ИСТИНА

A waveguide composed of three acoustic layers having dierent wave velocities and dierent densities is studied. The waveguide is excited by a point source with a pulse time prole. The receiver is put at some distance from the source, and the dependence of the acoustic pressure on time is recorded. It is well known that if the receiver is very far from the source, the received signal can be expressed through the excitation spectrum and the dispersion diagram of the waveguide. The velocities of propagation of wave components are equal to group velocities of the waveguide modes. However, not far from the source one can observe transient phenomena (such as a precursor or the rst arriving signal, FAS). Such phenomena can be described by using the analytic continuation of the dispersion diagram. Namely, in the domain of complex frequency one can find a branch corresponding to the precursor. Such a technique has been developed in [1] for a planar homogeneous elastic waveguide and in [2] for a two-layer waveguide. In the proposed talk we are developing this method for the example of a three-layer waveguide. Such an example is chosen since there can exist some new physical phenomena comparatively to the cases of [1, 2]. Namely, there can be an hierarchy of transient waves, which can be described by dierent contours on the Riemann surface of the dispersion diagram. In the talk we bring some order into the structure of the Riemann surface of a dispersion diagram of a layered waveguide. The main tool of this study is the presentation of the waveguide as a set of layers connected through the surfaces of variable rigidity. Zero rigidity corresponds to disjoint layers, and the innite rigidity corresponds to the layered waveguide under consideration. The position of the branch points of the Riemann surface can be easily found for asymptotically small rigidity, and then analytically continued with respect to rigidity to its innitely large values. The work is supported by NSF grant 14-22-00042. References [1] P.W. Randles and J. Miklowitz Int. J. Solids Struct., 7, 1031{1055 (1971). [2] A.V. Shanin, J. Acoust. Soc. Am., 141, 346{356 (2017).