导电材料结构电磁热弹性多场行为的理论研究
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摘要
弹性体电-磁-热-弹性多场理论的发展,对处于强电磁场和高温作用下的结构元件的强度和动态分析具有非常重要的意义。实际工况中,材料不可避免的处于电磁场和温度场的工作环境中,与之相关的力、磁、热、电分析成为结构优化和强度设计的需要。本文建立了一套较为完善的非线性电-磁-热-弹性相互作用的理论,研究了导电薄板在多脉冲磁场和内部固有电场作用下的电流密度分布及热效应,非均匀电磁场对热传导的影响规律,以及电磁场和温度场共同作用下导电薄板的非线性动力响应。
首先,电磁热弹性理论中包含了复杂的电磁场环境下电场和磁场间的感应关系,进而影响了导体内电磁力的大小和分布,同时针对电磁热效应引入了变温体力密度的概念。在给定的通电悬臂导电薄板多脉冲磁场作用下的物理模型的数值计算中,分析了感应电流密度、温度场、面内电磁体力和变温体力随时间的变化及板内分布形态,薄板在面内电磁体力和变温体力作用下的动态响应与板内固有电场值E0、多脉冲磁场最大磁场值B0、单位时间脉冲次数n以及脉冲参数τ有关。
其次,从微观Boltzmann方程推导出的电磁热传导方程填补并丰富了电磁场对热传导影响规律这一部分的理论,首次提出了非均匀电磁场对热传导过程影响的主要因素是电场梯度或磁场梯度,磁场对热传导的作用依赖于电场的存在,并从微观物理机理上对本文和已有的实验结果给予了解释。通过数值模拟给出了电磁场梯度沿热传导方向值为正或负,以及电磁场梯度值的大小对热传导升温速度和最终稳定温度的影响规律,数值结果定性上与实验结果总结的规律保持一致。
最后,针对非均匀电磁场和热载荷作用下的导电薄板,考虑了温度与形变的耦合作用,薄板挠度在面内电磁体力和变温体力作用下出现了拍振现象。拍振的周期和最大振幅在电磁场的作用下得到了大幅的提高,这对于板的稳定性研究具有重要的意义。
综上所述,通过本文的工作,完善了现有电-磁-热-弹性相互作用理论,为正确预测各类复杂电磁场环境下导电结构的力、磁、热、电特性提供了理论依据,同时也揭示了材料复杂电磁场环境下的物理本质。
With the development of multi-field theoretical for elastomers, it is important to analyze the intensity and dynamic stability of structure components under the effect of strong electromagnetic fields and high temperature. In actual working conditions, materials work in the environment of electromagnetic field and temperature field inevitably, so the relevant analysis of electro-magneto- thermo- mechanics becomes the necessity in the optimization of structure and intensity design. A more perfect theory for the nonlinear electro-magneto- thermo-elastic behaviors is established in this text, and the distribution of current density and thermal effect of conductive thin plate subjected to the multi-pulsed magnetic field and inner inherent electric field, the law of heat conduction influenced by non-uniform electromagnetic field and the nonlinear dynamic response of the plate under the electromagnetic field and temperature field are investigated.
Firstly, the induction between the electric field and magnetic field is included in the electro-magneto-thermo-mechanical theory, which has effect on the value and distribution of electromagnetic force. The conception of variable temperature volume force is also introduced by considering the electromagnetic heat effect. During the numerical calculation for the physical model that a current conducting thin plate is subjected to a transverse multi-pulsed magnetic field, the distribution forms of induced electric density, temperature field, in-plane electromagnetic volume forces, variable temperature volume force and also their variation with time are analyzed. We find that the dynamic response of plate impelled by in-plane components of electromagnetic force and variable temperature volume force is related to inner inherent electric field Eo, maximum value Bo of multi-pulsed magnetic field, pulse number n per unit of time and pulse parameterτ.
Secondly, the theory of heat conduction influenced by electromagnetic field is perfected by the electromagnetic heat conduction equation deduced from the Boltzmann equation, and the main influencing factors on the heat conductive process are the electric field gradient and the magnetic gradient which is proposed for the first time. Furthermore, the effect of magnetic field on heat conduction depends on the existence of electric field. The existing experimental results can all be discussed based on the mechanism of microcosmic physics. The numerical simulation reveals the rules that the heating rate of heat conduction and final stable temperature are determined by the positive or negative values of electric field gradient and magnetic gradient along the direction of heat conduction. The numerical results are qualitatively consistent with the experimental results.
Finally, the conductive thin plate subjected to the non-uniform electromagnetic field and thermal load is considered. The coupling effect between temperature and deformation makes the appearance of beat vibration phenomenon, which the deflection of plate is applied by the in-plane electromagnetic volume forces and variable temperature volume force. The period and the maximum amplitude of beat vibration are enhanced greatly owing to the effect of electromagnetic field, which is important for the research of stability of plate.
