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

Abstract

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.

Dispersion of elastic waves in the three-layered inhomogeneous sandwich plate embedded in the Winkler foundations

“…The governing equations have been reduced to ordinary differential equations with the help of specified boundary and interfacial conditions, the exact displacements along with stresses in corresponding layers, and exact ASDR have been computed analytically. Due to multiple industrial applications of soft-stiff layer combinations, 7 – 11 , 19 , 23 , 25 the exact ASDR and its related polynomial dispersion relation, as well as the SPDR, subject to the long-wave low-frequency region, have been investigated. Additionally, asymptotic formulas for the exact stresses and displacement have also been derived for the respective layer of the plate.…”

“…This section gives the asymptotic formulas corresponding to exact displacements and stresses earlier determined in Eqs. ( 9) and (10) for each layer of the plate. To achieve this objective, we make use of the following rescaling of wave number and frequency, respectively, of the form:…”

“…The waveguides, elastic plates, beams, laminates, panels, rods, as well as cylindrical shells, are some of the structures that may be found in multiply-bond layers, to highlight a few, see Refs. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] In terms of layered structure design and structural analysis, which frequently has contrasting material and geometrical parameters, such as size, volume density, and stiffness. Layered structures offer advantages such as high resistance, lightweight, and strength; additionally, they have static and dynamic excitations.…”