Cumulative second harmonics in weakly nonlinear plates and shells

Liu, Yang; Lissenden, Cliff J.; Rose, Joseph L.

doi:10.1117/12.2009896

Cited by 5 publications

(6 citation statements)

References 20 publications

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“…where u i is the displacement vector. Based on the potential given in (4) the stress-strain relation in terms of the third order elastic coefficients A B C , , in the tensor notation is given by [13] Here, S ik are the components of the second Piola-Kirchhoff stress tensor.…”

Section: Five-constant Nonlinear Elastic Theorymentioning

confidence: 99%

“…It is rarely used and not implemented in commonly used FEM software. In [12] and [13] a numerical simulation based on the third order stiffness parameters is developed and used to verify the cumulative effect of the second harmonic Lamb wave generation due to the material nonlinearity in aluminium. Furthermore, in [14] and [15] the generation of higher harmonic modes based on the S 0 -mode due to a breathing crack is simulated and analyzed.…”

Section: Introductionmentioning

confidence: 99%

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Numerical simulation of elastic wave propagation in isotropic media considering material and geometrical nonlinearities

Rauter

Lammering

2015

Smart Mater. Struct.

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In order to detect micro-structural damages accurately new methods are currently developed. A promising tool is the generation of higher harmonic wave modes caused by the nonlinear Lamb wave propagation in plate like structures. Due to the very small amplitudes a cumulative effect is used. To get a better overview of this inspection method numerical simulations are essential. Previous studies have developed the analytical description of this phenomenon which is based on the five-constant nonlinear elastic theory. The analytical solution has been approved by numerical simulations. In this work first the nonlinear cumulative wave propagation is simulated and analyzed considering micro-structural cracks in thin linear elastic isotropic plates. It is shown that there is a cumulative effect considering the S1–S2 mode pair. Furthermore the sensitivity of the relative acoustical nonlinearity parameter regarding those damages is validated. Furthermore, an influence of the crack size and orientation on the nonlinear wave propagation behavior is observed. In a second step the micro-structural cracks are replaced by a nonlinear material model. Instead of the five-constant nonlinear elastic theory hyperelastic material models that are implemented in commonly used FEM software are used to simulate the cumulative effect of the higher harmonic Lamb wave generation. The cumulative effect as well as the different nonlinear behavior of the S1–S2 and S2–S4 mode pairs are found by using these hyperelastic material models. It is shown that, both numerical simulations, which take into account micro-structural cracks on the one hand and nonlinear material on the other hand, lead to comparable results. Furthermore, in comparison to the five-constant nonlinear elastic theory the use of the well established hyperelastic material models like Neo–Hooke and Mooney–Rivlin are a suitable alternative to simulate the cumulative higher harmonic generation.

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Section: Five-constant Nonlinear Elastic Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical simulation of elastic wave propagation in isotropic media considering material and geometrical nonlinearities

Rauter

Lammering

2015

Smart Mater. Struct.

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“…Likewise, two local approaches, namely cellular automata finite element and local interaction simulation approach have been employed 39 to study second-harmonic guided wave generation in waveguides. On the other hand, conventional finite element methods incorporating material and geometric nonlinearities were extensively used 26,28,36,[40][41][42] to study second-harmonic guided wave propagation in waveguides, especially in plates and pipes. In this section, we discuss the results from finite element simulations concerning second-harmonic guided waves in plates.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Internal resonance is the first consideration; starting with phase matching and then assessing the secondary modes that have not just nonzero power flux, but significant power fluxes. 28 Other important considerations include: modal excitability given the selected transducer, proximity of nearby modes, dispersion, diffraction, and attenuation. In fact, the number of primary modes that generate internally resonant second harmonics that are measured by currently available transducers are so low that the generation of third harmonics was analyzed.…”

Section: Mode Selectionmentioning

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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“…A bilinear stiffness model 15 with changeable stiffness under different phases of a wave was also an attractive analytical model. Among numerical methods for simulating material nonlinearity or CAN, the local interaction simulation approach (LISA), 16,17 the finite element method (FEM) 18,19 and the time-domain spectral finite element method (SFE) 20 are representative methods. Many experimental studies have also been conducted on plate structures, focusing on material nonlinearity 21,22 and CAN induced by fatigue crack.…”

Section: Introductionmentioning

confidence: 99%

Fatigue crack detection in pipes with multiple mode nonlinear guided waves

Guan

Wang

et al. 2018

Structural Health Monitoring

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This study elaborates fundamental differences in fatigue crack detection using nonlinear guided waves between plate and pipe structures and provides an effective approach for analysing nonlinearity in pipe structures. For this purpose, guided wave propagation and interaction with microcrack in a pipe structure, which introduced a contact acoustic nonlinearity, was analysed through a finite element analysis in which the material nonlinearity was also included. To validate the simulation results, experimental testing was performed using piezoelectric transducers to generate guided waves in a specimen with a fatigue crack. Both methods revealed that the second harmonic wave generated by the breathing behaviour of the microcrack in a pipe had multiple wave modes, unlike the plate scenario using nonlinear guided waves. Therefore, a proper index which considered all the generated wave modes due to the microcrack was developed to quantify the nonlinearity, facilitating the identification of microscale damage and further assessment of the severity of the damage in pipe structures.

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Cumulative second harmonics in weakly nonlinear plates and shells

Cited by 5 publications

References 20 publications

Numerical simulation of elastic wave propagation in isotropic media considering material and geometrical nonlinearities

Numerical simulation of elastic wave propagation in isotropic media considering material and geometrical nonlinearities

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

Fatigue crack detection in pipes with multiple mode nonlinear guided waves

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