Lamb waves in stratified and functionally graded plates: discrepancy, similarity, and convergence

Кузнецов, С. В.

doi:10.1080/17455030.2019.1683257

Cited by 34 publications

(8 citation statements)

References 27 publications

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“…and the long-wave limiting velocity [29,35,36], which in the considered case coincides with the speed of sound in the rod [37]:…”

Section: Equation Of Statementioning

confidence: 67%

Oscillating Nonlinear Acoustic Waves in a Mooney–Rivlin Rod

Karakozova,

Kuznetsov

2023

Applied Sciences

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Harmonic wave excitation in a semi-infinite incompressible hyperelastic 1D rod with the Mooney–Rivlin equation of state reveals the formation and propagation of the shock wave fronts arising between faster and slower moving parts of the initially harmonic wave. The observed shock wave fronts result in the collapse of the slower moving parts being absorbed by the faster parts; hence, to the attenuation of the kinetic and the elastic strain energy with the corresponding heat generation. Both geometrically and physically nonlinear equations of motion are solved by the explicit Lax–Wendroff numerical tine-integration scheme combined with the finite element approach for spatial discretization.

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“…and the long-wave limiting velocity [29,35,36], which in the considered case coincides with the speed of sound in the rod [37]:…”

Section: Equation Of Statementioning

confidence: 67%

Oscillating Nonlinear Acoustic Waves in a Mooney–Rivlin Rod

Karakozova,

Kuznetsov

2023

Applied Sciences

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“…Two six-dimensional formalisms are known, Stroh formalism [15,16], see also previous works [1][2][3][4][5][6][18][19][20][21][22][23][24][25], and Cauchy formalism [26,27]. Both of these formalisms are equivalent in terms of the dispersion equations [28]. Considering Cauchy formalism, a new six-vector is introduced…”

Section: Semisimple Fundamental Matrixmentioning

confidence: 99%

Lamb waves at a non-semisimple degeneracy of the fundamental matrix

Kuznetsov

2024

Mathematics and Mechanics of Solids

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Anomalous guided waves appearing at a non-semisimple degeneracy of the fundamental matrix are observed and analyzed in the framework of the Cauchy sextic formalism. The non-semisimple degeneracy condition is explicitly constructed for the most general case of Lamb waves propagating in a traction-free layer with arbitrary elastic anisotropy. A new type of dispersion equation and the corresponding dispersion solution are obtained. The connection with surface waves of the non-Rayleigh type is discussed.

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“…Such composite plates, being vulnerable to the appearance of IGV, are widely used in aerospace, automotive, marine engineering, etc. [35][36][37][38][39] The ongoing analysis is based on the Cauchy sextic formalism and the exponential fundamental matrix method, 40 allowing constructing a dispersion equation and, using the geometrical condition (1.10), finding both the finite frequency and phase velocity related to large group velocity values belonging to the fundamental branches.…”

Section: Problem Statementmentioning

confidence: 99%

“…Herein, the dispersion equation is derived by using Cauchy sextic formalism and the exponential fundamental matrix method. 40…”

Section: Dispersion Equationmentioning

confidence: 99%

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On infinite group velocity in composite plates

Kuznetsov

2023

Jnl of Sandwich Structures & Materials

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The analytical and geometrical conditions for the possible appearance of the infinite group velocity (IGV) points belonging to the dispersion curves of Lamb waves propagating in traction-free plates are studied by a combined method comprising Cauchy sextic formalism and the exponential fundamental matrix method. According to the obtained geometrical condition, the IGV corresponds to the coincidence of a tangent line to any of the dispersion curves with a straight line passing through the origin. The developed technique is demonstrated by applying to the analysis of Lamb wave dispersion in three-layered plates with a soft inner core.

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Lamb waves in stratified and functionally graded plates: discrepancy, similarity, and convergence

Cited by 34 publications

References 27 publications

Oscillating Nonlinear Acoustic Waves in a Mooney–Rivlin Rod

Oscillating Nonlinear Acoustic Waves in a Mooney–Rivlin Rod

Lamb waves at a non-semisimple degeneracy of the fundamental matrix

On infinite group velocity in composite plates

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