## Treatise on materials science and technology, Volume 3 |

### From inside the book

Results 1-3 of 33

Page 8

The general method of practical solution for a given crystalline material of density

p and second-order elastic constants cy is to solve Eqs. (28) and (29) for the Ajfc

components for the

interest. These kik components are substituted into Eq. (30) along with the

density p and Eq. (30) is solved for the three plane wave speeds Vl,v2,v3. Next,

each of these wave speeds, in turn, is substituted along with ktk and p in all three

Eqs. (32) ...

The general method of practical solution for a given crystalline material of density

p and second-order elastic constants cy is to solve Eqs. (28) and (29) for the Ajfc

components for the

**wave normal**(crystallographic direction cosines /, m, n) ofinterest. These kik components are substituted into Eq. (30) along with the

density p and Eq. (30) is solved for the three plane wave speeds Vl,v2,v3. Next,

each of these wave speeds, in turn, is substituted along with ktk and p in all three

Eqs. (32) ...

Page 16

Therefore, in summary of plane wave propagation in an unbounded linear elastic

homogeneous isotropic solid, we find that in any arbitrary direction a pure mode

longitudinal wave may propagate and the energy flux associated with this wave

is in the same direction as the

mode transverse wave, with particle displacements anywhere in a plane

perpendicular to the

with this ...

Therefore, in summary of plane wave propagation in an unbounded linear elastic

homogeneous isotropic solid, we find that in any arbitrary direction a pure mode

longitudinal wave may propagate and the energy flux associated with this wave

is in the same direction as the

**wave normal**. Also in any arbitrary direction a puremode transverse wave, with particle displacements anywhere in a plane

perpendicular to the

**wave normal**, may propagate and the energy flux associatedwith this ...

Page 20

and consequently c=l, b = 0, c = 0 (92) and the energy flows in the same direction

as the

= 0, £3 = 0, £T = El (93) and consequently a = l, b = 0, c = 0 (94) and again the

energy flows in the same direction as the

plane wave propagation in the [100] direction of cubic crystals, we find that all

three waves propagate as pure modes, i.e., the direction of particle displacement

is ...

and consequently c=l, b = 0, c = 0 (92) and the energy flows in the same direction

as the

**wave normal**. For the transverse waves a = 0, /?2 + y2 = 1 and El = y"^ . E2= 0, £3 = 0, £T = El (93) and consequently a = l, b = 0, c = 0 (94) and again the

energy flows in the same direction as the

**wave normal**. Therefore in summary ofplane wave propagation in the [100] direction of cubic crystals, we find that all

three waves propagate as pure modes, i.e., the direction of particle displacement

is ...

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