Longitudinal wave propagation in axially functionally graded carbon nanotubes was investigated using three different solution methods: analytical, higher order Haar wavelet and Ritz methods. The results of the various solution methods were compared and validated. A weak form solution for the wave frequency was presented using the Lagrangian energy functional and the Ritz method. Exponential and power-law material grading variations were considered. Material grading parameters and grading nonlocality effects on the axial wave propagation frequency were investigated. The present study could be useful in the wave dynamic analysis of axially graded nanostructures.
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