[Show abstract][Hide abstract] ABSTRACT: A plate ray perspective for elastic wave propagation in hollow circular cylinders is presented in order to excite a predominant flexural mode, which in turn generates higher order harmonics due to nonlinear material behavior. The scattering angles are determined for the internally resonant higher order harmonics due to the interactions of two collimated waves. Primary waves that can generate strongly cumulative higher order harmonics are identified for mode self interactions and mutual interactions. A helical inter-digital transducer has been designed for the excitation of a single dominant flexural mode. Numerical evaluations that demonstrate cumulative second harmonic generation are undertaken for both torsional and longitudinal flexural waves. Quadratic sum and difference harmonic generation is observed for the mutual interaction between two primary torsional flexural wave modes.
Full-text · Article · Jun 2014 · Journal of Applied Physics
[Show abstract][Hide abstract] ABSTRACT: A mathematical framework to analyze the cumulative behavior of higher order harmonic generation due to the interaction of two collimated waves in a weakly nonlinear hollow circular cylinder is formulated in this article. A total number of (N + 1)(N + 2)/2 − 3 nonlinear boundary problems are formulated due to the Nth order mode interactions in a cylinder with Kth order nonlinearity (N ≤ K). The cumulative criteria for the second order harmonics (second harmonics, sum and difference harmonics) due to the quadratic interactions of two waves are examined based on the nonlinear forcing terms in curvilinear coordinates. These criteria are formulated by a synchronism condition, the circumferential orders of the primary modes, as well as the nature of the primary and the secondary wave fields, i.e., torsional or longitudinal. A generalized analysis that provides insight into the cumulative nature of the Nth order harmonics by Nth order interaction of two collimated waves is conducted by considering a cylinder with strain energy function written as Murnaghan's power series. The nature of the cumulative Nth order harmonics can be determined by the parity of the number of times the primary waves interact, and their circumferential orders.
Full-text · Article · Jun 2014 · Journal of Applied Physics
[Show abstract][Hide abstract] ABSTRACT: Long narrow piezoelectric fiber composite transducers that can generate planar ultrasonic guided waves are investigated for damage detection in plates. These strip transducers function well as actuators because the ultrasonic energy does not spread out and the signal remains strong. However, their suitability as sensors must be investigated because the received signal is integrated over the entire length of the transducer, potentially making them less sensitive to localized damage since the voltage is averaged over the length of the sensor. A segmented sensing scheme is introduced here and studied both numerically and experimentally. The strip transducer is subdivided into n segments, where n varies from 1 to 11, and the sensitivity to a through-thickness slot is assessed. The results indicate that there is a considerable improvement in defect sensitivity provided by segmented sensing. For a 130-mm-long strip transducer and a 15-mm-long slot, the transmission coefficient decreased from 0.86 to 0.70 to 0.59, while the reflection factor increased from 0.05 to 0.30 to 0.36 for the full 130-mm strip, a 31-mm-long segment, and a 7-mm-long segment, respectively.
No preview · Article · Mar 2014 · Journal of Intelligent Material Systems and Structures
[Show abstract][Hide abstract] ABSTRACT: Ultrasonic guided waves are finding increased use in a variety of Nondestructive Evaluation and Structural Health Monitoring applications due to their efficiency in defect detection using a sensor at a single location to inspect a large area of a structure and an ability to inspect hidden and coated areas for example. With a thorough understanding of guided wave mechanics, researchers can predict which guided wave modes will have a high probability of success in a particular nondestructive evaluation application. For example, in a sample problem presented here to access bond integrity, researchers may choose to use a guided wave mode which has high in-plane displacement, stress, or other feature at the interface. However, since material properties used for modeling work may not be precise for the development of dispersion curves, in many cases guided wave mode and frequency selection should be adjusted for increased inspection efficiency in the field. In this work, a phased array comb transducer is used to sweep over phase velocity - frequency space to tune mode excitation for improved defect characterization performance. A thin polycarbonate layer bonded to a thick metal plate is considered with a contaminated surface prior to bonding. Physicallybased features are used to correlate wave signals with defect detection. Features assessed include arrival time and the frequency of maximum amplitude. A pseudo C-scan plot is presented which can be used to simplify data analysis. Excellent results are obtained.
