## 1 Introduction
In general, for the locally resonant metamaterials, stiffness [30] and inertial properties [37] are the two significant mechanical parameters governing band gap formation. However, recently it has been observed that the band structure of locally resonant metamaterials can be tuned by electromechanical tuning parameters [38]. An electromechanical local resonator is a resonator that incorporates a piezoelectric transducer, with its piezoelectric layer typically connected to electrical circuits. In strong electromechanical coupling, the resonant frequency of the metamaterial changes due to the effect of the electromechanical coupling coefficient and the resistance of the shunt circuit [39]. Electromechanical coupling refers to the interaction between electrical and mechanical elements, where energy is exchanged between the two domains. Piezoelectric patches and shunt circuits embedded in metamaterials are used to modify the band structure of strongly coupled electromechanical metamaterials [40]. Passive electromechanical resonators [41] and active piezoelectric elements have been used for vibration control [42]. In this vibration control method, the charge and current flow associated with piezoelectric shunts are used to control vibrations. Moreover, periodic shunts are used to attenuate and localize the propagation of waves [43; 44]. They effectively dampen multimode vibrations in the beam and dissipate energy all without requiring external mechanical dampers. This indicates that piezoelectric layers, in conjunction with shunt circuits, can be used to vary the stiffness of the local resonators. Beyond that, piezoelectric-embedded locally resonant metamaterials have applications in biomedical devices [45], noise reduction, structural health monitoring, and the development of tunable acoustic devices [46]. Recent studies have investigated the impact of electromechanical resonators and shunt circuits on single-resonator mass-in-mass metamaterials for simultaneous energy harvesting and vibration reduction [47, 48]. These studies found that weakly coupled electromechanical resonators with shunted circuits minimally affect dispersion, enabling simultaneous energy harvesting with negligible impact on vibration control. However, strong electromechanical coupling can deform band structures, potentially merging acoustic and optical modes. [PERSON] et al. explored electromechanical metamaterials with resistor and inductor shunts [49]. In strongly coupled systems featuring a single resonator shunted to a resistor and inductor, triple passbands were observed. Despite the fact that several works have focused on the use of metamaterials for vibration attenuation and energy harvesting with electromechanical elements [50, 51], no research has investigated hierarchical mass-in-mass metamaterials incorporating electromechanical resonators and shunt circuits. [PERSON], [PERSON] and [PERSON] [52] studied the optimal energy harvesting performance of a multidegree-of-freedom configuration using a single unit cell. While this design includes multiple hierarchically configured local resonators, only a single piezoelectric layer and shunt circuit were associated with the main chain. Their results showed that a multiple degree-of-freedom energy harvester increases the power output density with an increase of overall mass compared to a single degree-of-freedom system. This work differs from the study of [PERSON], [PERSON] and [PERSON] [52] by adopting a hierarchical configuration of multiple electromechanical resonators and shunt circuits, without changing the overall mass equivalent to that of a comparable single resonator metamaterial. The hierarchy is designed in two types: the outward and inward configurations. The shunt circuits are integrated into the electromechanical resonator chain rather than the main chain.