Abstract

Structural vibration control is a promising method for mitigating the detrimental effects of excessive vibration in structures. It involves monitoring the dynamic behavior of a structure and implementing control strategies to reduce the vibration levels of the structure. Among various control methodologies, the semi-active control method adeptly combines the reliability characteristic of passive systems with the adaptability inherent in fully active systems, without requiring complex control hardware. Smart materials play a crucial role in implementing semi-active vibration control, and among them, magnetorheological (MR) materials have garnered substantial attention for their remarkable properties, including rapid response times and low energy consumption. Compared with MR fluids (MRFs) which can only provide variable damping, Magnetorheological elastomers (MREs) have field dependent viscoelastic properties in which both stiffness and damping properties can be effectively altered using the applied magnetic field. By incorporating MREs into the core of sandwich plates, it becomes possible to modify the continuous plate's vibration characteristics on-demand through application of an external magnetic field. Although employing complete coverage of the MRE core layer within a sandwich plate is likely to yield the best results in reducing vibration levels, it is essential to consider practical factors like mass limitations. Therefore, optimizing the topology of the MRE layer with a constrained volume fraction is of practical importance. The goal of the topology optimization process is to attain the desired vibration control performance while concurrently minimizing the mass or volume of the MRE layer. This enables the efficient utilization of MRE-based vibration control systems in real-world applications, where optimizing resources is crucial.
To achieve this end, first a finite element model has been formulated to evaluate the vibration behavior of MRE-based sandwich plate under dynamic loading. The plate is discretized with rectangular elements, each having 28 degrees of freedom and 4 nodes, enabling accurate estimation of the MRE-based sandwich plate's vibration characteristics.
An optimization problem based on the method of moving asymptotes (MMA), is subsequently formulated to identify the optimal topology of the MRE layer within the sandwich plate to minimize dynamic compliance yielding reduction in vibration amplitude. For material properties interpolation, an MRE-based penalization (MREP) model, based on solid isotropic material with penalization (SIMP) method, has been developed. To validate the accuracy of the proposed methodology, several numerical examples considering MRE-based sandwich plates under different loading and boundary conditions are provided. These examples illustrate the effectiveness of the proposed design optimization methodology for topology optimization of MRE-based sandwich panels to mitigate the vibration.