The magnetic-elasticity buckling problem of a current plate under the action of a mechanical load in a magnetic field was studied by using the Mathieu function. According to the magnetic-elasticity non-linear kinetic ...The magnetic-elasticity buckling problem of a current plate under the action of a mechanical load in a magnetic field was studied by using the Mathieu function. According to the magnetic-elasticity non-linear kinetic equation, physical equations, geometric equations, the expression for Lorenz force and the electrical dynamic equation, the magnetic-elasticity dynamic buckling equation is derived. The equation is changed into a standard form of the Mathieu equation using Galerkin＇s method. Thus, the buckling problem can be solved with a Mathieu equation. The criterion equation of the buckling problem also has been obtained by discussing the eigenvalue relation of the coefficients 2 and r/ in the Mathieu equation. As an example, a thin plate simply supported at three edges is solved here. Its magnetic-elasticity dynamic buckling equation and the relation curves of the instability state with variations in some parameters are also shown in this paper. The conclusions show that the electrical magnetic forces may be controlled by changing the parameters of the current or the magnetic field so that the aim of controlling the deformation, stress, strain and stability of the current carrying plate is achieved.展开更多
This paper aims at investigating the resonance frequencies and stability of a long Graphene Nano-Ribbon(GNR)carrying electric current.The governing equation of motion is obtained based on the Euler-Bernoulli beam mode...This paper aims at investigating the resonance frequencies and stability of a long Graphene Nano-Ribbon(GNR)carrying electric current.The governing equation of motion is obtained based on the Euler-Bernoulli beam model along with Hamilton’s principle.The transverse force distribution on the GNR due to the interaction of the electric current with its own magnetic field is determined by the Biot-Savart and Lorentz force laws.Using Galerkin’s method,the governing equation is solved and the effect of current strength and dimensions of the GNR on the stability and resonance frequencies are investigated.展开更多
基金National Natural Science Foundation of China(No.50275128)Natural Science Foundation of Hebei Province,China(No.A2006000190).
文摘The magnetic-elasticity buckling problem of a current plate under the action of a mechanical load in a magnetic field was studied by using the Mathieu function. According to the magnetic-elasticity non-linear kinetic equation, physical equations, geometric equations, the expression for Lorenz force and the electrical dynamic equation, the magnetic-elasticity dynamic buckling equation is derived. The equation is changed into a standard form of the Mathieu equation using Galerkin＇s method. Thus, the buckling problem can be solved with a Mathieu equation. The criterion equation of the buckling problem also has been obtained by discussing the eigenvalue relation of the coefficients 2 and r/ in the Mathieu equation. As an example, a thin plate simply supported at three edges is solved here. Its magnetic-elasticity dynamic buckling equation and the relation curves of the instability state with variations in some parameters are also shown in this paper. The conclusions show that the electrical magnetic forces may be controlled by changing the parameters of the current or the magnetic field so that the aim of controlling the deformation, stress, strain and stability of the current carrying plate is achieved.
文摘This paper aims at investigating the resonance frequencies and stability of a long Graphene Nano-Ribbon(GNR)carrying electric current.The governing equation of motion is obtained based on the Euler-Bernoulli beam model along with Hamilton’s principle.The transverse force distribution on the GNR due to the interaction of the electric current with its own magnetic field is determined by the Biot-Savart and Lorentz force laws.Using Galerkin’s method,the governing equation is solved and the effect of current strength and dimensions of the GNR on the stability and resonance frequencies are investigated.
