Finite amplitude waves in isotropic elastic waveguides with arbitrary constant cross-sectional area

Lima, Washington Jose Noberto de; Hamilton, Mark F.

doi:10.1016/j.wavemoti.2004.05.004

Cited by 60 publications

(48 citation statements)

References 5 publications

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“…Second harmonic, sum, and difference frequency generation in waveguides of arbitrary cross section w first investigated by De Lima and Hamilton. 30 The conditions for internal resonance were arrived at and also secondharmonic generation in cylindrical rods and shells was numerically demonstrated. Likewise, generalized higher harmonic generation in waveguides of arbitrary cross section was investigated.…”

Section: Nonlinear Guided Waves In Other Waveguidesmentioning

confidence: 99%

Review of nonlinear ultrasonic guided wave nondestructive evaluation: theory, numerics, and experiments

2015

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Abstract. Interest in using the higher harmonic generation of ultrasonic guided wave modes for nondestructive evaluation continues to grow tremendously as the understanding of nonlinear guided wave propagation has enabled further analysis. The combination of the attractive properties of guided waves with the attractive properties of higher harmonic generation provides a very unique potential for characterization of incipient damage, particularly in plate and shell structures. Guided waves can propagate relatively long distances, provide access to hidden structural components, have various displacement polarizations, and provide many opportunities for mode conversions due to their multimode character. Moreover, higher harmonic generation is sensitive to changing aspects of the microstructures such as to the dislocation density, precipitates, inclusions, and voids. We review the recent advances in the theory of nonlinear guided waves, as well as the numerical simulations and experiments that demonstrate their utility. 1 Introduction Nonlinear ultrasonic nondestructive evaluation uses interrogation signals at frequencies other than the excitation frequency to detect changes in structural integrity and characterize degradation of materials. Nonlinear ultrasonic methodologies provide improved sensitivity to damage and the ability to identify incipient damage relative to linear methods. In general, linear ultrasonic methods provide good sensitivity to macroscale damage such as long fatigue cracks. However, in many cases, once damage appears at the macroscale, the remaining life is short, severely limiting maintenance decisions. Thus, characterization of incipient damage could facilitate a paradigm shift in operations of structural systems from schedule-based to condition-based maintenance that would ultimately enhance safety and reduce life cycle costs. Nonlinear ultrasonics is a broad discipline 1,2 which encompasses many specialized techniques reliant upon nonlinear material behavior to detect and/or characterize incipient damage. Some of these include nonlinear resonant ultrasound spectroscopy, 3 nonlinear elastic wave spectroscopy, 4-6 and second-harmonic generation.

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Section: Nonlinear Guided Waves In Other Waveguidesmentioning

confidence: 99%

Review of nonlinear ultrasonic guided wave nondestructive evaluation: theory, numerics, and experiments

2015

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“…8 Müller et al 9 obtained analytical asymptotic solutions to Lamb waves and five mode types for the cumulative increase in the amplitude of the second harmonic wave with the propagation distance. The theoretical analysis was extended from plate like structures to cylindrical rod and pipe structures by de Lima et al 10 and Chillara et al 11 More recently, Liu et al demonstrated a method for the selection of primary modes with respect to the internal resonance, 12 also extended the work to higher order harmonics.…”

Section: Introductionmentioning

confidence: 99%

Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections

Zuo

Zhou²,

Fan

2016

AIP Advances

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Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonant frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.

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“…They also investigate axisymmetric longitudinal and torsional modes in pipes through analytical modeling and finite element simulations 12 . De Lima and Hamilton studied the higher harmonic generation of waves in waveguides having arbitrary cross-section and gave examples of cylindrical rods and shells 13 . They solved the nonlinear wave equation by a normal mode expansion method using a perturbation analysis, then investigated the cumulative condition for the longitudinal modes.…”

Section: Introductionmentioning

confidence: 99%

“…Full details can be found elsewhere [6][7][8][9][10][11][12][13][14][15] . A curvilinear coordinate system is used for the shell, and both kinematic and material nonlinearities are included in the formulation.…”

Section: Introductionmentioning

confidence: 99%

Cumulative second harmonics in weakly nonlinear plates and shells

2013

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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.

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Finite amplitude waves in isotropic elastic waveguides with arbitrary constant cross-sectional area

Cited by 60 publications

References 5 publications

Review of nonlinear ultrasonic guided wave nondestructive evaluation: theory, numerics, and experiments

Review of nonlinear ultrasonic guided wave nondestructive evaluation: theory, numerics, and experiments

Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections

Cumulative second harmonics in weakly nonlinear plates and shells

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