Dynamic Instability of Functionally Graded Carbon Nanotubes-Reinforced Composite Joined Conical-Cylindrical Shell

In this paper, dynamic instability of functionally graded carbon nanotubes (CNTs)-reinforced composite joined conical-cylindrical shell in supersonic flow is analyzed numerically. The higher-order shear deformation theory is applied to describe the stress–strain state of thin-walled structure. The assumed-mode method is used to derive the finite degrees-of-freedom dynamical system, which describes the structure motions. The structure motions are expanded by using the eigenmodes, which are obtained by the Rayleigh–Ritz method. The trial functions, which satisfy the continuity conditions at the cylindrical-cone junction, are used to obtain the eigenmodes. The properties of free vibrations of thin-walled structure are analyzed numerically. The dynamic instability of the joined conical-cylindrical shell in supersonic flow is analyzed using the characteristic exponents. As follows from the numerical study, the dynamic instability is arisen due to the Hopf bifurcation. The dependences of the supersonic flow critical pressure on the Mach number and the type of CNTs distribution are analyzed numerically.

Buckling of functionally graded carbon nanotubes reinforced composite joined spherical-cylindrical-spherical thin-walled structure

Functionally graded carbon nanotubes reinforced composite joined spherical-cylindrical-spherical thin-walled structure under the actions of axial and lateral distributed loads is considered. The static buckling of this structure is analyzed numerically. The Ritz method is used to derive the governing equations of the joined thin-walled structure buckling. Higher-order shear deformation theory is applied to describe the structure stress-strain state. The continuity conditions of the spherical-cylinder junction are derived. The displacements projections are chosen in the special form to satisfy these continuity conditions. The dependences of the buckling axial load on the CNTs distributions, CNTs volume fractions are analyzed numerically.

Vibration characteristics and damping properties of functionally graded carbon nanotubes reinforced hybrid composite skewed shell structures under hygrothermal conditions

The present article deals with the vibration and damping characteristics of functionally graded carbon nanotubes reinforced hybrid composite skewed shell structure in different hygrothermal conditions. Carbon nanotube reinforced polymer as a matrix phase and carbon fibre as a reinforcing phase are used, and carbon fibre is graded with uniform distribution along the thickness direction for the shell panel according to the power law distribution. The Mori–Tanaka scheme and strength of materials are used to determine the mechanical properties of such functionally graded carbon nanotubes reinforced hybrid composite materials. Finite element modelling has been done by considering an eight-noded shell element with the transverse shear effect according to Mindlin’s hypothesis, and an oblique coordinate system is used for the functionally graded carbon nanotubes reinforced hybrid composite skewed shell structures. Damping is incorporated into such carbon nanotube–based hybrid skewed shell structure based on the Rayleigh damping model. A MATLAB-based in-house computer code has been developed for the proposed formulation and verified with published research work before using for the present dynamic analysis of functionally graded carbon nanotubes reinforced hybrid composite skewed shell structure under hygrothermal conditions. The effect of the carbon nanotube, carbon fibre, material distribution as per power law index and hygrothermal conditions on the damping behaviour of such functionally graded carbon nanotubes reinforced hybrid composite skewed shell structures have been studied. Furthermore, parametric studies are carried out for the first resonant frequency, absolute amplitude, settling time and carbon nanotube impact on the vibrational behaviour of different functionally graded carbon nanotubes reinforced hybrid composite skewed shell structures under different hygrothermal conditions.

Nonlinear Vibration Analysis of Functionally Graded Carbon Nanotubes Sandwich Cylindrical Panels

In this research, we investigate the nonlinear vibration of functionally graded carbon nanotubes (FG-CNTs) for simply supported sandwich cylindrical panels. The sandwich consisting of three layers formed of (FG-CNTs) and isotropic material as (CNT, ALMINUME, CNT). Mechanical properties of the sandwich media are acquired according to a refined rule of blend approach. The governing equations were derived using a first-order deformation theory (FOSDT). Four kinds of carbon nanotubes of sandwich cylindrical panels were analyzed. The volume fraction of CNTs is varied. The properties of nonlinear responses and free vibration are studied. The numerical approach employs the fourth-order Runge-Kutta and Galerkine procedure. Which conducted for the dynamic analysis of the panels to present the natural frequencies and non-linear dynamic response expression. The results show that; the natural frequencies and the nonlinear vibration amplitude decrease with the volume fraction and thickness ratio increase. The nonlinear vibration amplitude response increases when increasing the excitation force. The initial imperfection and the elastic foundation have a minor impact on the nonlinear vibration response of the panel. The Pasternak Foundation has a larger impact than the Winkler foundation. The structure formed of FG-CNT present an excellent choice for high-performance of engineering applications.