Page 258 - Introduction to Continuum Mechanics

242 The Elastic Solid

or,

and the resulting wave has the form,

We note, that not only the wavelength but the amplitude of the resulting wave is inversely
proportional to the forcing frequency.

5.9 Plane Equivoluminal Wave
Consider the motion

This infinite train of plane harmonic wave differs from that discussed in Section 5.8 in that it
is a transverse wave: the particle motion is parallel to 62 direction, whereas the disturbance is
propagating in the ej direction.
For this motion, the strain components are

and

and the stress components are

Substitution of 7)y and «,- in the equations of motion, neglecting body forces, gives the phase
velocity cj to be

Since, in this motion, the dilatation e is zero at all times, it is known as an equivoluminal wave.
It is also called a shear wave.