## 4 Design of an MRE-Based Adaptive Seismic Isolator
### Magnetic Circuit Analysis  
To study the magnetic circuit of the novel MRE isolator device, finite element analysis via ANSYS is carried out to simulate and illustrate the effectiveness and the reliability of this design. MRE models and their modified versions are used as isolator finite element model parameters by taking the effect of MWCNTs into account. Figure 12 shows the distribution of the magnetic flux inside the isolator when the applied current is 0.85: (a) is the smart mesh with mesh level 4 (1 denotes finest mesh and 10 represents coarsest mesh), (b) shows the distribution of the magnetic flux line, (c) is the magnetic flux density vector, and (d) is the contour plot of the magnetic flux density.  
The maximum magnetic flux density is 0.799 T for MRE and 0.823 T for MRE with MWCNTs. The magnetic flux reaches strongest, both within the bottom plate, between steel block and yoke. The magnetic flux line passes through the yoke and magneto-rheological \"smart layers\", which forms a closed loop. The strength of the magnetic flux density is relatively uniform within the \"smart layers\" and weakens both near the air and the edges of top and bottom plates. Based on this, the \"smart layers\" are designed in the center of the angular magnetic coil with steel laminates and steel blocks as a whole to increase the permeability. The key issue for designing the isolator is to form a stable, enclosed magnetic path with \"smart\" materials of high permeability. By optimizing the design structure, the energy loss of the magnetic field can be achieved at a reasonable level and in an efficient way. A comparative study for complete and incomplete design is conducted to study the importance of each part of the magnetic path.  
Figure 13 shows the distribution of the contour of magnetic flux density for incomplete design. For incomplete design, magnetic flux density at the missing part has a fast descending trend. The average value of the magnetic flux density of each \"smart\" layer (50 MRE, or MRE with MWCNTs, and 49 laminated steel sheets in total) is measured, with an external magnetic flux density of 0.85 T, and is shown in Figure 14. In this figure, CD is the complete design. ICD1, ICD2 and ICD3 represent incomplete designs without the upper steel block, yoke and upper steel plate, respectively.  
Figure 12: Finite Element Modeling of Isolator.  
ML denotes the layer of MRE, MNL denotes the layer of MRE with MWCNTs, and SL represents the steel sheet between laminated MRE. For all design schemes, the magnetic flux density has a descending trend. This is due to the fact that the gap between the steel yoke and the top plate increases the possibility of energy loss.  
Thus, the closer the location is to the upper plate and the gap, the more magnetic energy is dissipated. For a complete design, with the layer of MRE or steel sheet increasing, the value of magnetic flux density decreases and weakens steadily. For all the areas of incomplete design, magnetic flux density dramatically decreases.  
The maximum magnetic flux density for the incomplete design is about 0.255 T and 0.26 T for MRE laminate and MRE with MWCNTs laminate, respectively. Specifically, for ID1, the magnetic flux density first decreases and then has an abrupt rise. This is because the missing of upper steel block makes the magnetic flux redistributed and it concentrates the magnetic flux lines at the corner of the upper MRE layer. Therefore, a complete design of MRE core area is laminated with steel sheets together with steel blocks attached at the end of the laminated structure, which makes the magnetic flux circuit coherent as a whole. This design can also shift the weakening magnetic field away from the MRE laminate core area, and, at the same time, the narrow magnetic path between the yoke and the bottom plate makes the magnetic circuit have stronger connection.  
Figure 14: Magnetic Flux Density for Different Design Schemes, (**a**) MRE and Steel Laminate, (**b**) MRE with MWCNTs and Steel Laminate.  
Figure 13: Incomplete Design.