平行导线间轴向运动导电梁主-内联合共振EI北大核心CSCD

研究轴向运动导电梁在平行导线产生的磁场环境中的主-内联合共振问题。基于电磁场基本理论和哈密顿原理,导出轴向运动梁在外激励和磁场共同作用下的非线性振动方程。针对一端夹支一端铰支的导电梁,采用多尺度法求解方程,得到非线性方程的近似解析解和幅频响应方程,并对稳态解的稳定性进行了分析。通过算例,得到系统前两阶幅值随频率调谐参数、外激励力、轴向速度、电流强度等参数的变化规律。结果表明:系统发生主-内联合共振时一阶和二阶响应都被激发,且存在不同的多解区域;一阶和二阶幅值的稳态解个数在几个多解区域同步变化,其个数取决于外激励力、运动速度和电流强度值。

Principal-internal joint resonance of an axially moving conductive beam between parallel conductors

Here,the principal-internal joint resonance of an axially moving conductive beam in a magnetic field generated by parallel conductors was studied.Based on the basic theory of electromagnetic field and Hamiltonian principle,the nonlinear vibration equation of the axially moving beam under the combined action of external excitation and magnetic field was derived.For the conductive beam clamped at one end and hinged at the other end,the multi-scale method was used to solve the equation to obtain the approximate analytical solution of the nonlinear equation and the amplitude-frequency response equation,and the stability of the steady-state solution was analyzed.Through an example,variation laws of the first two order amplitudes of the system with change of frequency-tuning parameters,external excitation force,axial velocity,current intensity and other parameters were obtained,respectively.The results showed that both the first-order and second-order responses are excited when the system’s principal-internal joint resonance occurs,and there are different multi-solution regions;the number of steady-state solutions of the first-order and second-order amplitudes changes synchronously in several multi-solution regions,and this number depends on external excitation force,moving speed and current intensity.