Energy conservation and pulse propagation in an elastic medium with quadratic nonlinearity

Cantrell, John H.; Yost, William T.

doi:10.1063/1.4748963

Cited by 3 publications

(2 citation statements)

References 20 publications

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“…The phenomenon of the static displacement generation in structures during the finite amplitude sinusoidal ultrasonic wave propagation was initially explored by Thurston and Shapiro [23]. Later, this topic was mainly studied by two scientific groups respectively led by Cantrell [24][25][26][27][28] and Jacob [21,22,[29][30][31][32]. The contributions of these two groups put forward the development of the technique using the static displacement in nonlinear ultrasonics for NDT and SHM applications.…”

Section: Introductionmentioning

confidence: 99%

Numerical study on static component generation from the primary Lamb waves propagating in a plate with nonlinearity

Wan

Tse

Zhang

et al. 2018

Smart Mater. Struct.

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Under the discipline of nonlinear ultrasonics, in addition to second harmonic generation, static component generation is another frequently used nonlinear ultrasonic behavior in non-destructive testing (NDT) and structural health monitoring (SHM) communities. However, most previous studies on static component generation are mainly based on using longitudinal waves. It is desirable to extend static component generation from primary longitudinal waves to primary Lamb waves. In this paper, static component generation from the primary Lamb waves is studied. Two major issues are numerically investigated. First, the mode of static displacement component generated from different primary Lamb wave modes is identified. Second, cumulative effect of static displacement component from different primary Lamb wave modes is also discussed. Our study results show that the static component wave packets generated from the primary S0, A0 and S1 modes share the almost same group velocity equal to the phase velocity of S0 mode tending to zero frequency cplate. The finding indicates that whether the primary mode is S0, A0 or S1, the static components generated from these primary modes always share the nature of S0 mode. This conclusion is also verified by the displacement filed of these static components that the horizontal displacement field is almost uniform and the vertical displacement filed is antisymmetric across the thickness of the plate. The uniform distribution of horizontal displacement filed enables the static component, regardless of the primary Lamb modes, to be a promising technique for evaluating microstructural damages buried in the interior of a structure. Our study also illustrates that the static components are cumulative regardless of whether the phase velocity of the primary and secondary waves is matched or not. This observation indicates that the static component overcomes the limitations of the traditional nonlinear Lamb waves satisfying phase velocity matching condition to achieve cumulative second harmonic generation. This nature also enables the primary Lamb waves excited at a low center frequency to generate static component used for inspecting large-scale structures with micro-scale damages.

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Section: Introductionmentioning

confidence: 99%

Numerical study on static component generation from the primary Lamb waves propagating in a plate with nonlinearity

Wan

Tse

Zhang

et al. 2018

Smart Mater. Struct.

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“…12, these analytical results do obey the Law of Energy Conservation. In an effort to understand the experimentally observed right-triangular shape of the quasistatic displacement pulse reported by Yost and Cantrell, 2 we explored several other aspects of the problem that might potentially be responsible to such observations.…”

Section: Discussionmentioning

confidence: 52%

Finite-size effects on the quasistatic displacement pulse in a solid specimen with quadratic nonlinearity

Nagy

Jacobs

2013

The Journal of the Acoustical Society of America

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There is an unresolved debate in the scientific community about the shape of the quasistatic displacement pulse produced by nonlinear acoustic wave propagation in an elastic solid with quadratic nonlinearity. Early analytical and experimental studies suggested that the quasistatic pulse exhibits a right-triangular shape with the peak displacement of the leading edge being proportional to the length of the tone burst. In contrast, more recent theoretical, analytical, numerical, and experimental studies suggested that the quasistatic displacement pulse has a flat-top shape where the peak displacement is proportional to the propagation distance. This study presents rigorous mathematical analyses and numerical simulations of the quasistatic displacement pulse. In the case of semi-infinite solids, it is confirmed that the time-domain shape of the quasistatic pulse generated by a longitudinal plane wave is not a right-angle triangle. In the case of finite-size solids, the finite axial dimension of the specimen cannot simply be modeled with a linear reflection coefficient that neglects the nonlinear interaction between the combined incident and reflected fields. More profoundly, the quasistatic pulse generated by a transducer of finite aperture suffers more severe divergence than both the fundamental and second order harmonic pulses generated by the same transducer.

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Quasistatic pulse generation of ultrasonic guided waves propagation in composites

Jiang

Deng

et al. 2022

Journal of Sound and Vibration

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Energy conservation and pulse propagation in an elastic medium with quadratic nonlinearity

Cited by 3 publications

References 20 publications

Numerical study on static component generation from the primary Lamb waves propagating in a plate with nonlinearity

Numerical study on static component generation from the primary Lamb waves propagating in a plate with nonlinearity

Finite-size effects on the quasistatic displacement pulse in a solid specimen with quadratic nonlinearity

Quasistatic pulse generation of ultrasonic guided waves propagation in composites

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