Traveling Wave Modal Frequency Analysis of Rotating Functional Gradient Carbon Nanotubes Conical Shells

In order to promote the application of functional gradient materials in aerospace and other engineering fields, the traveling wave vibration characteristics on the conical shell of rotating functional gradient carbon nanotubes are analyzed. Firstly, the energy equation of the system is derived based on the fine-scale mechanical model. Next, the displacement function is constructed by introducing Chebyshev polynomials and the modal frequency equation of the conical shell is solved by using Rayleigh–Ritz method. The effects of ceramic volume fraction exponent, boundary conditions and carbon nanotube volume fraction on the modal frequencies of traveling waves of conical shells with rotating functional gradients are analyzed by arithmetic examples. Results indicate that when the ceramic volume fraction exponent is in the interval from 0 to 5, the V-shaped distribution has the most significant effect on the structure traveling wave mode frequency; With the increase of rotation speed, the stronger the effect of boundary constraint, the more stable the shell structure; the larger the volume fraction of carbon nanotubes in the matrix, the higher the traveling wave modal frequency.