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[en] A sound knowledge of both the propagating and the evanescent waves in waveguides is very essential for nondestructive evaluation. Guided propagating waves have received considerable attention. However, the research on guided evanescent waves is quite limited, because it is relatively difficult to find the roots of evanescent modes, especially for demanding cases such as those involving anisotropy and curved structures. This paper presents an analytical approach, based on the orthogonal function technique, to solve the evanescent waves in spherical curved plates composed of fiber reinforced composites. The proposed approach can transform the set of partial differential equations for the acoustic waves into a simple eigenvalue problem that can give the generally complex wave numbers and the field profiles. Results are compared with the available data to check the validity of the present approach, and the convergence is also discussed. Three-dimensional dispersion curves of the guided evanescent waves in various spherical curved plates are obtained using the proposed approach, the effects of different radius/thickness ratios and anisotropy on the dispersion characteristics of guided evanescent waves are illustrated, and the displacement amplitude distributions are also discussed to analyze the specificities of the guided evanescent waves.