An improved layerwise formulation for free vibrations of multilayered FG truncated conical shells reinforced by carbon nanotubes

Abstract

A consistent layerwise/zigzag model is established for multilayered truncated conical shells reinforced by carbon nanotubes (CNTs) with material properties continuous at the interfaces between the layers. The present formulation describes the composite multilayered shell as an assembly of individual homogenous layers with zigzag strain–stress representation along the thickness direction. For this purpose, a modified mixed variational statement has been utilized including stresses and displacements in each layer as independent fields. A displacement field is introduced for each layer involving shear deformations and through-thickness stretching stains, and a stress field is assumed satisfying the continuity conditions for the elastic properties at the interfaces between the layers, as well as, the loading conditions on the external shell faces. For the considered multilayered conical shells, governing and constitutive equations are derived with the required edges conditions. Free vibrations are investigated for single- and multi-layer truncated conical shells reinforced by CNTs across the shell thickness with different functionally graded (FG) schemes. An assessment for the accuracy of the present formulation is made by comparing some present results for frequency parameters with their corresponding published ones. The effect of the thickness stretching strains on the free vibrations of CNT-reinforced cylindrical and conical shells is demonstrated.