1. Introduction

1. Introduction

2. Energy harvesters with a single pendulum

Figure 1. Classification of pendulum energy harvesting technologies.

2. Pendulum energy harvesters

At thpreshold amplitude. To solve this problem,ent, many scholars have studied the characteristics of simple pendulum structure. Jia et al. [41] appli1] adopted a pendulum structure for electromagnetic energy harvesting. The application of a pendulum structure can re to reduce the resonancet amplitude threshold. In addition, some studies have shown that the pendulum structures produced satisfactoryshow excellent effects on low-the low frequency and broadband energy- harvesting performance [42]. Dai et al. [43] equipped a vibration-energy harvester with3] established a theoretical model of a single pendulum. The authors established a theoretical model of the structure energy converter, and calculated the ratio betweenof the half-peak bandwidth andto the center frequency. TheirCorrelation analysis revealed that the bandwidth of the pendulum energy harvester was broadened. From the above analysis, shows that the pendulum structure is suitable for increasing the conversion efficiency of the esuccessfully improves the bandwidth of energy harvesting.

Kercik under low-frequency conditions and for broadening the bandwidth.

et al. [4] studied a coupled vibratory pendulum system. Figure 62a shows the primarymain structure of the system, comprisiincluding a tuned- mass damper and two independent energy- harvesting devices. The effectsinfluence of magnetic levitation and rotating harvesters on vibration absorption have been is analyzed. In addition to, the performance of penndulum systems, their applications in vibration mitigation and tructure energy conversion have been explored. For instance, structural vibration is a significant problem occurring during the operation of ofharvesting system can also be applied to shock absorption, such as the offshore wind turbines (OWTs) [60]. Therefore, OWTs have been[5]. In order to effectively mitigate the effects of vibration, OWT is equipped with various structures tohock absorb vibrationing structures. Jahangiri et al. [61] utilized an ] used electromagnetic generator to replace as instead of linear damper fors to capture energy harvesting. They developed a three-dimension. The main structure of the device is a spherical pendulum structure that couldthat absorbs vibrations and harvestcollects energy in boththe x and y directions. The schematic diagram is shown in Figure 6b. When the wind turbine vibrates, the swing of the pendulum induces the relative motion of the coils and magnets. Simulation results indicated that di2b. The simulation results show that the axial and radial displacement of the nacelle wais reduced by approximatelybout 70% and 77% in the axial and radial directions, respectively. Shen et al. [627] proposed a self-powered vibration reduction and monitoring system based on athe pendulum structure. The primarymain structure is shown in Figure 6c. 

Figure 2. (a) Electromagnetic energy harvester with a pendulum-tuned mass damper [594]. Reprinted with permission from Ref. [594]. Copyright 2020, Elsevier. (b) OWTs with a pendulum-tuned mass damper [61]. Adapted with permission from Ref. [61]. Copyright 2019, Elsevier. (c) Self-powered vibration reduction and monitoring system [627]. Reprinted with permission from Ref. [627]. Copyright 2012, Elsevier.

Piezownelectric in Figure 9a, the proposed system could be applied to convert the inertial kineticenergy harvesting is widely used for vibration energy of driverless buses. Experimental results showed that theconversion [8, 9]. Piezoelectric energy harvester could generate the maximum output power of 1.233 mW, and it could harvest multiple types of kineticing technology has many advantages, such as higher energy to self-powered sensors of driverless buses. This was confirmed in another similar study [81]. Additionally, Shukla density, higher voltage and lower mechanical damping [10]. Daniel et al. [82] develop11] proposed a pendulumiezoelectric energy harvester (Figure 9b) ing system that can be equipped on the human body to capture energy from waistline movement. The pendulum comprises multiple strikers that can bend compliant piezoelectric units. The maximum output power could reach 290 μW with PVDF units when the strikers were separated by 23 mm. Bao et al. [83] designed a handheld human motion energy harvester, aapplied to the sea bottom. In another study, Zhang et al. [12] designed a new multidirectional pendulum energy harvester based on homopolar repulsion. As shown in Figure 9c. According to the inertial pendulum principle3a, the magnetic rotor can rotate and capture kinetic energy when the human body moves. Treadmill experiments revealed that the proposed structure could generate average power of 0.18μW 6 km·h^-1.

