Xiaoqiao He

ACTIVE CONTROL OF FGM PLATES WITH INTEGRATED PIEZOELECTRIC SENSORS AND ACTUATORS

Abstract In this paper, a finite element formulation based on the classical laminated plate theory is presented for the shape and vibration control of the functionally graded material (FGM) plates with integrated piezoelectric sensors and actuators. The properties of the FGM plates are functionally graded in the thickness direction according to a volume fraction power law distribution. A constant velocity feedback control algorithm is used for the active control of the dynamic response of the FGM plate through closed loop control. The static and dynamic responses are presented in both tabular and graphical forms for an FGM plate of aluminum oxide/Ti–6A1–4V material composition. The effects of the constituent volume fractions and the influence of feedback control gain on the static and dynamic responses of FGM plates are examined.

Vibration of nonlocal Timoshenko beams

This paper is concerned with the free vibration problem for micro/nanobeams modelled after Eringens nonlocal elasticity theory and Timoshenko beam theory. The small scale effect is taken into consideration in the former theory while the effects of transverse shear deformation and rotary inertia are accounted for in the latter theory. The governing equations and the boundary conditions are derived using Hamiltons principle. These equations are solved analytically for the vibration frequencies of beams with various end conditions. The vibration solutions obtained provide a better representation of the vibration behaviour of short, stubby, micro/nanobeams where the effects of small scale, transverse shear deformation and rotary inertia are significant. The exact vibration solutions should serve as benchmark results for verifying numerically obtained solutions based on other beam models and solution techniques.

Resonance analysis of multi-layered graphene sheets used as nanoscale resonators.

A stacked plate model for the vibration of multi-layered graphene sheets (MLGSs), in which the van der Waals (vdW) interaction between layers is described by an explicit formula, is presented. Explicit formulae are derived for predicting the natural frequencies of double- and triple-layered graphene sheets, and they clearly indicate the effect of vdW interaction on the natural frequencies. The natural frequencies are calculated for various numbers of layered graphene sheets, and the results show that the vdW interaction has no influence on the lowest natural frequency (classical frequency) of an MLGS but plays a significant role in all higher natural frequencies (resonant frequencies) for a given combination of m and n. The vibration modes that are associated with the classical frequencies for each sheet of an MLGS are identical. In contrast, the vibration modes that are associated with the resonant frequencies are non-identical and give various vibration patterns, which indicates that MLGSs are highly suited to use as high frequency resonators.

Inelastic buckling of carbon nanotubes

A hybrid continuum mechanics and molecular mechanics model is developed in this letter to predict the critical strain of the inelastic buckling of armchair and zigzag carbon nanotubes (CNTS) with beamlike buckle shapes. The explicit analytical buckling results of the hybrid model are verified by molecular dynamics simulations via the MATERIALS STUDIO software package and by available research findings. The simplicity and effectiveness of the model make it possible to further predict and produce benchmark solutions for the size-dependent buckling results of CNTs. The hybrid model enables thorough understanding of the stability behavior of CNTs and is useful for their applications.

Mechanical properties of carbon nanocones

In this paper, the elastic and plastic properties of single-walled carbon nanocones (CNCs) under tension are investigated employing molecular dynamics simulation. The force-deformation responses of CNCs are obtained and compared with those of carbon nanotubes (CNTs). CNCs with a larger apex angle present a larger failure strength but a smaller maximum strain under tension. Following this law, CNTs exhibit the smallest failure strength but greatest maximum strain due to their zero conical angles. The mechanical properties such as Young’s modulus, elastic strain limit, and ultimate force are determined and discussed.

The effect of van der Waals interaction modeling on the vibration characteristics of multiwalled carbon nanotubes

An elastic multiple shell model is used for the vibration analysis of multiwalled carbon nanotubes (MWCNTs). The van der Waals (vdW) interaction between any two layers of the MWCNT is modeled as the radius-dependent function. Based on the simplified Donnell shell equations, explicit formulas are obtained for the radial-dominated natural frequencies and mode shapes of double- and triple-walled carbon nanotubes. The natural frequencies are calculated for MWCNT with various radii and number of tubes. The numerical results show that the effect of vdW interaction on the torsionally and longitudinally dominated natural frequencies is very small and can be neglected, and the vdW interaction has only a small influence on the lowest radial-dominated natural frequency, but plays a significant role in the higher radial-dominated natural frequencies for various combinations of m (number of longitudinal) and n (number of circumferential) waves in the mode even for the MWCNTs of small innermost radius. Especially, due ...

