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Nonlinear dynamic elasticity
International Tables for Crystallography (2013). Vol. D, Section 1.3.7, pp. 95-98 [ doi:10.1107/97809553602060000902 ]
... interpreted from the same theoretical basis, namely nonlinear dynamical elasticity. A first step in the development of nonlinear dynamical elasticity is ... the general equations of motion for elastic waves propagating in a solid under nonlinear elastic conditions. Then, these equations are restricted ... to elastic waves propagating either in an isotropic or in a cubic medium. The next step is the examination of ...
Small-amplitude waves in a strained medium
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.5, p. 97 [ doi:10.1107/97809553602060000902 ]
Small-amplitude waves in a strained medium 1.3.7.5. Small-amplitude waves in a strained medium We now consider the propagation of small-amplitude elastic waves in a homogeneously strained medium. As defined previously, or a are ...
Harmonic generation
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.4, p. 97 [ doi:10.1107/97809553602060000902 ]
... coordinates in the medium free of stress are denoted either a or . The notation is used when we have to ... describe refers to the propagation of an elastic wave in a medium free of stress (natural state) and the coordinates will ... be denoted . Let us first examine the case of a pure longitudinal mode, i.e. The equations of motion, (1.3.7.7) ...
Cubic media (most symmetrical groups)
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.3.2, pp. 96-97 [ doi:10.1107/97809553602060000902 ]
Cubic media (most symmetrical groups) 1.3.7.3.2. Cubic media (most symmetrical groups) In this case, the strain-energy density becomes Differentiating (1.3.7.8) with respect to the strain, one obtains All other . From (1.3.7.5), we derive the stress components: In this particular case, the three components of the equation of motion are ...
Isotropic media
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.3.1, p. 96 [ doi:10.1107/97809553602060000902 ]
Isotropic media 1.3.7.3.1. Isotropic media In this case, the strain-energy density becomes Differentiating (1.3.7.6) with respect to the strains, we get All the other . From (1.3.7.5), we derive the stress components: Note that this tensor is not symmetric. For the particular problem discussed here, the three components of the ...
Wave propagation in a nonlinear elastic medium
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.3, pp. 95-97 [ doi:10.1107/97809553602060000902 ]
Wave propagation in a nonlinear elastic medium 1.3.7.3. Wave propagation in a nonlinear elastic medium As an example, let us consider the case of a plane finite amplitude wave propagating along the axis. The ...
Equation of motion for elastic waves
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.2, p. 95 [ doi:10.1107/97809553602060000902 ]
Equation of motion for elastic waves 1.3.7.2. Equation of motion for elastic waves For generality, these equations will be derived in the X configuration (initial state). It is convenient to obtain the equations of motion with the aid of Lagrange's equations. In the absence of body forces, these equations ...
Introduction
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.1, p. 95 [ doi:10.1107/97809553602060000902 ]
... interpreted from the same theoretical basis, namely nonlinear dynamical elasticity. A first step in the development of nonlinear dynamical elasticity is ... the general equations of motion for elastic waves propagating in a solid under nonlinear elastic conditions. Then, these equations are restricted ... to elastic waves propagating either in an isotropic or in a cubic medium. The next step is the examination of ...
Experimental determination of third- and higher-order elastic constants
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.6, pp. 97-98 [ doi:10.1107/97809553602060000902 ]
... been widely used; however, the measurement of ultrasonic velocities in a solid under hydrostatic pressure cannot lead to the whole set ... comments: `According to equation of motion, the wave front is a material plane which has unit normal k in the natural state; a wave front moves from the plane to the plane ...
International Tables for Crystallography (2013). Vol. D, Section 1.3.7, pp. 95-98 [ doi:10.1107/97809553602060000902 ]
... interpreted from the same theoretical basis, namely nonlinear dynamical elasticity. A first step in the development of nonlinear dynamical elasticity is ... the general equations of motion for elastic waves propagating in a solid under nonlinear elastic conditions. Then, these equations are restricted ... to elastic waves propagating either in an isotropic or in a cubic medium. The next step is the examination of ...
Small-amplitude waves in a strained medium
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.5, p. 97 [ doi:10.1107/97809553602060000902 ]
Small-amplitude waves in a strained medium 1.3.7.5. Small-amplitude waves in a strained medium We now consider the propagation of small-amplitude elastic waves in a homogeneously strained medium. As defined previously, or a are ...
Harmonic generation
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.4, p. 97 [ doi:10.1107/97809553602060000902 ]
... coordinates in the medium free of stress are denoted either a or . The notation is used when we have to ... describe refers to the propagation of an elastic wave in a medium free of stress (natural state) and the coordinates will ... be denoted . Let us first examine the case of a pure longitudinal mode, i.e. The equations of motion, (1.3.7.7) ...
Cubic media (most symmetrical groups)
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.3.2, pp. 96-97 [ doi:10.1107/97809553602060000902 ]
Cubic media (most symmetrical groups) 1.3.7.3.2. Cubic media (most symmetrical groups) In this case, the strain-energy density becomes Differentiating (1.3.7.8) with respect to the strain, one obtains All other . From (1.3.7.5), we derive the stress components: In this particular case, the three components of the equation of motion are ...
Isotropic media
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.3.1, p. 96 [ doi:10.1107/97809553602060000902 ]
Isotropic media 1.3.7.3.1. Isotropic media In this case, the strain-energy density becomes Differentiating (1.3.7.6) with respect to the strains, we get All the other . From (1.3.7.5), we derive the stress components: Note that this tensor is not symmetric. For the particular problem discussed here, the three components of the ...
Wave propagation in a nonlinear elastic medium
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.3, pp. 95-97 [ doi:10.1107/97809553602060000902 ]
Wave propagation in a nonlinear elastic medium 1.3.7.3. Wave propagation in a nonlinear elastic medium As an example, let us consider the case of a plane finite amplitude wave propagating along the axis. The ...
Equation of motion for elastic waves
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.2, p. 95 [ doi:10.1107/97809553602060000902 ]
Equation of motion for elastic waves 1.3.7.2. Equation of motion for elastic waves For generality, these equations will be derived in the X configuration (initial state). It is convenient to obtain the equations of motion with the aid of Lagrange's equations. In the absence of body forces, these equations ...
Introduction
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.1, p. 95 [ doi:10.1107/97809553602060000902 ]
... interpreted from the same theoretical basis, namely nonlinear dynamical elasticity. A first step in the development of nonlinear dynamical elasticity is ... the general equations of motion for elastic waves propagating in a solid under nonlinear elastic conditions. Then, these equations are restricted ... to elastic waves propagating either in an isotropic or in a cubic medium. The next step is the examination of ...
Experimental determination of third- and higher-order elastic constants
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.6, pp. 97-98 [ doi:10.1107/97809553602060000902 ]
... been widely used; however, the measurement of ultrasonic velocities in a solid under hydrostatic pressure cannot lead to the whole set ... comments: `According to equation of motion, the wave front is a material plane which has unit normal k in the natural state; a wave front moves from the plane to the plane ...
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