【摘要】 在磁场环境中,给出轴向运动导电梁的动能、势能及电磁力虚功的表达式,在此基础上,根据Hamilton原理,建立磁场中轴向运动导电梁在两端铰支边界条件下的非线性自由振动方程.应用Galerkin方法离散运动方程,单自由度时,得到一个含3次非线性项的带阻尼的Duffing方程,利用改进的微分变换方法给出位移的近似解,并与Runge-Kutta数值方法进行比较.最后通过算例给出梁的轴向运动速度及梁的截面惯性矩对位移的影响.更多还原

【Abstract】 In magnetic field,based on the expressions of kinetic energy,potential energy and virtual work done by electromagnetic forces,the vibration equation of a magnetic-elastic axial movement beam with hinged ends boundary conditions is deduced by using Hamilton principle.The non-linear partial differential equation of the axially moving beam is discretized using Galerkin’s method,and a cubic Duffing equation with damping effect is obtained in the case of single degree of freedom.Then the equation is solved by modified differential transform method(MDTM) and the result is contrasted with Runge-Kutta method.Numerical results show the influences of the axial motion velocity and cross sectional moment of inertia on the displacement of the beam.更多还原