Acoustic attenuation in the layers of a microwave transducer at the excitation of longitudinal and shear elastic waves by a piezoelectric of the 6mm symmetry class

M. A. Grigor’ev; A. V. Tolstikov; Yu. N. Navrotskaya

doi:10.1134/1.1626178

Acoustic attenuation in the layers of a microwave transducer at the excitation of longitudinal and shear elastic waves by a piezoelectric of the 6mm symmetry class

Acoustical Physics ◽

10.1134/1.1626178 ◽

2003 ◽

Vol 49 (6) ◽

pp. 668-676 ◽

Cited By ~ 1

Author(s):

M. A. Grigor’ev ◽

A. V. Tolstikov ◽

Yu. N. Navrotskaya

Keyword(s):

Elastic Waves ◽

Symmetry Class ◽

Acoustic Attenuation

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Acoustic attenuation coefficients for polycrystalline materials containing crystallites of any symmetry class

The Journal of the Acoustical Society of America ◽

10.1121/1.4921676 ◽

2015 ◽

Vol 137 (6) ◽

pp. EL476-EL482 ◽

Cited By ~ 20

Author(s):

Christopher M. Kube ◽

Joseph A. Turner

Keyword(s):

Symmetry Class ◽

Polycrystalline Materials ◽

Acoustic Attenuation ◽

Attenuation Coefficients

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Erratum: Acoustic attenuation coefficients for polycrystalline materials containing crystallites of any symmetry class [J. Acoust. Soc. Am. 137, EL476–EL482 (2015)]

The Journal of the Acoustical Society of America ◽

10.1121/1.4927692 ◽

2015 ◽

Vol 138 (2) ◽

pp. 976-976 ◽

Cited By ~ 1

Author(s):

Christopher M. Kube

Keyword(s):

Symmetry Class ◽

Polycrystalline Materials ◽

Acoustic Attenuation ◽

Attenuation Coefficients

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Remarks on nonlinear elastic waves with null conditions

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2020039 ◽

2020 ◽

Vol 26 ◽

pp. 121

Author(s):

Dongbing Zha ◽

Weimin Peng

Keyword(s):

Initial Data ◽

Global Existence ◽

Elastic Waves ◽

Wave Equations ◽

Alternative Proof ◽

Classical Solutions ◽

Small Initial Data ◽

Hyperelastic Materials ◽

Variational Structure ◽

Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

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