Preface Acknowledgments 1. Introduction 2. Dispersion principles 3. Unbounded isotropic and anisotropic media 4. Reflection and refraction 5. Oblique incidence 6. Waves in plates 7. Surface and subsurface waves 8. Finite element method for guided wave mechanics 9. The semi-analytical finite element method (SAFE) 10. Guided waves in hollow cylinders 11. Circumferential guided waves 12. Guided waves in layered structures 13. Source influence on guided wave excitation 14. Horizontal shear 15. Guided waves in anisotropic media 16. Guided wave phased arrays in piping 17. Guided waves in viscoelastic media 18. Ultrasonic vibrations 19. Guided wave array transducers 20. Introduction to guided wave nonlinear methods 21. Guided wave imaging methods Appendix A: ultrasonic nondestructive testing principles, analysis and display technology Appendix B: basic formulas and concepts in the theory of elasticity Appendix C: physically based signal processing concepts for guided waves Appendix D: guided wave mode and frequency selection tips.

Ultrasonic Guided Waves in Solid Media

This work assumes a basic familiarity with the finite element method. For those readers desiring a better understanding of the method, there are a number of excellent books varying from an introductory treatment to advanced topics listed in the bibliography [1] [2] [3] [4] [5]. In this chapter, we will review the fundamentals of the finite element method and introduce the notation which will be used throughout the book. For the examples shown in this book, either first or second order elements were used. For the worked examples first order triangles are used. The use of first order triangular elements simplifies the arguments and in no way reduces generality. In all cases the procedures given in this book can be used with high order and/or curved elements.

Introduction to Finite Elements

Structural Health Monitoring system based on a concept of Lamb wave focusing by the piezoelectric array

Laminated composites are susceptible to delamination due to their weak transverse tensile and interlaminar shear strengths as compared to their in-plane properties. Delamination damage can occur in...

Delamination detection and quantification on laminated composite structures with Lamb waves and wavenumber analysis

Heat transfer in metal foams and designed porous media

The guided wave (GW) field excited by a wedge-shaped, anisotropic piezocomposite transducer, surface-bonded on an isotropic substrate is investigated with applications to large area structural health monitoring. This investigation supports the development of the composite long-range variable-direction emitting radar (CLoVER) transducer. The analysis is based on the three-dimensional equations of elasticity, and the solution yields expressions for the field variables that are able to capture the multimodal nature of GWs. The assumption of uncoupled dynamics between the actuator and substrate is used, and their interaction is modeled through shear tractions along the transducer's radial edges. A similar problem is modeled using three-dimensional finite element simulations to assess the spatial and transient accuracy of the solution. Experimental tests are also conducted on pristine structures to validate the accuracy of the theoretical approach. The experimental studies employ CLoVER transducers developed in-house, and their manufacturing procedure is briefly described. Frequency response experiments based on piezoelectric sensors are conducted to assess the performance of the solution in the frequency domain. These tests are complemented by laser vibrometer measurements that allow the spatial and temporal evolution of the solution to be evaluated. The numerical simulations and experimental tests show that the wave time of arrival, radial attenuation, and azimuthal distribution are well captured by the theoretical solution.

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Guided wave excitation by a CLoVER transducer for structural health monitoring: theory and experiments

Convective heat transfer in aluminum metal foam sandwich panels is investigated with potential applications to actively cooled thermal protection systems in hypersonic and reentry vehicles. The size eects of the metal foam core are experimentally investigated and the eects of foam thickness on convective transfer are established. Four metal foam specimens are utilized with a relative density of 0.08 and pore density of 20 ppi in a range of thickness from 6.4 mm to 25.4 mm in increments of approximately 6 mm. An exact-shapefunction nite element model is developed that envisions the foam as randomly oriented cylinders in cross o w with an axially varying coolant temperature eld. Our experimental results indicate that larger foam thicknesses produce increased heat transfer levels in metal foams. Initial FE simulations using a fully developed, turbulent velocity prole show the potential of this numerical tool to model convective heat transfer in metal foams. Metal foam sandwich panels have been proposed as alternative multi-functional materials for structural thermal protection systems in hypersonic and re-entry vehicles 1 . 2 This type of construction oers numerous advantages over other actively cooled concepts because of the unique properties of metal foams. These materials, when brazed between metallic face sheets, are readily suited to allow coolant passage without the addition of alien components that may compromise structural performance. Moreover, the mechanical properties can be varied to suit dieren t structural needs by varying the foam relative density. From a heat transfer point of view, these materials have been shown to be exceptional heat exchangers primarily due to the increased surface area available for heat transfer between the solid and uid phases. The thermo-mechanical response of metal foam sandwich panels has been recently studied and characterized. 2 In particular, it has been shown that using air as coolant at sucien tly high velocities, the strain due to buckling of these structures under thermo-mechanical loads can be virtually eliminated. The implementation of these materials in thermal protection systems, however, requires that a proper heat transfer model exists that allows the coupling between the thermo-mechanical and heat transfer problems to be properly analyzed. In other words, it is necessary to understand how dieren t foam properties such as relative density, pore density, and foam thickness will aect the heat loads that this type of structural component can remove. Heat transfer in metal foams has been a subject of active research in recent years. Lu et al. 3 developed an analytical model envisioning the foam as an array of mutually perpendicular cylinders subjected to cross-o w. In this study, a closed-form expression for the convective coecien t of a foam-lled channel with constant wall temperatures was presented based on foam geometry and material and uid properties. These authors reported that the simplifying assumptions used in their analysis were likely to lead to an over-prediction of the actual heat transfer level. This model has been partially validated by Bastawros and Evans 4 who performed forced convection experiments on aluminum foams adhered to silicon substrate face sheets. These authors reported that the predictions of Lu et al. 3 regarding the dependence of the convective coecien t on coolant velocity and strut diameter were qualitatively consistent with their observations, but that the foam thickness eects were not adequately modeled. In particular, they reported that the heat dissipation rate

