Complex Rayleigh Waves in Nonhomogeneous Magneto-Electro-Elastic Half-Spaces

The complex Rayleigh waves play an important role in the energy conversion efficiency of magneto-electro-elastic devices, so it is necessary to explore the wave propagation characteristics for the better applications in engineering. This paper modifies the Laguerre orthogonal polynomial to investigate the complex Rayleigh waves propagating in nonhomogeneous magneto-electro-elastic half-spaces. The improved method simplifies the calculation process by incorporating boundary conditions into the constitutive relations, shortens the solving time by transforming the solution of wave equation to an eigenvalue problem, and obtains all wave modes, including real and imaginary and complex wavenumbers. The three-dimensional curves of full frequency spectrum and phase velocities are presented for the better description of the conversion from complex Rayleigh wave modes to real wave ones; besides, the displacement distributions, electric and magnetic potential curves are obtained in thickness and propagation directions, respectively. Numerical results are analyzed and discussed elaborately in three cases: variation of nonhomogeneous coefficients, absence of magnetism, and absence of electricity. The results can be used to optimize and fabricate the acoustic surface wave devices of the nonhomogeneous magneto-electro-elastic materials.

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Three-dimensional interfacial wave theory of dendritic growth: (II). non-axi-symmetric global wave modes and selection criterion of pattern formation

Chinese Physics B ◽

10.1088/1674-1056/18/2/047 ◽

2009 ◽

Vol 18 (2) ◽

pp. 686-698 ◽

Cited By ~ 9

Author(s):

Chen Yong-Qiang ◽

Tang Xiong-Xin ◽

Xu Jian-Jun

Keyword(s):

Pattern Formation ◽

Dendritic Growth ◽

Three Dimensional ◽

Selection Criterion ◽

Wave Theory ◽

Interfacial Wave ◽

Wave Modes

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Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-021-01475-0 ◽

2021 ◽

Vol 72 (2) ◽

Author(s):

Mircea Bîrsan

Keyword(s):

Energy Density ◽

Constitutive Model ◽

Strain Energy Density ◽

Strain Energy ◽

Shell Theory ◽

Constitutive Relations ◽

Three Dimensional ◽

Classical Shell Theory ◽

Three Dimensional Elasticity ◽

General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

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Numerical Analysis of Acoustical Propagation Characteristics in Central Equatorial Pacific Ocean with Ridges of Seabed Used by Three-Dimensional Parabolic Equation Method

Japanese Journal of Applied Physics ◽

10.1143/jjap.39.3212 ◽

2000 ◽

Vol 39 (Part 1, No. 5B) ◽

pp. 3212-3215 ◽

Cited By ~ 4

Author(s):

Takenobu Tsuchiya ◽

Takashi Okuyama ◽

Nobuyuki Endoh ◽

Toshiaki Nakamura ◽

Iwao Nakano

Keyword(s):

Parabolic Equation ◽

Numerical Analysis ◽

Pacific Ocean ◽

Three Dimensional ◽

Equatorial Pacific ◽

Equation Method ◽

Propagation Characteristics ◽

Equatorial Pacific Ocean ◽

Parabolic Equation Method ◽

Central Equatorial Pacific

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Measurements of Rayleigh-wave phase velocities in Nevada: Implications for explosion sources and the Massachusetts Mountain earthquake

Bulletin of the Seismological Society of America ◽

10.1785/bssa0720041329 ◽

1982 ◽

Vol 72 (4) ◽

pp. 1329-1349

Author(s):

H. J. Patton

Keyword(s):

