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| Circumferential evanescent guided waves in functionally graded cylindrical curved plates |
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Abstract Evanescent wave modes are substantially different from the propagating modes，which are associated with non-real wavenumbers and decay exponentially or damped with propagation distance. Such modes with complex wavenumbers play an important role in the detection of the shape and size of defects, but it is very difficult to obtain the complex solutions of the dispersion equation which correspond to evanescent waves, especially for demanding cases such as those involving composite materials and curved structures. An improved orthogonal polynomial method is proposed to deal with the problems of evanescent guided waves in a functionally graded cylindrical curved plate in this paper. The proposed method can convert the complex differential equations with variable coefficients into an eigenvalue problem and obtain all the purely real, purely imaginary and complex solutions but without iterative process. The validity of the proposed method is illustrated by specific numerical examples. Three dimensional full dispersion curves of the guided waves in various graded cylindrical curved plates are obtained, and the effects of different radius-thickness ratios and graded fields on the dispersion characteristics of guided evanescent waves are illustrated. The displacement amplitude and stress distributions are also discussed to analyze the specificities of the evanescent guided waves. Numerical results show that there are only purely real and purely imaginary branches for circumferential SH waves, but for circumferential Lamb-like waves there are purely real, purely imaginary and complex branches. Most complex branches collapse onto the minima of purely imaginary branches and local inflection points occasionally appear on higher order real branches. Complex branches exhibit both local vibration and local propagation, and they will turn into real branches with increasing frequency. Both the radius-thickness ratio and the graded field have significant effects on dispersion curves. With the increase of the radius-thickness ratio, the decay of evanescent waves is faster. All the results presented in this work can provide theoretical guidance for ultrasonic nondestructive evaluation.
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Received: 18 December 2017
Published: 28 October 2018
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2018, Vol. 39 
