Wave pattern produced by a heat source moving with constant velocity on the top of an infinite plate

Within the framework of linear, isotropic elasticity theory the wave pattern produced by a heat source moving with constant velocity on the top of an infinite plate is computed. Both the transient effects associated with the initial conditions and the damping of the waves are neglected. If the travel speed of the heat source is smaller than the velocity of the surface waves, dispersive flexural waves will be excited. The frequency of these waves is proportional to the square of the wave number if the wavelength is much larger than the thickness of the sheet. In this limiting case it is found that the crest of the waves makes an angle of 90 degrees with the travel direction, and this result is independent of the travel speed as long as the parabolic approximation remains valid for the dispersion relation of flexural waves.