate through the structures are slightly increased with the increase of the piezoelectric constant.     

Thermally generated stress waves in a dispersive elastic rod

The propagation of thermally generated stress waves in a dispersive elastic rod was investigated both experimentally and analytically. In the experimental investigation, the end of a circular colored-glass rod was heated very rapidly by the deposition of luminous energy from a Q-switched ruby laser. The light from the laser was directed parallel to the axis of the rod and deposited on the polished end of the rod. The depth of deposition was of the same order as the radius of the rod. The length of the energy pulse from the laser was 20 nsec. This results in heating at such a rate that it can be considered as instantaneous when compared to the mechanical response of the material used. The resulting stress wave was measured using a thin quartz crystal in a Hopkinson pressure-bar arrangement. Radial inertia precluded the use of the simple wave equation; Love's modified wave equation was used to describe the motion. The thermoelastic problem was reduced to a homogeneous partial differential equation with appropriate initial and boundary conditions which is solved by the separation of variables technique. The experimental results are in good agreement with Love's theory. The amplitude of the stress waves was found to be directly proportional to the total energy deposited. The very short stress pulses generated by Q-switched laser deposition on the end of the thin rod gave rise to the higher modes of longitudinal wave propagation. The existence of wave propagation in a thin rod at near dilatational velocities was experimentally confirmed. It is concluded that the experimental techniques developed can be used to model stress-wave generation due to electromagnetic-energy depositions. Also, laser deposition provides an efficient means for generating the higher modes of longitudinal wave propagation in thin rods. Paper was presented at 1968 SESA Spring Meeting held in Albany, N. Y., on May 7–10. This work was supported by the U. S. Atomic Energy Commission at University of California, Lawrence Radiation Laboratory, Livermore, Calif.     

The propagation of elastic stress waves in a conical shell under axial impulsive loading

The propagation of elastic stress waves in a conical shell subjected to axial impulsive loading is studied in this paper by means of the finite element calculation and model experiments. It is shown that there are two axisymmetrical elastic stress waves propagating with different velocities, i.e., the longitudinal wave and the bending wave. The attenuation of these waves while propagating along the shell surface is discussed. It is found in experiments that the bending wave is also generated when a longitudinal wave reflects from the fixed end of the shell, and both reflected waves will separate during the propagation due to their different velocities. Southwest Institute of Structural Mechanics     

Primary wave transmission in systems of elastic rods with granular interfaces

We study analytically and numerically primary pulse transmission in one dimensional systems of identical linearly elastic non-dispersive rods separated by identical homogeneous granular layers composed of n beads. The beads interact elastically through a strongly (essentially) nonlinear Hertzian contact law. The main challenge in studying pulse transmission in such strongly nonlinear media is to analyze the ‘basic problem’, namely, the dynamical response of a single intermediate granular layer, confined from both ends by barely touching linear elastic rods subject to impulsive excitation of the left rod. The analysis of the basic problem is carried out under two basic assumptions; namely, of sufficiently small duration of the shock excitation applied to the first layer of the system, and of sufficiently small mass of each bead in the granular interface compared to the mass of each rod. In fact, the smallness of the mass of the bead defines the small parameter in the asymptotic analysis of this problem. Both assumptions are reasonable from the point of view of practical applications. In the analysis we focus only in primary pulse propagation, by neglecting secondary pulse reflections caused by wave scattering at each granular interface and considering only the transmission of the main (primary) pulse across the interface to the neighboring elastic rod. Two types of shock excitations are considered. The first corresponds to fixed time duration (but still much smaller compared to the characteristic time of pulse propagation through the length of each rod), whereas the second type corresponds to a pulse duration that depends on the small parameter of the problem. The influence of the number of beads of the granular interface on the primary wave transmission is studied, and it is shown that at granular interfaces with a relatively low number of beads fast time scale oscillations are excited with increasing amplitudes with increasing number of beads. For a larger number of beads, primary pulse transmission is by means of solitary wave trains resulting from the dispersion of the original shock pulse; in that case fast oscillations result due to interference phenomena caused by the scattering of the main pulse at the boundary of the interface. Considering a periodic system of rods we demonstrate significant reduction of the primary pulse when transmitted through a sequence of granular interfaces. This result highlights the efficacy of applying granular interfaces for passive shock mitigation in layered elastic media.     

