The problem of propagation of guided elastic waves near curved surfaces and in layers of nonconstant thickness is investigated. Rigorous solutions for such problems are not available, and a method is shown for the construction of high frequency asymptotic solutions for such problems in two dimensions. The method is applied to Love waves, which are SH-waves in an elastic layer, Rayleigh waves, which are elastic waves guided by a single free surface, and Lamb waves, which are SV-waves guided in a plate or layer with two free surfaces. The procedure shown breaks the second-order boundary-value problems which have to be solved into successions of simpler problems which can be solved numerically. Some numerical examples for Rayleigh waves are carried out in order to demonstrate the utility of our method. The method shown is useful for a large variety of guided wave problems, of which the ones we treat are just examples.

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