The Magneto-Elastic-Plastic Dynamic Analysis For Conductive Rectangular Thin Plates

In engineering practical, the electromagnetic apparatus and devices (i.e. the first wall structure of fusion rector, superconductive coils carrying with current, work pieces electromagnetic forming) will produce the eddy current, and then generate Lorentz force when they work or run under the strong magnetic pulse. The electromagnetic structure will vibrate driving by Lorentz force. Hence it is very important and essential to study the characteristic of distribution of the eddy current and the dynamic response of the conductive plate with the electromagnetic-mechanics coupling.In this dissertation, we gave some qualitative analyses on the critical magnetic field values and some numerical simulation results on the characteristically behaviors of conductive rectangular thin plates, such as the vibration of elastic-plastic, and dynamic stabilities under combined the transverse and in-plane magnetic fields.Firstly, a series solution of eddy current expressed by analytical method is given for eddy current problems under the transverse magnetic fields, the critical magnetic values of magneto instability the conductive rectangular plate are obtained based on stability theory of thin plate .The analytical results indicated that the critical values of magnetic field are decreasing with the increase of the ratio of length to thickness, the conductivity and frequency of the thin plates.Secondly, based on the structure basic of electromagnetic and mechanical and equations of conductive media, the theoretical governing equations of the coupling electro-magneto-mechanics are built, based on these, basic equations for small-deformation problems of conductive thin plates under the condition of the coupling electro-magneto-mechanics interaction are established.Finally, a numerical code is established to quantitatively simulate the behaviors of the nonlinearly multi-coupling problems by the finite element method, the distribution of eddy current on the conductive rectangular thin plates is studied firstly, and then some mechanics characteristics of the conductive rectangular plate, such as, amplitude of vibration, frequency of vibration etc. varying with the applied magnetic field are displayed. The critical magnetic field values of magnetic-instability varying with the ratios of length to thickness, magnitude of the transverse impulse magnetic field and the parameter of magnetic pulse are also studied respectively. All these results indicate that there have remarkable differences on the dynamics responses and instability between the conductive plate with elastic-plastic deformation and only with elastic deformation and all these results are very useful in the safe design, control or evaluate of the electromagnetic structures in the engineering practical.