Mathematical models arising from a survey of ferromagnetic materials under magnetisation

Ab This paper focuses on mathematical models describing the mechanical behavior of ferromagnetic materials under magnetization. Through combination of the electromagnetic field theory with the theory of elastic mechanics, several nonlinear systems of fourth-order partial differential equations were deduced. By making further assumption, the first-order approximation of the above equations was established, of which the solutions are good enough for engineering application.     

正弦电磁场中铁磁材料数学模型

将电磁场理论与弹性力学理论相结合，建立了描述铁磁材料在正弦电磁场中的数学模型，并对该模型一类的4阶非线性偏微分方程的解进行了讨论．给出其一阶近似后得到的线性偏微分方程的解析表达式和数值计算方法．计算结果表明，本方法是有效的．     

正弦电磁场中磁性材料力学特性分析

将电磁场理论与弹性力学理论相结合，分析了磁性材料在正弦电磁场中的力学特性。首先，介绍磁场力的一般数学表达式，随后依据电力设备磁路的对称性给出其磁场力简化数学模型，再根据电力设备中磁性材料的物理和几何特点建立其力学模型，最后将上述两种模型相结合导出描述正弦电磁场中磁性材料力学特性的数学模型，并给出其数值计算方法。这些数学模型可用于对由于磁路中存在涡流而产生的大型电力变压器铁心及其它电力设备振动和噪声进行定性和定量分析。