交变磁场和力场联合激励铁磁圆板的主共振

Primary resonance of ferromagnetic circular plate excited by alternating magnetic field and excitation force

研究铁磁圆板在交变磁场及横向简谐激励作用下的非线性主共振问题。针对磁场环境中铁磁圆板,在给出了圆薄板的形变势能、应变势能、动能的基础上,应用哈密顿变分原理,推得了磁场中铁磁圆板的磁弹性耦合非线性振动方程。基于软铁磁薄板的磁弹性耦合广义变分原理,推得了交变磁场环境中铁磁圆板所受的电磁力表达式。基于得到的圆板振动微分方程,应用伽辽金法进行了离散,推导出了相应的非线性强迫振动方程。利用多尺度法求解主共振问题,得到了幅频响应方程,并依据李雅普诺夫理论分析了解的稳定性。通过算例,给出了圆板的幅频特性曲线图以及振幅随磁场强度、激励力变化的特性曲线图。结果表明,振幅在共振区域显著增大,且随着圆板厚度的减小、磁场强度以及激励力幅值的增大,共振区域扩大。

Nonlinear primary resonance of ferromagnetic circular plate in alternating magnetic field excited by harmonic force is investigated.For ferromagnetic circular plate in magnetic field,on the basis of the deformation potential energy,the strain potential energy and the kinetic energy of the circular plate,the magnetoelastic coupling nonlinear vibration equations of the ferromagnetic circular plate in magnetic field are derived through the application of the Hamilton variational principle.Based on magnetoelastic coupling of ferromagnetic thin plate generalized variational principle,the magnetic force expression of ferromagnetic circular plate under magnetic field is obtained.According to the differential equations of circular plate vibration,the Galerkin method is applied to discrete the equation,and the corresponding nonlinear forced vibration equations are derived.The method of multiple scales is used to solve the primary resonance problem,and the amplitude frequency response equation is obtained.Based on Lyapunov theory,the stability of the solution is analyzed.By some examples,the amplitude frequency characteristic curve of ferromagnetic circular plate and the characteristic curve of amplitude with magnetic field intensity and excitation force are given.The results show that the amplitude increases significantly in the resonance region,and with the decrease of the thickness of the circular plate,the intensity of the magnetic field and the amplitude of the excitation force,the resonance region expands.