## 1 Introduction  
The motors that are used in our lives serve their intended purposes of use with the number of revolutions per minute (rpm) adjusted to users' needs. Such RPM adjustments act as the variable-frequency excitation of mechanical systems. Vibrations generated by variable-frequency excitation can cause resonance of mechanical systems. A common way to prevent such failure or damage due to resonance is to use a dynamic vibration absorber. The dynamic vibration absorber is attached to a mechanical system to absorb or dampen vibrations at designed frequencies. It is widely known as a technology for forced reduction of vibrations and can inhibit vibrations very effectively where the vibration frequency remains constant. Moreover, it is easily applicable to existing systems without major alterations to their structures [1; 2; 3]. For that reason, until recently, the dynamic vibration absorber has been reported to have a wide variety of applications [4; 5; 6]. However, the vibration-reducing performance of a dynamic vibration absorber deteriorates if the excitation frequency is variable. Installing multiple dynamic vibration absorbers has been proposed as a solution to the resonance problem [7; 8]. Among others, [PERSON] et al. proposed a dual dynamic vibration absorber [7]. A typical way to build a system with multiple dynamic vibration absorbers is to attach several single-degree-of-freedom (SDOF) dynamic vibration absorbers. The multiple-dynamic-vibration-absorber system is designed by optimizing the stiffness and damping ratio of each SDOF dynamic vibration absorber such that a vibration reduction is achieved in a targeted frequency range. However, such a multiple-dynamic-vibration-absorbersystem is difficult to install because of its large bulk. Another problem is that a resonance frequency is generated between two adjacent frequencies designed for vibration reduction performance. In an attempt to overcome this problem, [PERSON] et al. adjusted the damping ratio to reduce the resonance of newly generated frequencies. Nevertheless, the vibration reduction performance deteriorated at existing target frequencies. Therefore, reducing vibrations caused by variable-frequency excitation requires a tunable dynamic vibration absorber, which helps reduce vibrations depending on the new variable frequency. The idea of the tunable dynamic vibration absorber is that the vibration absorber's natural frequency varies to correspond with the variable excitation frequency. Any variation in the natural frequency of the tunable dynamic vibration absorber occurs as a result of a change in its mass or stiffness. However, the mass of the dynamic vibration absorber is unlikely to vary every moment, so changes should be made in stiffness. To this end, research has been carried out on momentary changes in stiffness that can lead to variations in the natural frequency of a tunable dynamic vibration absorber and on how to control such changes [9]. Studies of stiffness-variable dynamic vibration absorbers are conducted mainly with shape-memory alloys [10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. A problem with stiffness-variable dynamic vibration absorbers using shape-memory alloys is that their response rates should be improved. An MRE-based dynamic vibration absorber has been recently proposed to solve that problem [20]. Magnetorheological elastomers (MREs) are a class of smart materials whose mechanical properties vary due to an externally applied magnetic field with magnetic reactive particles (MRPs) mixed in a rubber matrix [20; 21; 22; 23; 24; 25; 26]. Elastomers such as natural rubber (NR) and silicone are commonly used as matrices, and when a magnetic field is externally applied, their shear modulus is varied by a force of electromagnetic attraction between MRPs. [PERSON] et al. [27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42] presented a concept of the MRE-based dynamic vibration absorber based on the mechanism of shear modulus variation with the applied magnetic field.