/pdf/convective-heat-transfer-in-open-cell-metal-foams-53seot2fnz.pdf

Convective heat transfer in open cell metal foams

The guided wave (GW) fleld excited by piezoelectric wafers and piezocomposite transducers in carbon-flber composite materials is experimentally investigated with applications to structural health monitoring. This investigation supports the characterization of the Composite Long-range Variable-direction Emitting Radar (CLoVER) transducer introduced by the authors. A systematic approach is followed where composite conflgurations with difierent levels of anisotropy are analyzed. In particular, unidirectional, cross-ply [0/90]6S, and quasi-isotropic [0/45/-45/90]4S IM7-based composite plates are employed. A combination of laser vibrometry and flnite element analysis is used to determine the inplane wave speed and peak-to-peak amplitude distribution in each substrate considered. The results illustrate the efiect of the material anisotropy on GW propagation through the steering efiect where the wave packets do not generally travel along the direction in which they are launched. After characterizing the efiect of substrate anisotropy on the GW fleld, the performance of the CLoVER transducer to detect damage in various composite conflgurations is explored. It is found that the directionality and geometry of the device is efiective in detecting the presence and identifying the location of simulated defects in difierent composite layups.

/pdf/guided-wave-structural-health-monitoring-using-clover-5956gigx1p.pdf

Guided wave structural health monitoring using CLoVER transducers in composite materials

Structural health monitoring (SHM) is the component of damage prognosis systems responsible for interrogating a
structure to detect, locate, and identify any damage present. Guided wave (GW) testing methods are attractive
for this application due to the ability of GWs to travel over long distances with little attenuation and their
sensitivity to different damage types. The Composite Long-range Variable-direction Emitting Radar (CLoVER)
transducer is introduced as an alternative concept for efficient damage interrogation and GW excitation in GW-based
SHM systems. This transducer has an overall ring geometry, but is composed of individual wedge-shaped
sectors that can be individually excited to interrogate the structure in a particular direction. Each wedge-shaped
sector is made with piezoelectric fibers embedded in an epoxy matrix surrounded by an interdigitated
electrode pattern. The multiple advantages over alternative transducer concepts are examined. In particular, it
is shown that the geometry of each sector yields actuation amplitudes much larger than those obtained for a ring
configuration under similar electric inputs. The manufacture and characterization procedures of these devices
are presented, and it is shown that their free strain performance is similar to that of conventional piezocomposite
transducers. Experimental studies of damage detection simulating the proposed damage interrogation approach
are also presented.

Design and characterization of the CLoVER transducer for structural health monitoring

The increasing use of composite materials in multiple engineering applications has emphasized the need for structural health monitoring (SHM) technologies capable of detecting, locating, and classifying structural defects in these materials. Guided wave (GW) methods of fer an attractive solution for SHM due to their tunable sensitivity to different defects and their ability to interrogate large structural surfaces. The complications associated with the material anisotropy and directionality in composites result in an increased need for accurate and efficient simulation tools to characterize GW excitation and propagation in these materials. This paper presents a theoretical model based on three-dimensional elasticity to characterize GW excitation by finite-dimensional transducers in composite laminates. The theory uses an eigenbasis expansion for a bulk transversely isotropic material combined with Fourier transforms, the global matrix approach, and residue theory to find the displacement field excited by an arbitrarily shaped finite-dimensional transducer. Experimental results obtained in a cross-ply composite laminate are used to assess the accuracy of the theoretical solution. Keywords: structural health monitoring (SHM), guided wave s (GW), transducer design, composite materials.

Ken I. Salas

Papers

Guided wave excitation by a CLoVER transducer for structural health monitoring: theory and experiments

Convective heat transfer in open cell metal foams

Guided wave structural health monitoring using CLoVER transducers in composite materials

Design and characterization of the CLoVER transducer for structural health monitoring

Characterization of guided-wave propagation in composite plates