Figuronment, exhibiting immense application potential in low-frequencye 3. (a) Multi-directional pendulum kinetic energy harvesting. Further, Pan et al. ter [8612]. developed a piezoelectric(b) Human waistline movement energy harvester comprising an inverted piezoelectric beam and pendulum. The mode coupling in the structure was beneficial for producing a snap-through[13]. Reprinted with permission from Ref. [13]. Copyright 2014, Elsevier. (c) Hand-held human motion. The maximum power of the h energy harvester was 51[14].6 μW at stoc

Chastic excitations. Li n et al. [8715] investigated a haprvester comprising a horizontally placed cantilever beam and pendulum. In this structure, the pendulum was able to swing freely under excioposed a rotation and induce the dynamic buckling of the beam. The response of the hal wind energy harvester was analyzed under harmonic and random excitations. Furthermore, to increase conversion efficiency, multi-directional energy harvesting has become another optimization method for the pebased on magnetic double-pendulum structureystem. As such, Bao et al. [88] proposed a magnethown ic pendulum piezoelectric energy harvester for multidirectional energy harvesting, as shown in Figure 10c. In th Figure 4a. Izadgoshatsb study, internal resonance was induced through nonlinear coupling between the magnetic et al. [16] applied the double pendulum and cantilever beam. This harvester could capture vibrational system to human movement energy in multiple dircollections through internal resonance. Experimental results indicated that the structure could generate the maximum output power of 0.64 mW at 7.5 Hz. Xu, as shown in Figure 4b. Sun et al. [8917] inveustigated a multidirectional energy harvester based on a pendulum ball that can freely swing in three-dimensional space (Figure 10d). Nonlinear coupling ed the internal resonance between the cantidoublever and pendulum ball enableand the conversion of vibrational energy in multiple directions, and this system showed a simpler structure and higher efficiency than conventional designs with multiple cantilever beams. Mo antilever beam to expand the bandwidth of the piezoelectric energy collector (Figure 4c). Selyutskiy et al. [9018] designed a piezoeflectric energy harvester based on a U-shaped beam and pendulum. This harvester was able to capture multidirectionaluid-induced vibrational energy and operate at a low frequency.

Figure 10. (a) Ultra-low-frequency energy harvesting based on frequency up-conversion [84]. (b) Impact-driven low-frequency energy harvester [85]. (c) Multi-directional energy harvesting based on magnetic single pendulum [88]. (d) Multi-directional energy harvesting based on pendulum in three-dimensional space [89].

                                                                                            Figure 15. Pricollector based on a double pneumary structure of double ic pendulum.

Chen et al. [119] proposed a rotational wind energy harvester based on a magnetic double-pendulum system. As shown in Figure 18a, the proposed structure generates electric power by coupling the double pendulum with nonlinear magnetic interaction. Owing to the dynamic characteristics of the double pendulum, this system can reduce the magnetic resistance torque at low rotational speeds. Experimental results indicated that the system was able to generate the maximum output power of 1.25 mW at a rotational speed of 557.31 rpm. Izadgoshasb et al. [120] applied a double pendulum system to human motion energy harvesting, as shown in Figure 18b. The piezoelectric cantilever beam is driven by a double pendulum through magnets. The authors compared three configurations using the mechanical shaker and human motion tests: cantilever beam, single pendulum, and double pendulum. The double pendulum exhibited the best effect. Sun et al. [121] expanded the bandwidth of a piezoelectric energy harvester by utilizing the internal resonance between the double pendulum and cantilever beam (Figure 18c). The experimental results showed that the double-pendulum harvester showed excellent broadband energy harvesting ability. Selyutskiy et al. [122] designed a flow-induced vibration energy harvester based on a double aerodynamic pendulum. In this system, the piezoelectric element is connected to the first pendulum and undergoes deformation under the rotation of the pendulum (Figure 18d). This harvester may be suitable for wind energy harvesting.

Figure 18. Figure 4. (a) Rotational wind energy harvester based on magnetic double pendulum [1195]. (b) Double-pendulum energy harvester applied in human motion energy conversion [1206]. Reprinted with permission from Ref. [1206]. Copyright 2019, Elsevier. (c) Piezoelectric cantilever beam coupled with double pendulum [1217]. (d) Flow-induced vibration energy harvester based on double aerodynamic pendulum [1228].

4. Discussion

3. Conclusion

5. Conclusions

This study reviews the researches on the theoretical analyses of the single and double pendulums and their applications in energy harvesting. The different energy-conversion mechanisms, design schemes, and optimal structures of pendulum-like energy harvesters have been summarized in the literature. Based on the existing research, single-pendulum energy harvesters are predominantly applied in ultra-low-frequency environments and for multi-directional energy harvesting. The working conditions of pendulum energy harvesters are <10 Hz, which mainly include ocean wave and human motion energy. Furthermore, single-pendulum systems can be combined with the other functions, such as mechanical motion rectifiers and structural damping. In addition, energy harvesting based on the double pendulums has attracted much research attention. Bas

Red on the above summary, we predict several future research directions and potential applications of pendulum-type energy harveerencesters:

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