Rayleigh Wave ◽

Rayleigh Waves ◽

Moment Tensor ◽

Test Site ◽

P Wave ◽

Stress Axis ◽

Phase Velocities ◽

Wave Phase ◽

Single Station ◽

Source Phase

abstract Single-station measurements of Rayleigh-wave phase velocity are obtained for paths between the Nevada Test Site and the Livermore broadband regional stations. Nuclear underground explosions detonated in Yucca Valley were the sources of the Rayleigh waves. The source phase φs required by the single-station method is calculated for an explosion source by assuming a spherically symmetric point source with step-function time dependence. The phase velocities are used to analyze the Rayleigh waves of the Massachusetts Mountain earthquake of 5 August 1971. Measured values of source phase for this earthquake are consistent with the focal mechanism determined from P-wave first-motion data (Fischer et al., 1972). A moment-tensor inversion of the Rayleigh-wave spectra for a 3-km-deep source gives a horizontal, least-compressive stress axis oriented N63°W and a seismic moment of 5.5 × 1022 dyne-cm. The general agreement between the results of the P-wave study of Fischer et al. (1972) and this study supports the measurements of phase velocities and, in turn, the explosion source model used to calculate φs.

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Geographical interpretation of measurements of average phase velocities of surface waves over great circular and great semi-circular paths

Bulletin of the Seismological Society of America ◽

10.1785/bssa0540020571 ◽

1964 ◽

Vol 54 (2) ◽

pp. 571-610

Author(s):

George E. Backus

Keyword(s):

Spherical Harmonics ◽

Rayleigh Waves ◽

Seismic Station ◽

Great Circle ◽

Explicit Formulas ◽

Phase Velocities ◽

Rapid Accumulation ◽

Generalized Spherical Harmonics ◽

Geographical Position ◽

The Difference

ABSTRACT If the averages of the reciprocal phase velocity c−1 of a given Rayleigh or Love mode over various great circular or great semicircular paths are known, information can be extracted about how c−1 varies with geographical position. Assuming that geometrical optics is applicable, it is shown that if c−1 is isotropic its great circular averages determine only the sum of the values of c−1 at antipodal points and not their difference. The great semicircular averages determine the difference as well. If c−1 is anisotropic through any cause other than the earth's rotation, even great semicircular averages do not determine c−1 completely. Rotation has negligible effect on Love waves, and if it is the only anisotropy present its effect on Rayleigh waves can be measured and removed by comparing the averages of c−1 for the two directions of travel around any great circle not intersecting the poles of rotation. Only great circular and great semicircular paths are considered because every earthquake produces two averages of c−1 over such paths for each seismic station. No other paths permit such rapid accumulation of data when the azimuthal variations of the earthquakes' radiation patterns are unknown. Expansion of the data in generalized spherical harmonics circumvents the fact that the explicit formulas for c−1 in terms of its great circular or great semicircular integrals require differentiation of the data. Formulas are given for calculating the generalized spherical harmonics numerically.

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Use of reciprocity theorem for obtaining Rayleigh wave radiation patterns

Bulletin of the Seismological Society of America ◽

10.1785/bssa0560040925 ◽

1966 ◽

Vol 56 (4) ◽

pp. 925-936 ◽

Cited By ~ 1

Author(s):

I. N. Gupta

Keyword(s):

Rayleigh Wave ◽

Rayleigh Waves ◽

Three Dimensional ◽

Reciprocity Theorem ◽

Point Sources ◽

Dimensional Case ◽

Wave Radiation ◽

Radiation Patterns ◽

Homogeneous Half Space ◽

Double Couple

abstract The reciprocity theorem is used to obtain Rayleigh wave radiation patterns from sources on the surface of or within an elastic semi-infinite medium. Nine elementary line sources first considered are: horizontal and vertical forces, horizontal and vertical double forces without moment, horizontal and vertical single couples, center of dilatation (two dimensional case), center of rotation, and double couple without moment. The results are extended to the three dimensional case of similar point sources in a homogeneous half space. Haskell's results for the radiation patterns of Rayleigh waves from a fault of arbitrary dip and direction of motion are reproduced in a much simpler manner. Numerical results on the effect of the depth of these sources on the Rayleigh wave amplitudes are shown for a solid having Poisson's ratio of 0.25.

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