[Show abstract][Hide abstract] ABSTRACT: Presently, good understanding of second harmonic generation in a weakly nonlinear plate has been obtained, yet the limited number of primary excitations constrains the use of second harmonics in field measurements. The cumulative characteristics of third harmonic generation in a cubic nonlinear plate has been investigated. The power flux analysis shows that primary wave fields are capable of generating a cumulative third harmonic that is of the same nature. Further synchronism analysis shows that the primary shear-horizontal modes are holo-internal-resonant with third harmonic fields, which will be advantageous in experimental measurements. A nonlinear finite element simulation confirms that the primary SH1 mode generates a cumulative sh3 third harmonic mode.
[Show abstract][Hide abstract] ABSTRACT: Guided wave was widely studied for plate and pipe due to the great application area. Guided wave has advantage on long distance inspection for an inaccessible area and apart from transducer. Quite often shrink fit structures were found in nuclear power facilities. In this paper, two pipes were designed with perfect shrink fit condition for Stainless Steel 316. The displacement distribution was calculated with boundary condition. The interface wave propagation pattern was analyzed by the numerical modeling. The experimental results show a possibility of weld delamination and defect detection.
[Show abstract][Hide abstract] ABSTRACT: A few sample problems are presented that demonstrate the importance of mode and frequency selection when using ultrasonic guided waves for nondestructive evaluation.
[Show abstract][Hide abstract] ABSTRACT: Ultrasonic guided wave tomography utilizes an array of permanently
mounted transducers to detect and image defects like corrosion, cracks
and delamination in structures. It is critical for successful tomography
imaging to avoid the influences from external environmental conditions
like water loading and changes in temperature. Water loading is
particularly challenging as it affects the guided wave propagation in
the structure. However, by taking advantage of the physical properties
of guided waves it is possible to reduce its effect on the tomography
images. Modal points on the dispersion curves can be found that have low
out-of-plane displacement in their wave structure and hence no leakage
into the liquid on the structure. In this paper, the omnidirectional
excitation of desired guided wave modes with annular array transducers
is discussed. Guided wave tomography of a steel plate like structure
with a corrosion defect is studied under water loading conditions. The
influence of water loading is overcome by exciting symmetric guided wave
modes (S1) in the structure. Utilizing guided wave mode
control it is shown that the defects in the structure can be easily
discriminated from any artifacts in the images due to the liquid layer.
No preview · Article · Dec 2013 · Smart Materials and Structures
[Show abstract][Hide abstract] ABSTRACT: Interface waves traveling along the boundary between two solids have been studied for nearly a century. However, little attention has been given to the case where interface waves travel at the boundary between a soft and stiff solid and when the soft material is relatively light and viscoelastic. In this paper, the characteristics of interface waves that propagate along a soft-stiff boundary are described. These waves are similar to a leaky Rayleigh-like wave on the stiff solid in terms of the wave velocity and displacement wave structure. Analytical and finite element models are used to model and simulate wave propagation. An example problem of bond evaluation for coatings on metal structures is considered. Experiments on 2.5 cm thick steel plate with 2.5 cm viscoelastic coatings show good agreement to models. Additionally, the results of models and experiments show several promising features that may be used to evaluate bonds in a non-destructive evaluation approach.
