۱- Introduction

۲- Modeling of FG-CNTRC laminated cylindrical shells with NPR

۳- Solution procedure

۴- Numerical results and discussion

۵- Concluding remarks

References

Abstract

This paper presents an investigation on the nonlinear flexural vibrations of carbon nanotube-reinforced composite (CNTRC) laminated cylindrical shells with negative Poisson’s ratios in thermal environments. The material properties of the CNTRCs are temperature-dependent and the functionally graded (FG) in a piece-wise pattern in the thickness direction of the shell. An extended Voigt (rule of mixture) model is employed to estimate the CNTRC material properties. The motion equations for the nonlinear flexural vibration of FG-CNTRC laminated cylindrical shells are based on the Reddy’s third order shear deformation theory and the von Kármán-type kinematic nonlinearity, and the effects of thermal environmental conditions are included. The nonlinear vibration solutions for the FG-CNTRC laminated cylindrical shells can be obtained by applying a singular perturbation technique along with a two-step perturbation approach. The effects of material property gradient, the temperature variation, shell geometric parameter, stacking sequence as well as the end conditions on the vibration characteristics of CNTRC laminated cylindrical shells are discussed in detail through a parametric study. The results show that negative Poisson’s ratio has a significant effect on the linear and nonlinear vibration characteristics of CNTRC laminated cylindrical shells.

Introduction

Composite laminated shell structures are widely used in structural applications owing to their specific higher strength-to-weight and stiffness-to-weight ratios, improved chemical and environmental resistance and the ability to tailor properties. These shell structures may be exposed to combined action of loading and various environmental conditions during their service life. This may lead to large amplitude vibration of the shells where the shell deflection may be in the order of the shell thickness. In this regard, the nonlinear vibration of composite laminated shells in thermal environments is an important consideration in engineering analysis and design. Many studies have been carried out on the nonlinear vibration behavior of composite laminated shells [1–۶]. As pointed out by Shen [6], unlike in the cases of composite laminated plates, there are unresolved discrepancies between the vibration results obtained by different authors for composite laminated cylindrical shells, in particular for the cases of angle-ply laminated cylindrical shells. With growing interest in the development and manufacturing of high-performance and lightweight composite shells, auxetic composite materials and structures appear to be potential candidates. A consequence of material possessing a negative Poisson’s ratio (NPR) is that many of its mechanical properties are predicted to be enhanced by classical elasticity theory. The auxetic materials have a wide variety of multifunctional applications, for example, in energy storage, biomedical, acoustics, photonics, and thermal management [7]. There are two ways to construct auxetic structures. One way is to use auxetic metamaterial as sandwich core [8]. Another way is to change the stacking sequence and orientation of the laminates to obtain auxetic laminated shells. The production of larger values of negative Poisson’s ratio requires both a particular stacking sequence and the individual ply material being highly anisotropic [9].