Transient Ultrasonic Waves in Multilayered Superconducting Plates

Transient response of multilayered superconducting tapes has been studied in this paper. These tapes are usually composed of layers of a superconducting material (like $YBa2Cu3O7−δ,$ or YBCO, for simplicity) alternating between layers of a metallic material (like nickel or silver). The tapes are thin, in the range of 100–200 μm. The superconducting layer is orthotropic with a thickness of 5–10 μm. In applications, tapes are long and have a finite width. In this paper, attention has been focused on the transient response of homogeneous and three-layered tapes assuming that the width is infinite and that the thickness of the superconducting layer is much smaller than the metal layer. The problem considered here is of general interest for understanding the effect of anisotropy of thin coating or interface layers in composite plate structures on ultrasonic guided waves. Three plate geometries are considered as prototype examples: a homogeneous nickel (Ni) layer, a three-layered YBCO/Ni/YBCO, and a three-layered Ni/YBCO/Ni. Transient response due to a line force applied normal to the surface of the tape has been studied by means of Fourier transforms and direct numerical integration. Numerical results are presented using an exact model and a first-order approximation to the thin YBCO layer. The first-order approximation simplifies the problem to that of a homogeneous isotropic plate subject to effective boundary conditions representing the thin anisotropic layers. Both are seen to agree well (except when the center frequency of the force is high) and capture the coupling of the longitudinal, S, (or flexural, A) motion and the shear-horizontal (SH) motion. Detailed analysis of the influence of the thin layers, especially their anisotropy, on this coupling and the transient response shows significant differences among the three cases. The model results provide insight into the coupling phenomenon and indicate the feasibility of careful experiments to exploit the significant changes in the transient response caused by coupling for the determination of the in-plane elastic constants of thin coating or interface layers.