###### Abstract  
In this study, an interconnected metamaterial was proposed to suppress flexural vibration. The interconnected metamaterial can improve the manufacturing and installation processes in terms of convenience because it can be fabricated in the form of a modular multi-celled structure with a single-phase material. To evaluate the vibration reduction performance of the metamaterial, stopband analysis was performed, as it solves an iterative eigenvalue problem for the wave vector domain. In order to identify the Bloch mode that contributes to flexural vibration, a concept to extract the Bloch mode based on the modal strain energy was proposed. The vibration-reduction performance of the interconnected metamaterial was numerically verified by using a frequency-response analysis of the multi-celled structure. The interconnected metamaterial proposed in this study was fabricated by using a 3D printer. Finally, the vibration-reduction performance of the multi-celled structure was experimentally verified by using impact testing. interconnected metamaterial; stopband; 3D printing; vibration reduction +
Footnote †: journal: Applied Sciences  
analytical model for calculating the stopband of a beam-shaped periodic structure [15]. In 2019, [PERSON] et al. proposed locally resonant metamaterials based on panel springs comprising acrylic plastic and magnets [11]. This locally resonant metamaterial was applied to the vehicle dash panel to reduce the vibration and radiated noise of the panel. In 2020, a genetic-algorithm-based topology optimization method for a locally resonant metamaterial was proposed to tailor the stopband in the target frequency band [10]. In this work, an interconnected metamaterial in which the resonators of each unit structure are connected was proposed. The interconnected metamaterial is possible to be fabricated by modular manufacturing with single-phase materials. It is relatively advantageous to be applied to industrial applications. However, due to the interaction of each resonator, vibrational waves in interconnected metamaterials propagates not only through the host structure but also through the resonators. To suppress a flexural vibration with the metamaterial, a stopband should be calculated by extracting the Bloch mode that contributes to the bending mode of the host structure from the other modes. In 2006, a modal strain energy-based decomposition method was developed for damage localization of 3D frames [16]. In 2020, [PERSON] et al. developed an automation selection algorithm that selects the appropriate vibration mode, using the modal strain energy and modal assurance criteria [17]. As shown in these two kinds of works in the literature, it is possible to classify the Bloch modes concerning the dynamic property of the mode shape. Moreover, applying these locally resonant metamaterials to practical industrial problems is a difficult task. Furthermore, manufacturing them by general manufacturing processes such as casting or stamping is challenging because almost of locally resonant metamaterials have complicated shapes and consist of multiple materials [18; 19; 20; 21; 22]. In addition, because each unit-cell structure must be attached to the host structure with a regular unit-cell size, installing this type of metamaterial requires considerable effort. In this work, we proposed the systematic method to evaluate the stopband of an interconnected metamaterial based on modal strain energy. The unit structure is divided into resonator and host structure, and modal strain energy for each part is calculated to separate the Bloch mode that contributes to the flexural wave was extracted from among the Bloch modes. The interconnected metamaterial can be fabricated by a modular manufacturing process that uses a single-phase material. The interconnected metamaterial proposed in this study is composed of only polylactic acid (PLA) plastic and can be manufactured by injection molding. Since the molds have been expensive to manufacture, a 3D printer was used in this work.