Existence and uniqueness of Stoneley waves

Chadwick, P.; Borejko, P.

doi:10.1111/j.1365-246x.1994.tb03960.x

Cited by 43 publications

(22 citation statements)

References 7 publications

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“…This recovers the explicit secular equation for Stoneley waves in two homogeneous isotropic elastic halfspaces presented in [31][32][33]. We introduced R in the secular equation (5.22) for Stoneley waves to call readers' attention that R = 0 is a secular equation for Rayleigh waves [33].…”

Section: Orthotropic Materialsmentioning

confidence: 80%

Secular Equations for Rayleigh and Stoneley Waves in Exponentially Graded Elastic Materials of General Anisotropy under the Influence of Gravity

Ting

2011

J Elast

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The Stroh formalism is employed to study Rayleigh and Stoneley waves in exponentially graded elastic materials of general anisotropy under the influence of gravity. The 6 × 6 fundamental matrix N is no longer real. Nevertheless the coefficients of the sextic equation for the Stroh eigenvalue p are real. The orthogonality and closure relations are derived. Also derived are three Barnett-Lothe tensors. They are not necessarily real. Secular equations for Rayleigh and Stoneley wave speeds are presented. Explicit secular equations are obtained when the materials are orthotropic. In the literature, the secular equations for Stoneley waves in orthotropic materials are obtained without using the Stroh formalism. As a result, it requires computation of a 4 × 4 determinant. The secular equation presented here requires computation of a 2 × 2 determinant, and hence is fully explicit. A Rayleigh or Stoneley wave exists in the exponentially graded material under the influence of gravity if the wave can propagate in the homogeneous material without the influence of gravity. As the wave number k → ∞, the Rayleigh or Stoneley wave speed approaches the speed for the homogeneous material.

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Section: Orthotropic Materialsmentioning

confidence: 80%

Secular Equations for Rayleigh and Stoneley Waves in Exponentially Graded Elastic Materials of General Anisotropy under the Influence of Gravity

Ting

2011

J Elast

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“…The nonleaky Stoneley wave exists in rather restricted cases only [6]. The fluid-decoupled Stoneley wave (our terminology) is less known, and we give corresponding existence and uniqueness results in section 5 for the nonleaky case.…”

Section: Finite P-limit Waves At Low Frequenciesmentioning

confidence: 98%

“…With p(ω) as the zero trajectory, it follows from the remark in section 3 on higher-order terms in (3.5) and (3.8) that I S (p(ω)) for the particular solid region in (4.2) is O(ω 2 ) as ω tends to zero. The Y 5 appearing in (2.24) will be a linear combination of the elements (4,5) and (6,5) of the matrix in Lemma 3.3.…”

Section: Interface Conditions With Linear Slipmentioning

confidence: 99%

“…(ii) " µ −1 " appearing in the elements (1,4), (1,6), (3,4), (3,6) is changed to " ( µ −1 ) + k −1 T "; (iii) the elements (1,2), (1,5), (2,6), (5,6) are also modified, but not in a way that is important to us (they remain O(ω 2 p)). Downloaded 11/18/14 to 130.159.70.209.…”

Section: Interface Conditions With Linear Slipmentioning

confidence: 99%

“…The basic asymptotic results in Lemma 3.3 will be modified in the following way: (i) " H " appearing in the elements (1,3), (1,6), (4,3), (4,6) is changed to…”

Section: Interface Conditions With Linear Slipmentioning

confidence: 99%

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A Class of Low-Frequency Modes in Laterally Homogeneous Fluid-Solid Media

Ivansson¹

1998

SIAM J. Appl. Math.

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By a fundamental wave mode in a laterally homogeneous fluid-solid medium, we mean a propagating mode that continues to exist as a propagating mode down to arbitrarily low frequencies. In underwater acoustics with a fluid medium having a pressure-release surface, there is no fundamental mode since each mode has a lower cutoff frequency. In plate acoustics there are two fundamental Lamb modes, a symmetric one (the quasi-longitudinal wave) and an antisymmetric one (the bending wave). There is also a fundamental mode for a fluid plate with rigid boundaries. In seismology, interface waves of Rayleigh-, Scholte-, and Stoneley-type are well known for certain media with one or two homogeneous half-spaces.The purpose of this paper is to give a unified treatment of a class of modes that is related to the fundamental modes. Specifically, we consider low-frequency P-SV modes whose complex phase velocities do not approach zero as fast as the frequency when the frequency is decreased towards zero. Utilizing the analyticity of the dispersion function, a complete characterization is given of these modes and the linearly visco-elastic fluid-solid media in which they occur. All the mentioned particular waves appear in a general setting, and we give asymptotic low-frequency expressions for the modal slownesses and mode forms. As the frequency approaches zero, the phase velocities of these waves will either tend to a nonzero constant or approach zero like the square root of the frequency. In addition, slow modes appear whose phase velocities approach zero like three other powers of the frequency: 1/3, 3/5, and 2/3. (The power 1/5 is possible as well, but only for certain leaky modes.) Concerning the power 1/3, we make a correction to a previous study by Ferrazzini and Aki. The powers 3/5 and 2/3 appear for certain bending-type waves that are slower than the classical bending wave. A less-known type of interface wave also emerges from the analysis. In the nonleaky case, we give precise conditions for its existence and uniqueness. The results can be directly extended to interface conditions with slip. In an extreme case with vanishing specific normal stiffness, we get yet another kind of interface wave.

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Elastic Waves in Solids 1

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Existence and uniqueness of Stoneley waves

Cited by 43 publications

References 7 publications

Secular Equations for Rayleigh and Stoneley Waves in Exponentially Graded Elastic Materials of General Anisotropy under the Influence of Gravity

Secular Equations for Rayleigh and Stoneley Waves in Exponentially Graded Elastic Materials of General Anisotropy under the Influence of Gravity

A Class of Low-Frequency Modes in Laterally Homogeneous Fluid-Solid Media

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