磁场和温度场作用下金属-陶瓷FGM圆柱壳固有振动  

Natural Vibration of Metal⁃Ceramic Functionally Graded Cylindrical Shells under Magnetic and Temperature Fields

作　　者：周琦 胡宇达[1,2] ZHOU Qi;HU Yuda(School of Civil Engineering and Mechanics,Yanshan University,Qinhuangdao 066004,Hebei,China;Hebei Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structure,Yanshan University,Qinhuangdao,066004,Hebei,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：《力学季刊》2023年第4期891-903,共13页Chinese Quarterly of Mechanics

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

摘　　要：针对温度场中的金属-陶瓷功能梯度圆柱壳,基于物理中面下Love非线性薄壳理论,考虑物性参数沿厚度的梯度分布规律,得到含热应力项的内力和内力矩的表达式.根据电磁和弹性理论,得出磁场环境中导电功能梯度壳体的涡流洛伦兹力模型,给出动能、应变能及其变分表达式.应用哈密顿变分原理和伽辽金离散法,建立功能梯度圆柱薄壳的磁热弹耦合振动方程,推得两端简支约束下非轴对称振动壳体的固有频率特征方程.通过算例,得到功能梯度圆柱壳的固有频率变化曲线图,阐明了磁场、温度、材料属性及结构尺寸对振动频率的影响规律.结果表明:周向波数增大,固有频率呈现先减小后增大的趋势;磁感应强度增加,电磁阻尼效应逐渐明显,固有频率值减小;壳体厚度的增大、长度的减小和温度的大幅升高,使刚度项系数减小,固有频率值增加.Based on the Love nonlinear shell theory on physics nature surface for the physical midplane,considering the gradient distribution of physical parameters along the thickness,the expressions of internal forces and internal moments with thermal stress terms are obtained for the metal-ceramic functionally graded cylindrical shell in the temperature field.According to the electromagnetic and elastic theories,the eddy current Lorentz force model of the conductive functionally graded shell in magnetic field is obtained,and the kinetic energy,strain energy and their vibrational formulas are given.Applying the Hamiltonian principle and the Galerkin method,the magneto-thermoelastic coupling vibration equations of the functional gradient thin shell are established,and the characteristic equation of non-axisymmetric vibration frequency for the shell with simply supported conditions is obtained.Through numerical calculation,the curves of natural frequency for the functional gradient thin shell are plotted.The effects of magnetic field,temperature,material properties,and structure size on the vibration frequency are clarified.The results indicate that with the increase of circumferential wave number,the natural frequency decreases first and then increases.As the magnetic induction strength increases,the electromagnetic damping effect increases,and the value of the natural frequency decreases.The increase in thickness,decrease in length,and significant increase in temperature result in the decrease of stiffness coefficient,which in turn leads to the increase of the natural frequency.

关 键 词：功能梯度壳体 固有振动 磁场 温度场 物理中面 

分 类 号：O322[理学—一般力学与力学基础] O442[理学—力学]