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A simplified Flugge shell equations are proposed as the governing equations of motion for carbon nanotubes studied here. For the double-walled nanotubes, the deflection of nested tubes is considered to be coupled through the van der Waals interaction between two adjacent nanotubes. Effects of filled fluid property and nanotube diameter on the wave propagation are investigated and analyzed based on the proposed elastic continuum model. The theoretical investigation may give a useful reference for potential design and application of nanoelectronics and nanodevices. 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