磁场作用功能梯度壳体磁弹耦合动力学模型  

A Magnetoelastic Coupling Dynamical Model for Functional Gradient Shells Under Magnetic Field Actions

作　　者：胡宇达[1,2] 廖峰 HU Yuda;LIAO Feng(School of Civil Engineering and Mechanics,Yanshan University,Qinhuangdao,Hebei 066004,P.R.China;Hebei Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structures,Yanshan University,Qinhuangdao,Hebei 066004,P.R.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：《应用数学和力学》2023年第11期1341-1353,共13页Applied Mathematics and Mechanics

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

摘　　要：针对电磁场环境中金属-陶瓷功能梯度圆柱壳体结构,基于物理中面下的几何关系和Hooke定律,确定了圆柱薄壳体的非线性本构关系.根据Kirchhoff-Love弹性理论,给出了非均质弹性壳体的变形应变能、动能及其变分运算式.基于电磁弹性理论,得出了电磁场作用下磁性功能梯度壳体所受涡流Lorentz力和磁化力模型.应用Hamilton广义变分原理,建立功能梯度薄壳体的磁弹性耦合非线性振动方程组,得出了描述功能梯度结构的具有变形场与电磁场耦合特征的动力学理论模型.通过对磁场中功能梯度壳体固有振动问题的举例分析,得到了壳体振动特征方程和固有频率变化规律,表明磁场和材料体积分数指数的增大能够使频率值减小,而在周向波数影响曲线中出现频率最小值的情形.研究方法可为多场耦合系统理论建模及动力学分析提供参考.For metal-ceramic functional gradient cylindrical shells in electromagnetic fields,the nonlinear con-stitutive relations were determined based on the geometry and Hooke’s law on the physical neutral surface.Ac-cording to the Kirchhoff-Love theory,the strain energy expression and the kinetic energy expression with its variational operator were given for the heterogeneous elastic shell.The model of the eddy current Lorentz force and the magnetization force for ferromagnetic functional gradient shells under electromagnetic field actions,was derived with the electromagnetic elasticity theory.The magnetoelastic coupling nonlinear vibration equa-tions for the shell were obtained by means of Hamilton’s variational principle,and the dynamical model descri-bing the coupling characteristics of the deformation field and the electromagnetic field was established for func-tional gradient structures.Through numerical examples for natural vibrations of functional gradient shells,the characteristic equation and the natural frequency variation law were obtained.The results show that,the natural frequency decreases with the magnetic induction intensity and the material volume fraction index,and the phe-nomenon of minimum frequency will occur in the circumferential wave number influence curves.This study pro-vides a reference for the theoretical modeling and dynamic analysis of multi-field coupling systems.

关 键 词：功能梯度圆柱壳 磁弹性 动力学模型 电磁场 Hamilton变分原理 

分 类 号：O322[理学—一般力学与力学基础] O343.7[理学—力学]