Propagation of Plane Waves in an Elastic Medium With Couple Stress

Abstract

In the present work the propagation of plane waves in a microelastic medium having only couple strees is studied. The fundamental field equations are first written in a vectorial form, then they are partitioned into simpler systems by assuming field variables as the şum of the irrotational and solenoidal vectorial fields. After having cast the equations into a suitable form the plane wave solutions are sought and it is shown that six type of waves, which travel with different velocities, can exist in such a medium. All waves, with the exception of longitudinal displacement waves appear to possess a dispersive character. It is shown that a cut-off frequency exists for one kind of rotation and one kind of displacement wave. Finally a formal solution of the equations is given for an infinite medium bu making use of Fourier transforms.