No abstract

In this paper, a nonlocal Bernoulli-Euler beam model is established based on the theory of nonlocal elasticity. Frequency equations and modal shape functions of beam structures with some typical boundary conditions are derived based on the model. The corresponding dynamic properties are presented and discussed in detail, which are shown to be very different from those predicted by classic elasticity theory when nonlocal effects are significant. The results can be applied to modeling and characterization of size-dependent mechanical properties of micro- or nanoelectromechanical system (MEMS or NEMS) devices.

In the paper, a general thin plate theory including surface effects, which can be used for size-dependent static and dynamic analysis of plate-like thin film structures, is proposed. This theory is a modification and generalization of the thin plate model in [Lim, C.W., He, L.H., 2004. Size-dependent nonlinear response of thin elastic films with nanoscale thickness. Int. J. Mech. Sci. 46, 1715-1726]. With the general theory, the governing equations of Kirchoff and Mindlin plate models including surface effects are derived, respectively. Some numerical examples are provided to verify the validities of the theory.

No abstract

Investigations of wave and vibration properties of single-or multi-walled carbon nanotubes based on nonlocal beam models have been reported recently. However, there are numerous inconsistencies in the handling of the governing equations, applied forces, and boundary conditions based on some of the reported nonlocal beam models. In this paper, the consistent equations of motion for the nonlocal Euler and Timoshenko beam models are provided, and some issues on the nonlocal beam theories are discussed. The models are then applied to the studies of wave properties of single-and double-walled nanotubes. The wave and vibration properties of the nanotubes based on the presented nonlocal beam equations are studied, and scale effects are discussed.

In this work we derive local gradient and Laplacian estimates of the Aronson-Bénilan and Li-Yau type for positive solutions of porous medium equations posed on Riemannian manifolds with a lower Ricci curvature bound. We also prove similar results for some fast diffusion equations. Inspired by Perelman's work we discover some new entropy formulae for these equations.

A non-local plate model is proposed based on Eringen's theory of non-local continuum mechanics. The basic equations for the non-local Kirchhoff and the Mindlin plate theories are derived. These non-local plate theories allow for the small-scale effect which becomes significant when dealing with micro-/nanoscale plate-like structures. As illustrative examples, the bending and free vibration problems of a rectangular plate with simply supported edges are solved and the exact non-local solutions are discussed in relation to their corresponding local solutions.

D in the upper truncated power-law function is closely associated with the degree of confinement during ice breakup. Its decrease with the distance into MIZ indicates the weakening of confinement conditions on floes owing to wave attenuation. The g of the Weibull distribution characterizes the degree of homogeneity in a data set. It also decreases with distance into MIZ, implying that floe size distributes increase in range. Finally, a statistical test on floe size is performed to divide the whole MIZ into three distinct zones made up of floes of quite different characteristics. This zonal structure of floe size also agrees well with the trends of floe shape and floe size distribution, and is believed to be a straightforward result of wave-ice interaction in the MIZ.