Narrow Results

Considering both the nonlocal scale and material length scale effects, we investigate vibration and stability behaviors of functionally graded nanoplates with axial motion in order to model the two-dimensional nanobelt in nanoengineering. The nonlocal strain gradient theory is applied and the differential nonlocal strain gradient constitutive relation is adopted. Using the physical neutral plane of a functionally graded thin plate, we derive the governing equation of motion for the functionally graded nanoplate with axial motion via Hamilton’s principle, where the kinematic characteristics are introduced into the dynamic behaviors. The governing equation is numerically solved using the Galerkin method. Effects of the nonlocal scale and material length scale parameters, axial velocity, gradient index, biaxial pre-tensions and aspect ratio are discussed. The results demonstrate that complex frequencies of the functionally graded nanoplate with axial motion decrease with an increase of axial velocity in the subcritical region, while the moving nanoplate experiences a divergent instability or flutter instability in the supercritical region. Natural frequency and critical speed decrease with the increase of the nonlocal scale parameter while increase with the increase of the material length scale parameter, reflecting the nonlocal softening and strain gradient hardening mechanisms, respectively. Besides, natural frequency and critical speed increase with the increase of the biaxial pre-tensions and aspect ratio, but decrease with the increase of the gradient index. In particular, the influences of the gradient index and size or weight of functionally graded nanoplates on the critical speed are explored.

The transient response of a circular nanoplate subjected to the normal impact by a nanosphere (e.g., C${}_{60}$) is investigated theoretically. The nanoplate is modeled by the Kirchhoff thin plate theory. Gurtin–Murdoch’s theory is employed to account for the surface effects of the nanoplate with surface elasticity and surface residual stress. The van der Waals interaction between the nanosphere and the nanoplate is also taken into account. The governing equations for the vibration of the nanoplate impinged by a rigid nanosphere are established by using the Hamilton’s principle. The displacement field in the circular nanoplate is obtained by using the Fourier–Bessel expansion method. We reveal some physical mechanisms in the nanoimpact problem that are different from those in macroscopic impact problems, and surface effects have pronounced influences on the dynamic responses of a plate when its thickness shrinks to a few nanometers.

Influence of surface energy on an interaction problem between a flexible circular nanoplate and a nanolayer is examined by using a variational formulation and the GM surface theory. The nanoplate is resting in smooth contact on the supporting nanolayer, and subjected to axisymmetric vertical loadings. The normal traction at the plate–layer interface is written in terms of generalized coordinates obtained from the flexibility equations derived from Green’s function and Hankel integral transform technique. A numerical solution scheme is then implemented into a computer code, and the convergence and accuracy of the proposed solution are verified with existing solutions. A set of numerical solutions is illustrated to present an impact of the surface energy effects on this interaction problem. Both deflection and bending moment of the nanoplate show a considerable dependence on the relative plate stiffness and the surface material properties, and demonstrate the size-dependent behaviors.

Ultrathin Bi₂Te₃ nanoplates have been grown on an oxidized silicon substrate by a modified hot wall epitaxy (HWE) method, in which a quartz plate with holes was employed. The microstructures and optical properties of Bi₂Te₃ nanoplates were investigated by X-ray diffraction (XRD), scanning electron microscopy (SEM), atomic force microscope (AFM) and micro-Raman spectroscopy. The results show that ultrathin Bi₂Te₃ nanoplates with the thickness of about six quintuple layers (QLs) are obtained, which is difficult for the traditional HWE technique. The Raman vibration mode from the nanoplates exhibits an obviously red shift with decreasing thickness. The thickness variation of one nanoplate was obtained by the Raman map derived from the vibration frequency of mode and is in good agreement with the AFM result, which indicates that Raman map is an effective method to characterize the thickness difference of ultrathin Bi₂Te₃ nanoplates.

Systems with nanoscale dimensions have attracted great attention for many decades since they manifest interesting size-dependent behavior and have many possible technological applications. While significant progress has been made toward the experimental and theoretical understanding of various phenomena at nanoscale, much is yet is to be explored in fully comprehending how the interplay of several parameters such as shape, size and dimensionality affects the resulting properties. In this work, we study the nature of the interaction in a nanosystem consisting of a charged nanoplate and a charged nanowire. The two constituent nanostructures of this nanosystem represent important building blocks for bottom-up assembly processes. We consider a specific orientation of the two nanostructures and calculate exactly their interaction energy as a function of shape, size and relative distance. With help from suitable though nontrivial mathematical transformations, we are able to derive a closed form exact expression for such an interaction energy. It is shown that the interaction energy of this configuration is very sensitive to shape and depends in a nontrivial way on size and separation distance.