A fundamental property of solid materials is their stress state. Stress state of a solid or thin film material has profound effects on its thermodynamic stability and physical and chemical properties. The classical me...A fundamental property of solid materials is their stress state. Stress state of a solid or thin film material has profound effects on its thermodynamic stability and physical and chemical properties. The classical mechanical stress （σ^M） originates from lat- tice strain （e）, following Hooke＇s law： σ^M=Cε, where C is elastic constant matrix. Recently, a new concept of quantum electronic stress （o-QE） is introduced to elucidate the extrinsic electronic effects on the stress state of solids and thin films, which follows a quantum analog of classical Hooke＇s law： ~QE=E（An）, where E is the deformation potential of electronic states and An is the variation of electron density. Here, we present mathematical derivation of both the classical and quantum Hooke＇s law from density functional theory. We further discuss the physical origin of quantum electronic stress, arising purely from electronic excitation and perturbation in the absence of lattice strain （g=0）, and its relation to the degeneracy pressure of electrons in solid and their interaction with the lattice.展开更多
The stability of the rolling motion of near space hypersonic vehicles with rudder control is studied using method of qualitative analysis of nonlinear differential equations, and the stability criteria of the deflecte...The stability of the rolling motion of near space hypersonic vehicles with rudder control is studied using method of qualitative analysis of nonlinear differential equations, and the stability criteria of the deflected rolling motions are improved. The out- comes can serve as the basis for further study regarding the influence of pitching and lateral motion on the stability of rolling motion. To validate the theoretical results, numerical simulations were do^e for the rolling motion of two hypersonic vehicles with typical configurations. Also, wind tunnel experiments for four aircraft models with typical configurations have been done. The results show that： 1） there exist two dynamic patterns of the rolling motion under statically stable condition. The first one is point attractor, for which the motion of aircraft returns to the original state. The second is periodic attractor, for which the aircraft rolls periodically. 2） Under statically unstable condition, there exist three dynamic patterns of rolling motion, namely, the point attractor, periodic attractor around deflected state of rolling motion, and double periodic attractors or chaotic attrac- tors.展开更多
The configurations of near space hypersonic flying vehicles are considerably different from those of conventional aircrafts.Their configurations are relatively slender;hence their moment of inertia around the longitud...The configurations of near space hypersonic flying vehicles are considerably different from those of conventional aircrafts.Their configurations are relatively slender;hence their moment of inertia around the longitudinal axis is much smaller than those around the other two axes,resulting in strong coupling of rotations around the three axes.Thus,the stability analysis of rolling motion for such flying vehicles is more complicated than those for conventional aircrafts,and there is no available result of stability analysis which can readily be applied to such cases.This paper is mainly concerned with the stated problem.Considering the practical situation,our investigation is targeted a slightly simpler problem,namely the rolling stability of flying vehicle under known pitching motion.The stability criterion of rolling motion is obtained with and without lateral motions.We also conducted numerical simulation for the pitching-rolling coupled motions of flying vehicles by solving Navier-Stokes equations coupled with dynamic equations of flight.The results of simulation agree well with those of theoretical analysis and experiments.展开更多
基金supported by the DOE-BES program(Grant No.DE-04ER46148)NSF-MRSEC(Grant No.DMR-1121252)
文摘A fundamental property of solid materials is their stress state. Stress state of a solid or thin film material has profound effects on its thermodynamic stability and physical and chemical properties. The classical mechanical stress （σ^M） originates from lat- tice strain （e）, following Hooke＇s law： σ^M=Cε, where C is elastic constant matrix. Recently, a new concept of quantum electronic stress （o-QE） is introduced to elucidate the extrinsic electronic effects on the stress state of solids and thin films, which follows a quantum analog of classical Hooke＇s law： ~QE=E（An）, where E is the deformation potential of electronic states and An is the variation of electron density. Here, we present mathematical derivation of both the classical and quantum Hooke＇s law from density functional theory. We further discuss the physical origin of quantum electronic stress, arising purely from electronic excitation and perturbation in the absence of lattice strain （g=0）, and its relation to the degeneracy pressure of electrons in solid and their interaction with the lattice.
基金supported by the National Natural Science Foundation of China(Grant Nos.91216203 and 91216304)
文摘The stability of the rolling motion of near space hypersonic vehicles with rudder control is studied using method of qualitative analysis of nonlinear differential equations, and the stability criteria of the deflected rolling motions are improved. The out- comes can serve as the basis for further study regarding the influence of pitching and lateral motion on the stability of rolling motion. To validate the theoretical results, numerical simulations were do^e for the rolling motion of two hypersonic vehicles with typical configurations. Also, wind tunnel experiments for four aircraft models with typical configurations have been done. The results show that： 1） there exist two dynamic patterns of the rolling motion under statically stable condition. The first one is point attractor, for which the motion of aircraft returns to the original state. The second is periodic attractor, for which the aircraft rolls periodically. 2） Under statically unstable condition, there exist three dynamic patterns of rolling motion, namely, the point attractor, periodic attractor around deflected state of rolling motion, and double periodic attractors or chaotic attrac- tors.
基金supported by the National Natural Science Foundation of China(Grant Nos.91216203 and 91216304)
文摘The configurations of near space hypersonic flying vehicles are considerably different from those of conventional aircrafts.Their configurations are relatively slender;hence their moment of inertia around the longitudinal axis is much smaller than those around the other two axes,resulting in strong coupling of rotations around the three axes.Thus,the stability analysis of rolling motion for such flying vehicles is more complicated than those for conventional aircrafts,and there is no available result of stability analysis which can readily be applied to such cases.This paper is mainly concerned with the stated problem.Considering the practical situation,our investigation is targeted a slightly simpler problem,namely the rolling stability of flying vehicle under known pitching motion.The stability criterion of rolling motion is obtained with and without lateral motions.We also conducted numerical simulation for the pitching-rolling coupled motions of flying vehicles by solving Navier-Stokes equations coupled with dynamic equations of flight.The results of simulation agree well with those of theoretical analysis and experiments.
