## 1 Introduction
In this paper, however, we merely suggested the applicability of an MRE-based dynamic vibration absorber without evaluating its design and performance. For designing the MRE-based tunable dynamic vibration absorber, a target frequency for vibration reduction should be set, and the physical properties of the MRE should be evaluated. In particular, the MRE's shear modulus must be measured for use as the stiffness of the dynamic vibration absorber. A typical example of research on shear modulus measurements of MREs is a study by [PERSON] et al. [21; 22]. They evaluated the shear modulus of MREs with respect to MRPs and an applied electric current but not the rate of variation of shear modulus with the thickness of MREs. For that reason, it is necessary to evaluate how the MREs' shear modulus varies with the thickness of specimens and design an appropriate stiffness for the dynamic vibration absorber. In designing an MRE-based tunable dynamic vibration absorber, its mass is determined by a target frequency and the MRE's stiffness, and should also be optimized for maximum magnetic field. Recently, numerical and finite element analysis of magnetic-field application device for MRE was conducted by [PERSON] et al. [23]. However, further research is needed to be applied to ATOVA. A genetic algorithm that provides a means of finding optimal solutions was used as a way to optimize the design of the magnetic field. The genetic algorithm applies natural evolution and natural genetics to design optimization and uses a number of individuals simultaneously to find an optimal solution through multiple search paths. It reaches a final optimal solution by handing down the current individuals' good traits to the individuals of the next generation [43; 44]. Regarding the mass part of an MRE-based dynamic vibration absorber, the genetic algorithm should find globally optimal solutions for different design parameters. The coil's number of turns and radius are required for application of a magnetic field to the MRE-based ATDVA. The number of coil turns refers to the number of coil windings and is thus expressed as an integer, and the value of the radius should be set in compliance with the fabrication regulations. Therefore, an optimization technique (i.e., genetic algorithms) should be performed although the design parameters of the coil's number of turns and radius are difficult to apply to a numerical optimization formula because they are discontinuous functions that are not differentiable. It is therefore necessary to theoretically model the magnetic-field application device and the mass part of the MRE-based dynamic vibration absorber, and a sensitivity analysis should be conducted to find and select appropriate design parameters. A genetic algorithm must then find an optimal solution with the selected design parameters. The designed MRE-based dynamic vibration absorber allows the stiffness to vary and works to reduce vibrations in systems wherein the excitation frequency is variable. Thus, when an electric current is applied, there is a need to identify the stiffness of the MRE-based ATDVA. Further, there is also a need to identify how the applied electric current is related to the MRE-based ATDVA's vibration reduction frequency. Finally, for vibration reduction in those systems wherein the excitation frequency is variable, it is necessary to determine the vibration-reducing performance of the MRE-based ATDVA. This work evaluates the vibration-reducing performance of an MRE-based tunable dynamic vibration absorber for reducing the vibration of systems wherein the excitation frequency is variable. To this end, the vibration-reducing performance of the ATDVA is simulated for its applicability under the condition of variable-frequency excitation. For designing the MRE-based ATDVA, this study determines the natural frequencies of a plane plate targeted for vibration reduction. The MRE's shear modulus is evaluated in designing the stiffness part of the MRE-based ATDVA.