To sum up, the interaction theory of electro-magneto-thermo-elasticity is improved form our work. Simultaneously, the theoretical basis is provided for predicting the electric, magnetic, thermal and mechanical characteristics of conductive structure in various complex electromagnetic environments, as well as the physical essence of materials in complex electromagnetic field is revealed.
首先,电磁热弹性理论中包含了复杂的电磁场环境下电场和磁场间的感应关系,进而影响了导体内电磁力的大小和分布,同时针对电磁热效应引入了变温体力密度的概念。在给定的通电悬臂导电薄板多脉冲磁场作用下的物理模型的数值计算中,分析了感应电流密度、温度场、面内电磁体力和变温体力随时间的变化及板内分布形态,薄板在面内电磁体力和变温体力作用下的动态响应与板内固有电场值E0、多脉冲磁场最大磁场值B0、单位时间脉冲次数n以及脉冲参数τ有关。
其次,从微观Boltzmann方程推导出的电磁热传导方程填补并丰富了电磁场对热传导影响规律这一部分的理论,首次提出了非均匀电磁场对热传导过程影响的主要因素是电场梯度或磁场梯度,磁场对热传导的作用依赖于电场的存在,并从微观物理机理上对本文和已有的实验结果给予了解释。通过数值模拟给出了电磁场梯度沿热传导方向值为正或负,以及电磁场梯度值的大小对热传导升温速度和最终稳定温度的影响规律,数值结果定性上与实验结果总结的规律保持一致。
最后,针对非均匀电磁场和热载荷作用下的导电薄板,考虑了温度与形变的耦合作用,薄板挠度在面内电磁体力和变温体力作用下出现了拍振现象。拍振的周期和最大振幅在电磁场的作用下得到了大幅的提高,这对于板的稳定性研究具有重要的意义。
综上所述,通过本文的工作,完善了现有电-磁-热-弹性相互作用理论,为正确预测各类复杂电磁场环境下导电结构的力、磁、热、电特性提供了理论依据,同时也揭示了材料复杂电磁场环境下的物理本质。
With the development of multi-field theoretical for elastomers, it is important to analyze the intensity and dynamic stability of structure components under the effect of strong electromagnetic fields and high temperature. In actual working conditions, materials work in the environment of electromagnetic field and temperature field inevitably, so the relevant analysis of electro-magneto- thermo- mechanics becomes the necessity in the optimization of structure and intensity design. A more perfect theory for the nonlinear electro-magneto- thermo-elastic behaviors is established in this text, and the distribution of current density and thermal effect of conductive thin plate subjected to the multi-pulsed magnetic field and inner inherent electric field, the law of heat conduction influenced by non-uniform electromagnetic field and the nonlinear dynamic response of the plate under the electromagnetic field and temperature field are investigated.
Firstly, the induction between the electric field and magnetic field is included in the electro-magneto-thermo-mechanical theory, which has effect on the value and distribution of electromagnetic force. The conception of variable temperature volume force is also introduced by considering the electromagnetic heat effect. During the numerical calculation for the physical model that a current conducting thin plate is subjected to a transverse multi-pulsed magnetic field, the distribution forms of induced electric density, temperature field, in-plane electromagnetic volume forces, variable temperature volume force and also their variation with time are analyzed. We find that the dynamic response of plate impelled by in-plane components of electromagnetic force and variable temperature volume force is related to inner inherent electric field Eo, maximum value Bo of multi-pulsed magnetic field, pulse number n per unit of time and pulse parameterτ.
Secondly, the theory of heat conduction influenced by electromagnetic field is perfected by the electromagnetic heat conduction equation deduced from the Boltzmann equation, and the main influencing factors on the heat conductive process are the electric field gradient and the magnetic gradient which is proposed for the first time. Furthermore, the effect of magnetic field on heat conduction depends on the existence of electric field. The existing experimental results can all be discussed based on the mechanism of microcosmic physics. The numerical simulation reveals the rules that the heating rate of heat conduction and final stable temperature are determined by the positive or negative values of electric field gradient and magnetic gradient along the direction of heat conduction. The numerical results are qualitatively consistent with the experimental results.
Finally, the conductive thin plate subjected to the non-uniform electromagnetic field and thermal load is considered. The coupling effect between temperature and deformation makes the appearance of beat vibration phenomenon, which the deflection of plate is applied by the in-plane electromagnetic volume forces and variable temperature volume force. The period and the maximum amplitude of beat vibration are enhanced greatly owing to the effect of electromagnetic field, which is important for the research of stability of plate.
To sum up, the interaction theory of electro-magneto-thermo-elasticity is improved form our work. Simultaneously, the theoretical basis is provided for predicting the electric, magnetic, thermal and mechanical characteristics of conductive structure in various complex electromagnetic environments, as well as the physical essence of materials in complex electromagnetic field is revealed.
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