Free vibration analysis of functionally graded nanocomposite sandwich beams resting on Pasternak foundation by considering the agglomeration effect of CNTs

Abstract

In the present work, by considering the agglomeration effect of single-walled carbon nanotubes, free vibration characteristics of functionally graded (FG) nanocomposite sandwich beams resting on Pasternak foundation are presented. The carbon nanotubes (CNTs) volume fraction is graded through the thicknesses of face sheets according to a generalized power–law distribution. The material properties of the FG nanocomposite sandwich beam are estimated using the Eshelby–Mori–Tanaka approach based on an equivalent fiber. The equations of motion are derived based on Timoshenko beam theory and employing Hamilton's principle. Generalized differential quadrature technique as an efficient and accurate numerical tool is employed to obtain the natural frequencies of the structure. The verification study represents the accuracy of the solution for free vibration analysis of the nanocomposite sandwich beams resting on elastic foundation. Detailed parametric studies are carried out to investigate the influences of CNTs agglomeration, different profiles of CNT volume fraction such as symmetric, asymmetric, and classic, Winkler foundation modulus, shear elastic foundation modulus, length to span ratio, thicknesses of face sheets, and boundary conditions on the vibrational behavior of the structure. It is shown that the natural frequencies of structure are seriously affected by the influence of CNTs agglomeration. Results also represent the fact that utilizing FG nanocomposite sandwich beams in most agglomeration states improves the fundamental frequencies of the structure, but in some cases has a destructive effect on the vibrational characteristics.