## 1 Introduction
In order to adapt to the low-frequency and high-amplitude features of human motion, [PERSON] et al. [24] designed an impact harvester with a moving mass and piezoelectric bending structures. [PERSON] et al. [25] developed an impact-driven piezoelectric energy harvester to realize frequency up-conversion from human motion. In order to avoid the mechanical collision and increase the durability of the harvesters, [PERSON] et al. [26] developed a miniature piezoelectric energy harvester using magnetic repulsive forces to realize the non-contact frequency up-conversion. [PERSON] et al. [27] designed an inertial energy harvesting device utilizing rotating proof mass to achieve piezoelectric beam plucking through magnetic coupling. [PERSON] et al. [28] theoretically and experimentally investigated a vibration-based energy harvester with a rotating magnetic proof mass and piezoelectric bimorph beams. In comparison with linear motion, rotational motion is more widely existing in civil and industrial environments, such as wheels, tires, rotating machines, shafts, gas, and wind turbines, etc. Thus, energy harvesting from rotational motion to powering low-power electrical device is promising and achievable. Nonlinear vibration energy harvesters design reviewed above can be employed to harvest rotational energy. Depending on whether the whole structure or only the excitation source is rotational, rotational energy harvesters can be divided into two categories: rotating energy harvesters and rotation-excitation energy harvesters. For rotating energy harvesters, the whole device is under rotation. A compact, passive self-tuning rotational energy harvester comprising of a relatively rigid piezoelectric beam and a narrow, flexible driving beam with a tip mass is proposed by [PERSON] and [PERSON] [29]. [PERSON] and [PERSON] [30] proposed a rotational piezoelectric energy harvester with a tip mass at the rotating center to reduce the centrifugal force. [PERSON] et al. [31] designed a rotational energy harvesting system that consists of a primary piezoelectric elastic beam, an elastic beam, and two heavy masses jointed by a spring for low speed rotation applications. On the other side, rotation-excitation energy harvestersare designed to be composed of a non-rotational harvesting part and a rotational excitation source. [PERSON] et al. [32] proposed a piezoelectric transducer using bistable piezoelectric bimorphs for low speed wind energy harvesting. [PERSON] et al. [33] presented a piezo-windmill that is excited by rotating magnets to harvest low and wide range wind speed. [PERSON] and [PERSON] [34] developed a rotational harvester with bi-stability and frequency up-conversion to harness low rotation speed kinetic energy with a wide bandwidth. [PERSON] et al. [35] designed a magnetically coupled flexenational rotation energy harvester that consists of flexenational transducers and rotating magnets. [PERSON] et al. [36] proposed a rotational energy harvester and the corresponding experimental results showed that it could harvest wideband low-speed rotational energy. Nonlinear energy harvesting mechanism and frequency up-conversion are widely used in the design of energy harvesters. However, rare work has been proposed by combining multiple nonlinear mechanisms together for rotation energy harvesting, which is supposed to exhibit better performance. In order to optimize the structure and enhance the performance of the rotational energy harvester in [33], a magnetic axial coupling structure with an optimized magnetic frequency up-conversion mechanism is proposed in this paper. Therefore, a magnetic-coupled buckled beam piezoelectric rotational energy harvester (MBBP-REH) is designed for low speed rotational energy harvesting with a wide response bandwidth. This paper theoretically and experimentally investigated the dynamical characteristics of the improved rotational energy harvester. The characteristic responses of different design parameters are presented in this paper.