No preview · Article · Dec 2013 · The Journal of the Acoustical Society of America
[Show abstract][Hide abstract] ABSTRACT: Ultrasonic guided waves are fast emerging as a reliable tool for continuous structural health monitoring. Their multi-modal nature along with their long range propagation characteristics offer several possibilities for interrogating structures. Transducers commonly used to generate guided waves in structures excite multiple modes at any frequency; their complex scattering and reflection from defects and boundaries often complicates the extraction of useful information. Often it is desirable to control the guided wave modes propagating in a structure to take advantage of their unique properties for different applications. Earlier attempts at guided wave mode control involved developing fixed wavelength linear and annular array transducers. Their only disadvantage is that the transducer is limited to a particular wavelength and a change in wavelength necessitates a change in the transducer. In this paper, we propose the development of an annular array transducer that can generate mode controlled omnidirectional guided waves by independently controlling the amplitude and phase of the array elements. A simplified actuator model that approximates the transducer loading on the structure to a constant pressure load under the array elements is assumed and an optimization problem is set up to compute the excitation voltage and phase of the elements. A five element annular array transducer is designed utilizing 1–3 type piezocomposite materials. The theoretical computations are experimentally verified on an aluminum plate like structure by exciting A0 and S0 guided wave modes.
No preview · Article · Nov 2013 · Smart Materials and Structures
[Show abstract][Hide abstract] ABSTRACT: The third order harmonic generation (third harmonics as well as cubic sum and difference harmonics) due to the cubic interaction of two collimated elastic waves in a homogeneous, isotropic, weakly nonlinear plate is investigated by using a fourth order expansion of strain energy density to formulate the nonlinear boundary problems. Waves with both shear horizontal (SH) and Rayleigh Lamb (RL) nature are considered as primary or tertiary wave fields. The non-zero power flux condition is evaluated using characteristic parity matrices of the cubic nonlinear forcing terms and third order harmonic mode shapes. Results indicate that waves with either SH or RL nature receive power flux from a specific pattern of primary mode interaction. Further analytical evaluation of the synchronism condition enables identification of primary SH and RL modes that are able to generate cumulative third harmonics. The primary SH modes are shown to be holo-internal-resonant with third harmonic SH fields. This simply means that all points on the primary dispersion curves are internally resonant with third harmonics, which is not the case for second harmonics. Such flexibility will be advantageous for laboratory and field measurements.
[Show abstract][Hide abstract] ABSTRACT: The issue of non-destructive characterization of material microstructure with respect to precursors to macroscale damage initiation is addressed. Ultrasonic guided waves are known to be sensitive to material nonlinearity, which is evident through the generation of higher harmonic modes. Thus, nonlinear guided waves have strong potential to identify precursors to macroscale damage and revolutionize condition-based maintenance. Hollow cylindrical waveguides are analyzed herein. As guided waves are multi-modal, the first step in this direction is to identify a primary mode that generates a cumulative higher harmonic mode. The second step is to select transducers to emit the primary mode and receive both primary and secondary modes. After discussing mode and transducer selection, a simulation of second harmonic generation from localized microstructure evolution is presented.
[Show abstract][Hide abstract] ABSTRACT: The interface between an anisotropic composite material and a metallic material is inspected non-destructively for disbonded regions using ultrasonic guided waves. The material properties of the composite and metal have been tailored to demonstrate their effect on inspectability. The material properties have been designed to be either favorable or unfavorable to the existence of propagating Stoneley waves. Stoneley waves can exist because the layer thicknesses are large enough compared to the wavelength to be considered half-spaces. The existence of Stoneley waves between generally anisotropic materials depends on the elastic constants and densities in a complicated way. The range of material properties that allow Stoneley waves is small; however, when the vertically polarized shear wave speeds are similar in the two materials, the existence of Stoneley waves is generally possible. If the conditions do not strictly allow Stoneley waves, other interface waves can still exist such as leaky waves. Disbonds are inserted into the materials before bonding and are inspected using interface waves. Sensitivity to disbonds is determined and thus inspectability is demonstrated for cases that are favorable and unfavorable to Stoneley waves. Both numerical and physical experimental results are shown.
