摘要
研究磁场环境中受机械载荷作用圆柱薄壳的三阶超谐波共振问题。在给出横向磁场和机械动载共同作用下圆柱薄壳的振动方程基础上,应用伽辽金积分法,并进行无量纲化处理,进一步导出相应的非线性磁弹性振动微分方程。采用多尺度法对三阶超谐波共振问题进行求解,得到稳态运动下的幅频响应方程与解的稳定性判别式。通过算例,给出几种情况下反映振幅与各参数关系的曲线图,讨论机械与电磁参数对系统共振与解的稳定性的影响。
The 3-order superharmonic resonances of a thin cylindrical shell in an applied magnetic field subjected to mechanical loadings were studied.The vibration equations of the thin cylindrical shell under a uniform transverse magnetic field and mechanical loadings were obtained.Based on the Galerkin method and the dimensionless treatment,the nonlinear magnetoelastic vibration differential equation was derived.The 3-order superharmonic resonances were analyzed by the multiple scales method.The amplitude-frequency resonance equation of steady state motions and the stability discriminant of the solutions were derived respectively.By an example,some graphs reflecting the relations of the amplitudes and various parameters were given.The effect of mechanical and electromagnetic parameters on the resonances of the system and the stabilities of solutions were discussed.
出处
《机械强度》
CAS
CSCD
北大核心
2011年第1期11-14,共4页
Journal of Mechanical Strength
基金
河北省自然科学基金(E2010001254)
河北省教育厅自然科学项目(Z2006118)资助~~
关键词
磁弹性
圆柱薄壳
超谐波共振
稳定性
多尺度法
Magnetoelastic
Thin cylindrical shell
Superharmonic resonance
Stability
Multiple scales method
