Accurate knowledge of the velocity dispersion of Lamb modes is important for ultrasonic nondestructive evaluation methods used in detecting and locating flaws in thin plates and in determining their elastic stiffness coefficients. Lamb mode dispersion is also important in the acoustic emission technique for accurately triangulating the location of emissions in thin plates. In this research, the ability to characterize Lamb mode dispersion through a time-frequency analysis (the pseudo Wigner-Ville distribution) was demonstrated. A major advantage of time-frequency methods is the ability to analyze acoustic signals containing multiple propagation modes, which overlap and superimpose in the time domain signal. By combining time-frequency analysis with a broadband acoustic excitation source, the dispersion of multiple Lamb modes over a wide frequency range can be determined from as little as a single measurement. In addition, the technique provides a direct measurement of the group velocity dispersion. The technique was first demonstrated in the analysis of a simulated waveform in an aluminum plate in which the Lamb mode dispersion was well known. Portions of the dispersion curves of the A0, A1, S0, and S2 Lamb modes were obtained from this one waveform. The technique was also applied for the analysis of experimental waveforms from a unidirectional graphite/epoxy composite plate. Measurements were made both along, and perpendicular to the fiber direction. In this case, the signals contained only the lowest order symmetric and antisymmetric modes. A least squares fit of the results from several source to detector distances was used. Theoretical dispersion curves were calculated and are shown to be in good agreement with experimental results.

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Time-Frequency Analysis of the Dispersion of Lamb Modes

In thermoacoustic systems heat is converted into acoustic energy and vice versa. These systems use inert gases as working medium and have no moving parts which makes the thermoacoustic technology a serious alternative to produce mechanical or electrical power, cooling power, and heating in a sustainable and environmentally friendly way. A thermoacoustic Stirling heat engine is designed and built which achieves a record performance of 49% of the Carnot efficiency. The design and performance of the engine is presented. The engine has no moving parts and is made up of few simple components.

A high performance thermoacoustic engine

The simulation of acoustic emission waveforms resulting from failure during mechanical loading of carbon fiber reinforced plastic structures is investigated using a finite element simulation approach. For this investigation we focus on the dominant failure mechanisms in fiber reinforced structures consisting of matrix cracking, fiber breakage and fiber-matrix interface failure. To simulate the failure process accurately, we present a new acoustic emission source model that is based on the microscopic source geometry and micromechanical properties of fiber and resin. We demonstrate that based on this microscopic source model these failure mechanisms result in excitation of macroscopic plate waves. The propagation of these plate waves is described using a macroscopic three-dimensional model geometry which includes contributions of reflections from the specimen boundaries. We further present a model of the acoustic emission sensors used in experiments to simulate the influence of aperture effects. To enhance the understanding of correlation between macroscopically detectable acoustic emission signals and microscopic failure mechanisms we simulate the response to different source excitation times, crack surface displacements and displacement directions. The results obtained show good agreement with fundamental assumptions about the crack process reported by various other authors. The simulated acoustic emission signals obtained are compared to experimentally measured waveforms during four-point bending experiments of carbon fiber reinforced plastic structures. The simulated signals of fiber-breakage, matrix-cracking and fiber-matrix interface failure show systematic agreement with the respective experimental signals.

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Simulation of Acoustic Emission in Planar Carbon Fiber Reinforced Plastic Specimens