Preview · Article · May 2013 · The Journal of the Acoustical Society of America
[Show abstract][Hide abstract] ABSTRACT: The nonlinear forcing terms for the wave equation in general curvilinear coordinates are derived based on an isotropic homogeneous weakly nonlinear elastic material. The expressions for the nonlinear part of the first Piola-Kirchhoff stress are specialized for axisymmetric torsional and longitudinal fundamental waves in a circular cylinder. The matrix characteristics of the nonlinear forcing terms and secondary mode wave structures are manipulated to analyze the higher harmonic generation due to the guided wave mode self-interactions and mutual interactions. It is proved that both torsional and longitudinal secondary wave fields can be cumulative by a specific type of guided wave mode interactions. A method for the selection of preferred fundamental excitations that generate strong cumulative higher harmonics is formulated, and described in detail for second harmonic generation. Nonlinear finite element simulations demonstrate second harmonic generation by T(0,3) and L(0,4) modes at the internal resonance points. A linear increase of the normalized modal amplitude ratio A2/A1 (2) over the propagation distance is observed for both cases, which indicates that mode L(0,5) is effectively generated as a cumulative second harmonic. Counter numerical examples demonstrate that synchronism and sufficient power flux from the fundamental mode to the secondary mode must occur for the secondary wave field to be strongly cumulative.
Full-text · Article · May 2013 · The Journal of the Acoustical Society of America
[Show abstract][Hide abstract] ABSTRACT: Ultrasonic guided wave inspection of structures containing adhesively bonded joints requires an understanding of the interaction of guided waves with geometric and material discontinuities or transitions in the waveguide. Such interactions result in mode conversion with energy being partitioned among the reflected and transmitted modes. The step transition between an aluminum layer and an aluminum-adhesive-aluminum multi-layer waveguide is analyzed as a model structure. Dispersion analysis enables assessment of (i) synchronism through dispersion curve overlap and (ii) wavestructure correlation. Mode-pairs in the multi-layer waveguide are defined relative to a prescribed mode in a single layer as being synchronized and having nearly perfect wavestructure matching. Only a limited number of mode-pairs exist, and each has a unique frequency range. A hybrid model based on semi-analytical finite elements and the normal mode expansion is implemented to assess mode conversion at a step transition in a waveguide. The model results indicate that synchronism and wavestructure matching is associated with energy transfer through the step transition, and that the energy of an incident wave mode in a single layer is transmitted almost entirely to the associated mode-pair, where one exists. This analysis guides the selection of incident modes that convert into transmitted modes and improve adhesive joint inspection with ultrasonic guided waves.
Full-text · Article · May 2013 · The Journal of the Acoustical Society of America
[Show abstract][Hide abstract] ABSTRACT: The generation of cumulative second harmonic ultrasonic guided wave modes is analyzed with respect to their
applications for nondestructive evaluation (NDE) and structural health monitoring (SHM). Due to the multimodal nature
of guided waves, the selection of a primary wave mode that will generate a cumulative second harmonic is a critical first
step for NDE and SHM applications. Thus, the nonlinear boundary value problem that must be solved by perturbation
analysis is summarized and the results are tabulated for steel plates and circular cylindrical shells (pipes). The analysis
includes shear-horizontal and Lamb waves in plates and axisymmetric torsional and longitudinal waves in pipes.
Nonlinear finite element analyses that include kinematic and material nonlinearities are conducted for plate and pipe
geometries. An excitation is applied to both plate and pipe samples by a simulated interdigitated transducer; SH1 for the
plate and T(0,2) for the pipe. In each case a second harmonic mode having an orthogonal polarization is generated; S1
for the plate and L(0,4) for the pipe. In both cases the second harmonic grows linearly with propagation distance, and
therefore is cumulative. A third example simulation is presented that demonstrates mode mixing in a pipe. T(0,3) and
L(0,2) primary modes traveling in opposite directions intersect and generate significant harmonics at the sum and
difference frequencies. Mode mixing provides a great opportunity to expand the potential of harmonic generation for
NDE and SHM.
