Generation of guided waves in hollow cylinders by wedge and comb type transducers

It was shown by Denos C. Gazis in 19591 that in linearly elastic hollow circular cylinders there exists an infinite number of “normal modes”, each of which has its own propagation characteristics such as phase and group velocity as well as their own displacement and stress distributions throughout the cross section of the cylinder. It was also shown that, even for a given mode, these characteristics changed with changing frequency. In general, when such a cylinder is loaded by external forces, all of the modes of the structure will be excited in varying strengths determined by the characteristics of the applied loading. From a nondestructive evaluation (NDE) point of view, however, there are some modes which, due to their unique characteristics, are more sensitive to the quantities being measured or the defects being sought. It would be advantageous, therefore, to modify the applied loading so as to excite with appreciable amplitude only those modes which are found to be sensitive to the quantity being measured. In order to do this however, the relationship between the applied loading and the amplitudes of the generated modes must be understood. In this paper, the general problem of determining the amplitudes with which each propagating mode is generated due to the application of specific types of separable, time harmonic loading is investigated. (The more general problem of non-separable loading can be found in a recent paper2). The general results for separable loading are then specialized to two types of transducers commonly used in NDE to determine how the parameters of these two types of sources affect the amplitudes of the generated modes

Finite Size and Speciment Thickness Influence in Acousto-Ultrasonic NDE

Acousto-ultrasonics (AU) uses a pair of transducers to characterize distributed damage in composite plates. A transducer placed normal to the surface creates resonances which propagate as plate waves. Once the receiving transducer picks up the signal, simple analysis techniques, such as the zeroth or first moment of the power spectrum, are applied to create a Stress Wave Factor (SWF). The SWF is then used to quantify the damage state of the composite once the system has been properly trained

One Sided Inspection for Elastic Constant Determination of Advanced Materials

Knowledge of mechanical properties of a composite material is prerequisite to good engineering design. The problem of theoretically predicting the mechanical properties of a composite material as a function of the properties of its constituents has been thoroughly investigated by many authors [1–2]. In one general class of techniques, termed “effective modulus” theories, the composite is viewed as a homogeneous anisotropic material with “effective” elastic constants that are determined by the elastic constants of the constituent materials. All of these theories remove the microstructure of the composite from consideration and, as a result, cannot be expected to predict accurately the properties of the composite material over a wide range of deformation scales. One limitation which comes about from this “smearing” of the microstructure into a homogeneous continuum is that the effective modulus theories, and hence materials which are assumed to have “effective elastic constants”, are incapable of predicting frequency dispersion of waves, which is sometimes very pronounced in composite materials [3]

Analysis of the Wedge Method of Generating Guided Waves

The “wedge” method of generating guided waves in isotropic layers was analyzed both theoretically and experimentally by Viktorov et. al, in 1965 [1]. The main parts of the work were later reproduced in Viktorov’s now famous book on Rayleigh and Lamb waves [2]. Of several detailed observations made in these investigations, one was that: For optimal generation of a mode of a given wavenumber, k, the angle of the wedge should be “in the neighborhood” of the Snell’s law angle, θ i = sin−1(k/k w), where k w represents the wavenumber of the wave in the wedge[2]. Such a choice of incident angle was being used by experimentalists utilizing Lamb waves for nondestructive evaluation purposes [3–5] even before Viktorov’s analysis. The use of such an angle no doubt arose from the theory of (infinite) plane wave reflection/refraction at planar interfaces. In those cases, which are strictly of academic interest or for approximating real experimental conditions, Snell’s law holds exactly as a result of satisfaction of boundary conditions along the entire (infinite) interface.</p

Finite Size and Speciment Thickness Influence in Acousto-Ultrasonic NDE

Acousto-ultrasonics (AU) uses a pair of transducers to characterize distributed damage in composite plates. A transducer placed normal to the surface creates resonances which propagate as plate waves. Once the receiving transducer picks up the signal, simple analysis techniques, such as the zeroth or first moment of the power spectrum, are applied to create a Stress Wave Factor (SWF). The SWF is then used to quantify the damage state of the composite once the system has been properly trained.</p

Generation of guided waves in hollow cylinders by wedge and comb type transducers

It was shown by Denos C. Gazis in 19591 that in linearly elastic hollow circular cylinders there exists an infinite number of “normal modes”, each of which has its own propagation characteristics such as phase and group velocity as well as their own displacement and stress distributions throughout the cross section of the cylinder. It was also shown that, even for a given mode, these characteristics changed with changing frequency. In general, when such a cylinder is loaded by external forces, all of the modes of the structure will be excited in varying strengths determined by the characteristics of the applied loading. From a nondestructive evaluation (NDE) point of view, however, there are some modes which, due to their unique characteristics, are more sensitive to the quantities being measured or the defects being sought. It would be advantageous, therefore, to modify the applied loading so as to excite with appreciable amplitude only those modes which are found to be sensitive to the quantity being measured. In order to do this however, the relationship between the applied loading and the amplitudes of the generated modes must be understood. In this paper, the general problem of determining the amplitudes with which each propagating mode is generated due to the application of specific types of separable, time harmonic loading is investigated. (The more general problem of non-separable loading can be found in a recent paper2). The general results for separable loading are then specialized to two types of transducers commonly used in NDE to determine how the parameters of these two types of sources affect the amplitudes of the generated modes.</p

Adhesive Joint Evaluation Using Lamb Wave Modes with Appropriate Displacement, Stress, and Energy Distribution Profiles

One of the most elusive yet critical problem in adhesive joints characterization is that of ‘kissing bond’ wherein good contact exists among the adherend and the adhesive, however with no acceptable levels of adhesion. To date, the kissing bond is difficult to be detected reliably by any of the methods including conventional ultrasound and thermal waves. Kissing bond which is a manufacturing defect/anomaly will substantially compromise the load bearing capability of the adhesive joint by initiating adhesive failure (in contrast to cohesive failure wherein the failure occurs within the thickness of the adhesive layer instead of a failure at the interface). Attempts to develop methods of detection of kissing bonds have been unsuccessful to date.</p

Analysis of the Generation of Guided Waves Using Finite Sources: An Experimental Approach

The wedge method of generating guided waves in isotropic layers, originally analyzed theoretically and experimentally by Viktorov and colleagues [1–2], has recently been extended to encompass generally anisotropic layers and transducers with arbitrary pressure distributions [3–4]. One result of these analyses was that there is a continuous dependence of the excitation amplitude of any given mode on the incident angle of the wedge. In [3–4], explicit expressions were given for the excitation amplitude as a function of incident angle; given the transducer size, pressure profile and frequency. In this paper, predictions in [3–4] are tested against laboratory experiments to asses their validity.</p

One Sided Inspection for Elastic Constant Determination of Advanced Materials

Knowledge of mechanical properties of a composite material is prerequisite to good engineering design. The problem of theoretically predicting the mechanical properties of a composite material as a function of the properties of its constituents has been thoroughly investigated by many authors [1–2]. In one general class of techniques, termed “effective modulus” theories, the composite is viewed as a homogeneous anisotropic material with “effective” elastic constants that are determined by the elastic constants of the constituent materials. All of these theories remove the microstructure of the composite from consideration and, as a result, cannot be expected to predict accurately the properties of the composite material over a wide range of deformation scales. One limitation which comes about from this “smearing” of the microstructure into a homogeneous continuum is that the effective modulus theories, and hence materials which are assumed to have “effective elastic constants”, are incapable of predicting frequency dispersion of waves, which is sometimes very pronounced in composite materials [3].</p