Multiscale Theories and Applications:From Microstructure Design to Macroscopic Assessment for Carbon Nanotubes Networks

Carbon nanotube(CNT)networks enable CNTs to be used as building blocks for synthesizing novel advanced materials,thus taking full advantage of the superior properties of individual CNTs.Multiscale analyses have to be adopted to study the load transfer mechanisms of CNT networks from the atomic scale to the macroscopic scale due to the huge computational cost.Among them,fully resolved structural features include the graphitic honeycomb lattice(atomic),inter-tube stacking(nano)and assembly(meso)of CNTs.On an atomic scale,the elastic properties,ultimate stresses,and failure strains of individual CNTs with distinct chiralities and radii are obtained under various loading conditions by molecular mechanics.The dependence of the cohesive energies on spacing distances,crossing angles,size and edge effects between two CNTs is analyzed through continuum modeling in nanoscale.The mesoscale models,which neglect the atomic structures of individual CNTs but retain geometrical information about the shape of CNTs and their assembly into a network,have been developed to study the multi-level mechanism of material deformation and microstructural evolution in CNT networks under stretching,from elastic elongation,strengthening to damage and failure.This paper summarizes the multiscale theories mentioned above,which should provide insight into the optimal assembling of CNT network materials for elevated mechanical performance.

A new nonlinear force model to replace the Hertzian contact model in a rigid-rotor ball bearing system

A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then~ the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is cal- culated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally~ the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.

The Applications of Order Reduction Methods in Nonlinear Dynamic Systems

Two different order reduction methods of the deterministic and stochastic systems are discussed in this paper.First,the transient proper orthogonal decomposition(T-POD)method is introduced based on the high-dimensional nonlinear dynamic system.The optimal order reduction conditions of the T-POD method are provided by analyzing the rotor-bearing system with pedestal looseness fault at both ends.The efficiency of the T-POD method is verified via comparing with the results of the original system.Second,the polynomial dimensional decomposition(PDD)method is applied to the 2 DOFs spring system considering the uncertain stiffness to study the amplitude-frequency response.The numerical results obtained by the PDD method agree well with the Monte Carlo simulation(MCS)method.The results of the PDD method can approximate to MCS better with the increasing of the polynomial order.Meanwhile,the Uniform-Legendre polynomials can eliminate perturbation of the PDD method to a certain extent via comparing it with the Gaussian-Hermite polynomials.