Narrow Results

This paper investigates the free vibration of multi-walled carbon nanotubes (MWCNTs) with simply supported ends. Based on the nonlocal elasticity theory which allows the effects of small length scale and the more refined van der Waals (vdW) interaction formulas, the equation of motion is first derived and then solved analytically. The results reveal that the effects of the small length scale are significant for small aspect ratios and high radial vibration modes, and are instead insensitive to the number of layers of MWCNTs and weakly dependent on the wall thickness of MWNTs. This finding means that the effects of small length scale on complicated MWCNTs may be simplified to double-walled carbon nanotubes (DWCNTs) or even single-walled carbon nanotubes (SWCNTs).

We have studied structural, mechanical and dynamical properties of PdC and CdC compounds to predict the most stable structure. We have focused on seven binary structure types as rock salt (RS), caesium chloride (CsCl), zinc blende (ZB), wurtzite (WZ), tungsten carbide (WC), cadmium telluride (CdTe) and nickel arsenide (NiAs). For modelling exchange-correlation effects we have used generalized gradient (GGA) approximation based on Perdew–Burke–Ernzhorf functional (PBE). The polycrystalline elastic moduli such as Young's and shear moduli, Poisson's ratio, sound velocities, Debye temperatures and shear anisotropic factors have been presented for mechanically stable structures using second-order elastic constants calculated from the stress-strain relations. The results show that PdC is thermodynamically, mechanically and dynamically stable in ZB structure. On the other hand, while CdC is energetically in favor of RS structure, it is mechanically and dynamically stable in ZB structure.

In this paper a chaotic system is proposed via modifying hyperchaotic Chen system. Some basic dynamical properties, such as Lyapunov exponents, fractal dimension, chaotic behaviors of this system are studied. The conventional feedback, linear function feedback, nonlinear hyperbolic function feedback control methods are applied to control chaos to unstable equilibrium point. The conditions of stability to control the system is derived according to the Routh–Hurwitz criteria. Numerical results have shown the validity of the proposed schemes.

The presence of T2-Al₂MgC₂ compound has significant influence on the mechanical properties of magnesium alloys. The mechanical, electronic and dynamical properties of T2-Al₂MgC₂ under high pressure are investigated by plane wave pseudopotential method based on the first-principles calculation. The results show that T2-Al₂MgC₂ is mechanically stable under high pressure, the elastic constants except $C_{14}$ increase with the increase of pressure. This compound presents brittleness and the brittleness decreases with increasing pressure when $P<40$GPa, but it displays ductility when $P>40$GPa. T2-Al₂MgC₂ has strong anisotropy, and the anisotropy decreases with increasing pressure. T2-Al₂MgC₂ is an indirect bandgap semiconductor material. Our calculated bandgap is 1.893eV at ambient pressure, the bandgap first increases and then decreases with increasing pressure. The phonon band structure as well as the total and partial phonon density of the state under different pressures had been analyzed. The constant volume heat capacity $C_V$ and entropy S of T2-Al₂MgC₂ increase with increasing pressure.

Many studies have been done on different aspects of biped robots such as motion, path planning, control and stability. Dynamical properties of biped robot on a sloping surface such as equilibria and their stabilities, bifurcations and basin of attraction are investigated in this paper. Basin of attraction is an important property since it can determine the unseen conditions which affect the attractor of the system with multistabilities. By the help of basin of attractions, the paper claims that the strange attractors of compass-gait robot are hidden.