轴向冲击载荷作用下锥壳中弹性应力波传播的计算和实验研究

本文利用有限元分析和模型实验研究了在轴向冲击载荷作用下,锥壳中弹性应力波的传播、计算和实验结果表明,结构中存在着弹性纵波和弹性弯曲波的传播,它们传播的速度各不相同,使壳面承受不同的应力状态;讨论了纵波和弯曲波随壳面的衰减;实验指出,由于边界的影响,即使纵波的反射也会产生新的反射弯曲波沿锥面传播。     

Propagation of guided waves in pressure vessel

Pressure vessels usually operate under extremes of high/low temperatures and high pressures. Defect, such as crack and corrosion, can result in leakage or rupture failures, even catastrophic incidents. Guided wave-based structural health monitoring (SHM) technology is one of the most prominent options in non-destructive evaluation and testing (NDE/NDT) techniques. Propagation of guided waves in a typical pressure vessel is systematically investigated in this study for the application of guided wave-based SHM. Shape of the pressure vessel is a cylinder with two end caps. Because of geometric similarity, theory of guided wave propagation in the cylinderical structure is analyzed to study dispersive features of guided waves in the pressure vessel. Dispersion curves of three different types of guided wave modes, viz. the longitudinal, torsional and flexural modes, are calculated using theoretical method. Based on the analyses and experimental wave signals, central frequency and wave parameters of incident wave are optimized. Effect of contained liquid on propagation of guided waves, especially the L(0, 2) mode, in the pressure vessel is further investigated to minimize energy leakage of the wave to the contained liquid. The analytical method, finite element analysis (FEA) and experiments are applied to study propagation characteristics of guided waves in the pressure vessel, so as to demonstrate the feasibility of guided wave-based non-destructive evaluation and testing (NDE/NDT) for such kind of complex structures.     

Numerical modeling of PZT-induced Lamb wave-based crack detection in plate-like structures

This paper presents the numerical modeling and simulations of PZT-induced Lamb wave propagation in plate-like structures by using the spectral finite element method. A novel spectral plate finite element, which can efficiently model the three-dimensional (3D) behavior of Lamb waves, is proposed. In the formulation, linear displacement distributions in the thickness direction are assumed for both the PZT layer and the base plate. A way to avoid the thickness locking is proposed and used in the formulations. Two examples, one for the validation of the proposed two-dimensional (2D) spectral finite element and the other for the demonstration of crack detection in plates, are presented and discussed. The contact between the two faces of crack is considered. Numerical results show that (1) only the anti-symmetric mode is prone to thickness locking thus remedy should be made only on this part, (2) the proposed 2D spectral finite element can adequately model the Lamb wave propagation in plate-like structures and the complex scattering for the crack, and (3) crack location can be well determined by a PZT-induced Lamb wave-based diagnosis algorithm.     

Acceleration waves in constrained elastic rods

The problem of the propagation and decay of acceleration waves in nonlinear hyperelastic rods, subject to a general class of constraints, is treated herein. The growth-decay equation, clearly showing the effect of the constraints, is derived for all waves which can propagate in the rod. For a certain class of constraints, general enough to include most of the practical applications, the wave decay equation is found to have the same form as for a rod without constraints, provided the rod is initially at rest.     

Wave propagation analysis in anisotropic and inhomogeneous uncracked and cracked structures using pseudospectral finite element method

The work deals with the development of an effective numerical tool in the form of pseudospectral method for wave propagation analysis in anisotropic and inhomogeneous structures. Chebyshev polynomials are used as basis functions and Chebyshev–Gauss–Lobatto points are used as grid points. The formulation is implemented in the same way as conventional finite element method. The element is tested successfully on a variety of problems involving isotropic, orthotropic and functionally graded material (FGM) structures. The formulation is validated by performing static, free vibration and wave propagation analysis. The accuracy of the element in predicting stresses is compared with conventional finite elements. Free vibration analysis is carried out on composite and FGM beams and the computational resources saved in each case are presented. Wave propagation analysis is carried out using the element on anisotropic and inhomogeneous beams and layer structures. Wave propagation in thin double bounded media over long propagating distances is studied. Finally, a study on scattering of waves due to embedded horizontal and vertical cracks is carried out, where the effectiveness of modulated pulse in detecting small cracks in composites and FGMs has been demonstrated.     

Investigations on flexural wave propagation of a periodic beam using multi-reflection method

The flexural wave propagation in a periodic beam with a propagating disturbance is studied by the use of the multi-reflection method. A propagating wave is incident upon a discontinuity and gives rise to transmitted and reflected waves. Here all of the transmitted and reflected waves of given flexural wave incident upon the beam at some specified location are found and superposed, and the method is extended to the case of incident evanescent wave. The results of incident waves at some location between discontinuities in a periodic beam are concerned. The relation between the wave-field of incident waves and the wave-field of resulting waves on any segments is expressed. As an example, the application of the results to the analysis of a finite periodic beam with a propagating disturbance is then demonstrated. The influences of the number of cells on the energy associated with propagating waves are considered.