The influence of randomly oriented CNTs on the elastic properties of unidirectionally aligned composites

Investigating nonlinear vibrations of multi-scale truncated conical shell segments with carbon nanotube/fiberglass reinforcement using a higher order conical shell theory

“…Accordingly, determination of material properties for nano-composites is of much importance. For the nano-composite, two elastic moduli E 11 and E 22 , shear moduli G 12 and G 23 , and also bulk modulus K 23 must be defined 21…”

“…The associated parameters Z i ( i = 1, 2, 3, 4, 5) in equations (1)–(5) have the following descriptions 21…”

“…in which, based on the components of Eshelby’s tensor ( S ijkl ) which are provided in Appendix 1, L i have the following definitions 21…”

“…Four key factors for determining material properties of nano-composites are bulk modulus K ^ ; shear modulus G ^ ; Young’s modulus E ^ ; and Poisson’s ratio μ ^ , which may be expressed by 21…”

“…20 Although the Eshelby–Mori–Tanaka approach has high efficacy for multi-scale material modeling, it sometimes yields an asymmetric stiffness tensor for the composites, whereas the three-dimensional (3D) Mori–Tanaka’s stiffness tensor is always symmetric (see Table 1). 21 The latter can be used as an efficient tool for elastic properties definition of multi-scale composites. Although there are many publications on vibration analysis of multi-scale composite structures, there is no study on nonlinear vibrations of truncated conical shell segments made of hybrid epoxy/fiberglass/CNT material.…”