Page 262 - Introduction to Continuum Mechanics
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246 The Elastic Solid
sine (or cosine) must be of the form (2?r//)(x • e, z - ct - rj), where rj is an arbitrary constant.
Fig. 53
a) For longitudinal waves, u is parallel to e n, thus
In particular, if e n = ej,
(b) For transverse waves, u is perpendicular to e,,. Let e r be a unit vector perpendicular to
e,,. Then
The plane of e t and e,, is known as the plane of polarization. In particular, if e w = ej, e f = €2,
then
Example 5.9.4
In Fig. 5.4, all three unit vectors e n ,e rt and e n lie in the x\X2 plane. Express the
displacement components with respect to the*/ coordinates of plane harmonic waves for