A database of wideband acoustic emission (AE) modeled signals was used in Part 1 to examine the application of a wavelet transform (WT) to identify AE sources. The AE signals in the database were created by use of a validated three-dimensional finite element code. These signals represented the out-of-plane displacements from buried dipole sources in aluminum plates 4.7 mm thick and of small and large lateral dimensions. The surface displacement signals at three far-field distances were filtered with a 40 kHz high-pass filter prior to applying the WT. The WTs were calculated with AGU-Vallen Wavelet, a freeware software program. The effects of propagation distance, AE source type, and the depth of the AE source below the plate surface were examined. Specifically, a ratio of the WT magnitude (WT coefficient) from the fundamental anti-symmetric mode to that from the fundamental symmetric mode was studied for correlation with the AE source type. The WT magnitudes were those corresponding to a particular group velocity and signal frequency for each mode. For sources in the large plate located at the same depth, the ratios were able to distinguish different source types and exhibited only small changes with increasing propagation distance. But, when the variable of depth of the source was introduced, the ratios did not uniquely classify the AE source type. In the case of the small coupon plate specimen, reflections from the specimen edges distorted and complicated the WTs. Since the current coupon database excludes (except for one case) the parameter of changes in the distance of the source from the coupon sides, a full examination of these complications was not possible.

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A wavelet transform applied to acoustic emission signals: part 1: source identification #

Quantitative measurements of the amplitude and angular variation of acoustic emission (AE) events due to matrix cracking and delamination in large quasi-isotropic composite plate specimens are reported. A procedure for determining the minimum specimen size necessary to make quantitative measurements is presented. The amplitude of AE events is quoted as the absolute surface displacement of different guided wave modes and can therefore be used as the input to forward models of the AE process. Matrix cracking events are found to be dominated by the S0 guided wave mode and have a pronounced amplitude variation with angle. Events due to delamination growth are dominated by the A0 guided wave mode and have no clear angular dependence.

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Quantitative experimental measurements of matrix cracking and delamination using acoustic emission

A comparison was made between two approaches to predict acoustic emission waveforms in thin plates. A normal mode solution method for Mindlin plate theory was used to predict the response of the flexural plate mode to a point source, step-function load, applied on the plate surface. The second approach used a dynamic finite element method to model the problem using equations of motion based on exact linear elasticity. Calculations were made using properties for both isotropic (aluminum) and anisotropic (unidirectional graphite/epoxy composite) materials. For simulations of anisotropic plates, propagation along multiple directions was evaluated. In general, agreement between the two theoretical approaches was good. Discrepancies in the waveforms at longer times were caused by differences in reflections from the lateral plate boundaries. These differences resulted from the fact that the two methods used different boundary conditions. At shorter times in the signals, before reflections, the slight discrepancies in the waveforms were attributed to limitations of Mindlin plate theory, which is an approximate plate theory. The advantages of the finite element method are that it used the exact linear elasticity solutions, and that it can be used to model real source conditions and complicated, finite specimen geometries as well as thick plates. These advantages come at a cost of increased computational difficulty, requiring lengthy calculations on workstations or supercomputers. The Mindlin plat theory solutions, meanwhile, can be quickly generated on personal computers. Specimens with finite geometry can also be modeled. However, only limited simple geometries such as circular or rectangular plates can easily be accommodated with the normal mode solution technique. Likewise, very limited source configurations can be modeled and plate theory is applicable only to thin plates.

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Finite Element and Plate Theory Modeling of Acoustic Emission Waveforms

The requirements for dynamic finite-element modeling of the source dynamics and wave propagation of buried acoustic-emission point sources were examined. Maximum permissible source and cell sizes for point sources were determined as a function of the minimum wavelength for frequencies of interest These wavelengths were calculated from the source rise-times. For both buried monopoles and dipoles, finite-element predictions for both plates and half-spaces were compared with published results obtained from other approaches. The modeled signals were evaluated from the epicenter to a distance of 15 plate thicknesses for plates with a thickness of s 25 mm. The finite-element method provided accurate results and a practical means to analyze \ finite specimens, unlike most alternate approaches.

