Dispersion of Elastic Waves in Functionally Graded CNTs-Reinforced Composite Beams

This work deals with the wave propagation analysis in functionally graded carbon nanotubes (CNTs)-reinforced composite beams lying on an elastic medium. Despite the large amount of experimental and theoretical studies in the literature on the mechanical behavior of composite structures strengthened with CNTs, limited attention has been paid to the effect of an axial graduation of the reinforcing phase on the mechanical response of CNTs-reinforced composite beams. In this paper, CNT fibers are graded across the beam length, according to a power-law function, which expresses a general variation from a linear to parabolic pattern. An Euler-Bernoulli beam theory is considered herein to model the CNTs-reinforced composite structure resting on a Winkler–Pasternak foundation, whose governing equations are derived from the Hamiltonian principle. The theoretical solution of the problem checks for the sensitivity of the mechanical response to different parameters, i.e., the wave number, power index, Winkler and Pasternak coefficients, that could serve for further computational/experimental studies on the same problem, even from a design standpoint.