Buckling analysis of triple-walled carbon nanotubes embedded in an elastic matrix

Explicit formulas are obtained to describe the buckling behavior of triple-walled carbon nanotubes (CNTs) that are embedded in an elastic matrix, with van der Waals (vdW) interaction taken into consideration. The investigation is based on the continuum shell theory in which the individual tube is treated as a cylindrical shell. The elastic matrix surrounding the outermost tube is modeled as a Pasternak foundation to account for not only the normal stress, but also the shear stress between the outermost tube and the surrounding matrix. Numerical analyses are carried out to estimate the critical buckling load of triple-walled CNTs, and the results indicate that the critical buckling loads approach a constant of around 0.26N∕m with the increase of the innermost radii regardless of whether or not the triple-walled CNT is embedded in an elastic matrix. The effects of vdW interactions before and after buckling on the critical buckling load are also examined for triple-walled CNTs with various innermost radii.

FLOW-INDUCED INSTABILITY OF DOUBLE-WALLED CARBON NANOTUBES BASED ON AN ELASTIC SHELL MODEL

Double-walled carbon nanotubes (DWCNTs) are modeled based on Donnell’s shell theory, and flow-induced instability that is induced when pressure-driven fluid goes through the inner tube at a steady flow velocity is studied. The van der Waals (vdW) interaction between the inner and outer walls is taken into account in the modeling. The numerical simulations show that the vdW interaction has significant effects on the flow-induced instability of DWCNTs. The critical flow velocities and loss of stability are closely related to the ratio of the length to the outer radius. Donnell’s shell model for carbon nanotubes (CNTs) is preferred in simulations because it takes into account the shear effects in the walls. A comparison between the CNTs that are based on a Eulerian beam model and those that are based on Donnell’s shell model shows that when the 50-nm-radius tube length is shorter than 10 μm, the comparative errors between the Eulerian beam and Donnell’s shell models are greatly increased.

MODELING AND STRESS ANALYSIS OF SMART CNTs/FIBER/POLYMER MULTISCALE COMPOSITE PLATES

Modeling and nonlinear stress analysis of piezolaminated CNTs/fiber/polymer composite (CNTFPC) plates under a combined mechanical and electrical loading are investigated in this study. The governing equations of the piezoelectric CNTFPC plates are derived based on first-order shear deformation plate theory (FSDT) and von Karman geometric nonlinearity. Halpin–Tsai equations and fiber micromechanics are used in hierarchy to predict the bulk material properties of the multiscale composite. The CNTs are assumed to be uniformly distributed and randomly oriented through the epoxy resin matrix. An analytical solution is employed to determine the large deflection response and stress analysis of the nanocomposite plates. Finally, by solving some numerical examples for simply supported plates, the effects of the applied constant voltage, plate geometry, volume fraction of fibers and weight percentage of SWCNTs and MWCNTs on the deflection and stress analyses of the piezoelectric CNTs/fiber/polymer multiscale composite plate are studied. It is shown that the deflections significantly decrease with a small percentage of CNTs. Also, it is found that the SWCNTs reinforcement produces more pronounced effect on the bending and stress of the nanocomposite plates in comparison with MWCNTs.

Postbuckling of carbon nanotubes by atomic-scale finite element

This paper employs an atomic-scale finite element method (AFEM) to study the postbuckling behavior of carbon nanotubes (CNTs). The computed energy curves and critical strain for the (8, 0) single-walled CNT (SWNT) agree well with atomistic simulations. The AFEM is very fast and versatile owing to the efficiency of the finite element method. For the SWNT, the strain energy curves have obvious jumps at morphology changes, and during the smooth continuation stages of postbuckling, the strain energy varies approximately linearly with the strain. For the double-walled CNT, there are only small strain energy releases, and the strain energy also changes approximately piecewise linearly with the strain. The morphologies are obtained in detail. AFEM is computationally fast and is an alternative efficient way to study the postbuckling of CNTs.