[Show abstract][Hide abstract] ABSTRACT: Transducer arrays can be utilized in ultrasonic guided wave applications to achieve preferential excitation of particular points on a dispersion curve. These arrays are designed according to the principles of wave interference and the influence of the wavelength excitation spectrum. This paper develops the relationships between the peak wavelength in the excitation spectra and the element spacing of linear comb and annular arrays. The excitation spectra are developed by applying Fourier and Hankel transforms to the spatial loading distribution functions of the comb and annular arrays, respectively. Although the peak wavelength of excitation of a comb array is typically assumed to be equal to the element spacing, it is shown that this can be an inaccurate assumption for annular arrays. The ratio of element spacing to the peak wavelength in the excitation spectrum is termed the spacing compensation factor, and is dependent on the number of array elements and the inner radius. It is determined that the compensation factor is negligible for comb arrays but is crucial for annular arrays in order to achieve optimal mode selection. Finite element analyses and experimental data are used to verify the calculations and demonstrate the significance of the compensation factor.
No preview · Article · Jan 2013 · The Journal of the Acoustical Society of America
[Show abstract][Hide abstract] ABSTRACT: For structural health monitoring applications, ultrasonic guided wave mode control is critical for obtaining simple signals that can be easily analyzed as well as special modes and frequencies for improved sensitivity to certain defects. This paper discusses the development of an annular array transducer for omnidirectional guided wave mode control in plate like structures. Using a flexible piezoelectric material like polyvinlydine fluoride (PVDF), annular array transducers that are low cost, low profile and conformable to the structure can be made rapidly. Two different array patterns, namely ones of comb and inter-digital (IDT) type, are studied. The loadings of these transducers on a structure differ from one another and hence so do their source influences. An axi-symmetric finite element modeling is employed to study the surface displacement pattern of these two transducer configurations. The source influence of the transducer configurations is studied experimentally by exciting an anti-symmetric (A1) and a symmetric (S1) type guided wave mode in a steel plate. It was observed that IDT type transducers were able to couple well to the guided wave modes at the wavelengths that they are designed for. The comb type transducers have a weak coupling to symmetric guided wave modes at frequencies where the wave structure has high in-plane displacement and negligible out-of-plane displacement on the surface of the structure.
No preview · Article · Dec 2012 · Smart Materials and Structures
[Show abstract][Hide abstract] ABSTRACT: The nonlinear forcing terms for the wave equation in general curvilinear
coordinates are derived based on a hyperelastic material. The expressions for
the nonlinear part of the first Piola-Kirchhoff stress are specialized for
axisymmetric torsional and longitudinal fundamental wave fields in a cylinder.
The matrix characteristics of the nonlinear forcing terms and secondary mode
wavestructures are manipulated to analyze the higher harmonic generation due to
the guided wave mode self interactions and mutual interactions. It is proven
that both torsional and longitudinal mode secondary fields can be cumulative by
specific type of guided wave mode interactions. A method for the selection of
preferred fundamental excitations that generate strongly cumulative higher
harmonics is formulated, and described in detail for second harmonic
generation. Hyperelastic finite element models are built to simulate second
harmonic generation by T(0,3) and L(0,4) modes. A linear increase of the modal
amplitude ratio A2/A1^2 over the propagation distance is observed for both
cases, which indicates mode L(0,5) is effectively generated as cumulative
[Show abstract][Hide abstract] ABSTRACT: An ultrasonic guided wave based damage detection technique has been
developed for structural health monitoring (SHM) of composite structures
submerged in water. Specially designed guided wave transducers are
utilized to selectively excite and receive guided waves with dominant
shear horizontal particle displacements. It has been shown that the SH
type waves are insensitive to water loading conditions. With appropriate
water sealing, the transducers can be applied to composite structures
submerged in water. The guided wave signals collected from an underwater
composite structure are almost identical to the signals that are
obtained before the structure is submerged. Experiments have been
conducted to demonstrate the feasibility of damage detection in
underwater composite structures. A thick carbon/epoxy composite beam is
used as the test sample. Excellent damage detection results were
obtained for both dry and underwater tests.
No preview · Article · Mar 2012 · Proceedings of SPIE - The International Society for Optical Engineering