磁性功能梯度圆柱壳磁热弹性超谐波共振研究  

Magneto-thermoelastic super-harmonic resonance of magnetic functionally graded cylindrical shells

作　　者：姜雨泉 胡宇达[1,2] JIANG Yuquan;HU Yuda(College of Civil Engineering and Mechanics,Yanshan University,Qinhuangdao 066004,China;Hebei Provincial Key Lab of Mechanical Reliability for Heavy Equipment and Large Structures,Yanshan University,Qinhuangdao 066004,China)

机构地区：[1]燕山大学建筑工程与力学学院,河北秦皇岛066004 [2]燕山大学河北省重型装备与大型结构力学可靠性重点实验室,河北秦皇岛066004

出　　处：《振动与冲击》2024年第17期154-162,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(12172321);河北省自然科学基金资助项目(A2020203007)。

摘　　要：研究温度场和磁场中功能梯度(functionally graded, FG)圆柱薄壳1∶3阶超谐波共振问题。针对金属-陶瓷FG圆柱薄壳,采用热传导方程表征一维温度场沿壳体厚度分布特性;结合热弹性理论,并考虑几何非线性,确定了壳体物理中面下的本构关系;基于磁弹性理论,建立磁场环境下壳体所受洛伦兹力和磁化力模型。应用哈密顿变分原理推得磁热弹耦合非线性振动方程。利用伽辽金积分法得到两端简支FG圆柱薄壳的无量纲化非线性振动微分方程,确定了由静磁力和热内力所产生的静挠度特征方程。应用多尺度法对系统的1∶3阶超谐波共振问题进行近似解析求解,得到系统稳态运动下的幅频响应方程,并应用李雅普诺夫稳定性理论对稳态解进行稳定性分析。通过数值算例,得到不同物理和几何参数影响下系统的共振幅值变化曲线图、动相轨迹图及多值解的区域划分图。结果表明:系统体现为硬弹簧特性;增大激励力幅值、陶瓷侧温度,临界多值解的分岔点右移,共振区域变大;增大磁场强度,稳定解振幅减小。Here,the 1∶3 order super-harmonic resonance problem of functionally graded(FG)cylindrical thin shells was studied in temperature and magnetic fields.For metal-ceramic FG cylindrical thin shells,the heat conduction equation was adopted to characterize one-dimensional temperature field distribution characteristics along shell thickness.Combining with the theory of thermos-elasticity,considering geometric nonlinearity,the constitutive relation on shell physical neutral surface was determined.Based on the theory of magnetoelasticity,models of Lorentz force and magnetization force exerted on shell were established in magnetic field environment.Hamilton variational principle was applied to derive nonlinear magneto-thermoelastic coupled vibration equations.The non-dimensional nonlinear vibration differential equation of a simply supported FG cylindrical thin shell was obtained using Galerkin integration method,and the characteristic equation of static deflection generated by static magnetic force and thermal internal force was determined.The multi-scale method was applied to approximately and analytically solve the 1∶3 order super-harmonic resonance problem of the system,and obtain the amplitude-frequency response equation under system steady-state motion.Lyapunov stability theory was used to analyze the stability of the system’s steady-state solution.Through numerical examples,resonance amplitude variation curve diagrams,dynamic phase trajectory diagrams and region division diagrams of multi-value solution of the system under different physical and geometric parameters were obtained.The results showed that the system exhibits characteristics of hard springs;if increasing excitation force amplitude and temperature on ceramic side,bifurcation point of critical multi-value solution shifts to right,and resonance region becomes larger;if increasing magnetic field intensity,stable solution amplitude becomes smaller.

关 键 词：功能梯度圆柱壳 磁弹性 温度场 超谐波共振 多尺度法 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3