Guided wave in ultra-thin layered composite structure with weak and slip interface in different depth

In conjunction with the transfer matrix techniques for modeling ultrasonic wave in multilayered composite medium, the spring model for a weak interface and the interface condition of the slip interface, we have the generalized frequency equations for low-order mode guided waves in ultra-thin layered composites structure with a weak or slip interface in different depth, and the effect of the depth of the interface on the dispersion properties of low-order mode ultrasonic Lamb wave are analyzed. The "ultra-thin" here means that the thickness of the plate is only a fraction of the ultrasound wave-length so that the echoes from the front and the back of the surface cannot be separated in the time domain.