Modeling of buried monopole and dipole sources of acoustic emission with a finite element technique

The size of Stirling and Stirling‐type pulse tube cryocoolers is dominated by the size of the pressure oscillator. Such cryocoolers typically operate at frequencies up to about 60 Hz for cold‐end temperatures above about 60 K. Higher operating frequencies would allow the size and mass of the pressure oscillator to be reduced for a given power input. However, simply increasing the operating frequency leads to large losses in the regenerator. The simple analytical equations derived here show how the right combination of frequency and pressure, along with optimized regenerator geometry, can lead to successful regenerator operation at frequencies up to 1 kHz. Efficient regenerator operation at such high frequencies is possible only with pressures of about 5 to 8 MPa and with very small hydraulic diameters and lengths. Other geometrical parameters must also be optimized for such conditions. The analytical equations are used to provide guidance to the right combination of parameters. We give example numerical calculations with REGEN3.2 in the paper for 60 Hz, 400 Hz, and 1000 Hz operation of optimized screen regenerators and show that the coefficient of performance at 400 Hz and 1000 Hz is about 78 % and 68 %, respectively, of that for 60 Hz when an average pressure of 7 MPa is used with the higher frequency, compared with 2.5 MPa for 60 Hz operation. The 1000 Hz coefficient of performance for parallel tubes is about the same as that of the screen geometry at 60 Hz. The compressor and cold‐end swept volumes are reduced by a factor of 47 at 1000 Hz, compared with the 60 Hz case for the same input acoustic power, which can enable the development of microcryocoolers for MEMS applications.

Regenerator Operation at Very High Frequencies for Microcryocoolers

The capability of a three-dimensional dynamic finite element method for predicting far-field acoustic emission signals in thin plates of finite lateral extent, including their reflections from the plate edges, was investigated. A lead break (Hsu-Neilsen) source to simulate AE was modeled and used in the experimental measurements. For the thin plate studied, the signals were primarily composed of the lowest order symmetric (S0) and antisymmetric (A0) Lamb modes. Experimental waveforms were detected with an absolutely calibrated, wideband, conical element transducer. The conditions of lead fractures both on the surface of the plate as well as on the edge of the plate were investigated. Surface lead breaks preferentially generate the A0 mode while edge lead breaks generate the S0 mode. Reflections of developed plate waves from both normal and oblique incidence angles were evaluated. Particularly interesting for the case of the lead break on the plate edge were S0 waves produced by the interaction of a Rayleigh wave with the plate corner and by a bulk shear wave mode converting at the side edge. The Rayleigh wave, in this case, propagated along the specimen edge. For all cases considered, the experimental measurements were in good agreement with the predictions of the finite element model.

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Reflections of AE Waves in Finite Plates: Finite Element Modeling and Experimental Measurements

With a validated three-dimensional finite element code, the out-of-plane displacements corresponding to model sources of acoustic emission (AE) were calculated in aluminum plate samples of two different lateral dimensions. Both samples were 4.7 mm thick. The lateral dimensions were 480 mm by 25.4 mm, which represented a laboratory-size coupon, versus 1000 mm by 1000 mm, which represented a larger field-size sample. The displacement signals were calculated for positions of the receiver on the top plate surface at several different distances (in the far-field) from the source’s epicenter. The signals were predicted for the same propagation distances of source-to-receiver in both the large and small samples. Models of both point-like sensors as well as sensors with a large aperture were used. The signals were filtered with either a 40-kHz high-pass filter or a 100-to-300-kHz bandpass filter. The AE sources were modeled as either a point single dipole (both in-plane and out-of-plane) or a point multi-dipole located at different depths within the plate thickness. Analysis of the simulated AE signals shows that the superposition of edge reflections on the arrivals of the direct signal significantly distorts and amplifies AE signals in the laboratory-size coupon relative to a larger field-sized sample. This results in significantly larger AE signal features such as amplitude, duration, and energy in the laboratory-sized sample. Edge reflections also distort the frequency spectrum of signals in the small sample.

Agnes O'Gallagher

Papers

Finite Element and Plate Theory Modeling of Acoustic Emission Waveforms

Modeling of buried monopole and dipole sources of acoustic emission with a finite element technique

Regenerator Operation at Very High Frequencies for Microcryocoolers

Reflections of AE Waves in Finite Plates: Finite Element Modeling and Experimental Measurements

Effects of Lateral Plate Dimensions on Acoustic Emission Signals From Dipole Sources