Vibration Analysis of Functionally Graded Carbon Nanotubes Reinforced Composite Shell Structures

Abstract

Carbon fiber reinforced polymer composites shell structures have been extensively used in the diverse fields of engineering. These structures always possess load carrying capacity due to the special geometrical shapes, and they are also subjected to dynamic loads which cause vibrations. Hence, the study of vibration problems of such shell structures is of great importance. In the recent past, nanostructured materials have gained significant importance from a technological point of view for the wide range of engineering applications that involve high levels of performance and multi functionality. Particularly, carbon nanotubes (CNTs) have shown extraordinary potentials to become the new generation material. The addition of CNT with functionally Graded Materials not only provides enriched mechanical, electrical and thermal properties but that may eliminate the interlaminar stresses which usually exist in the traditional laminated composites due to mismatch of elastic modulus.
The present work deals with the vibration and damping analysis of two distinct types of structures. First type of structure is functionally graded carbon nanotubes reinforced composite (FG-CNTRC) shell structure which consists of carbon nanotube as reinforcing phase and polymer as matrix phase. Another type is functionally graded carbon nanotubes reinforced hybrid composite (FG-CNTRHC) shell structure which consists of conventional carbon fiber as reinforcing phase and single-walled carbon nanotubes (SWCNTs) based polymer as matrix phase. The material properties of FG-CNTRC shell structure are graded smoothly through the thickness direction of shell according to uniform distribution (UD) and some other functionally graded (FG) distributions (such as FG-Χ, FG-V and FG- ) of the volume fraction of CNTs and the effective material properties are estimated by employing Eshelby–Mori–Tanaka approach considering the randomly oriented agglomerated CNTs. The Eshelby–Mori–Tanaka approach in conjunction with strength of material approach is implemented to obtain the material properties of FG-CNTRHC materials. The material properties of FG-CNTRHCs are assumed to be graded through the thickness direction according to power law distributions of the volume fraction of carbon fibers and fiber orientations.
After determining the effective material properties of both structures an eight node shell element considering transverse shear effect according to Mindlin’s hypothesis has been formulated for finite element (FE) modelling and analysis of such functionally graded composite shell structures. The formulation of shell mid-surface in an arbitrary curvilinear coordinate system based on the tensorial notation has been presented. The Rayleigh damping model has been implemented in order to study the effects of carbon nanotubes (CNTs) on damping capacity of such shell structures. Different types of spherical shell panels have been analyzed in order to study the impulse and frequency responses. The influences of CNT volume fraction, CNT distribution, geometry of the shell, CNT agglomeration and material distributions on the dynamic behaviour of FG-CNTRC shell structures and the effects of CNT volume fraction, carbon fiber, geometry of the shell, power law index, CNT agglomeration and material distributions on the vibration damping characteristics of FG-CNTRHC shell structures have also been presented and discussed.
Various types of FG-CNTRC and FG-CNTRHC shell structures (such as spherical, ellipsoidal, doubly curved and cylindrical) have been analyzed and discussed in order to present the comparative studies in terms of settling time, first resonant frequency and absolute amplitude corresponding to first resonant frequency and considering without and with agglomeration effects of CNTs on vibrations responses of such shell structures are presented. The results show that the CNT agglomeration, CNT distribution and volume fraction of CNT have a significant effect on vibration and damping characteristics of the structures. It is also observed that the FG-CNTRHC shell structures have better dynamic responses compared to FG-CNTRC shell structure.