Abstract:

In order to investigate the influences of the randomness of physical parameters of constituent materials and constituent distribution on natural frequencies of a functionally graded carbon nanotube reinforced composite structure, a finite element dynamics model is developed for a beam structure with different arrangements of carbon nanotube by using the high-order shear deformation theory and generalized mixture law. The first-order perturbation method is used to introduce the random variables and the stochastic finite element model is established. The numerical characteristics relationships between natural frequencies and the randomness of physical parameters of constituent materials as well as constituent distribution are derived. The results show that the contribution of the randomness of physical parameters of constituent materials to the scattering of natural frequencies is much greater than the constituent distribution. The dispersion of natural frequencies for the carbon nanotube X-type decreases with the increase in volume fraction at the very beginning, and then turns to increase rapidly. However, O-type natural frequencies dispersion is still in the attenuated state.

Key words: functionally graded carbon nanotube reinforced composite material, first-order perturbation method, random variable, stochastic finite element, natural frequency