Theory of the oscillations of an ellipsoidal weld pool in laser welding

The weld bead formed when a laser is used for penetration welding usually exhibits a ripple pattern superimposed on the surface. The reasons for this are not clear but the frequencies most likely to be observed will be related to the natural frequencies of oscillation of the weld pool when it is molten. Postacioglu et at have already studied these frequencies in the case when the weld pool is almost circular and deep. When the welding speed is higher however, the weld pool is nearer to being ellipsoidal in shape. The frequency of the first asymmetric mode of oscillation is calculated, and is found to depend on the shape of the weld pool.