Recent Development of Piezoelectric Energy Harvesting Structures and the Technology of Frequency Up-converting Oscillators

doi:10.3901/JME.2022.20.027

Abstract

Abstract: Piezoelectric material is a kind of excellent electromechanical conversion element, has the advantages of small volume, low cost, reliability and so on. But how to design piezoelectric oscillators and efficiently scavenge ambient vibration energy, is still a key technical problem needed to be solved in the corresponding field. Three kinds of typical piezoelectric oscillators based on the resonant frequency matching strategy, represented by constant resonant frequency, resonant frequency tuning and wideband operating frequency structures, are the partial solution to the problem mentioned above. However, the problems such as the low output power and the reliability of oscillating structures are still existing, while harvesting the ambient low or ultra-low frequency vibration energy. To up-convert the excitation frequency into high oscillation frequency of piezoelectric structures through mechanical frequency up-conversion technology, is a reasonable approach and can break through the low power density limitation of piezoelectric elements under the condition of ultra-low frequency. Several kinds of mechanical frequency up-conversion techniques are distinguished and introduced, especially for an internal resonance based frequency up-conversion approach in nonlinear vibration systems. Such approach has the advantages of low threshold of excited acceleration, less energy losses during the frequency conversion stage, etc., broadening the mechanical frequency up-conversion research in the field of piezoelectric oscillators.

Key words: vibration energy harvesting, piezoelectric oscillator, resonant frequency matching, frequency up-conversion, internal resonance

CLC Number:

TB122
TB535

WU Yipeng, LI Sen, LAN Chunbo, ZHOU Shengpeng, XIE Weitai, QIU Jinhao, JI Hongli. Recent Development of Piezoelectric Energy Harvesting Structures and the Technology of Frequency Up-converting Oscillators[J]. Journal of Mechanical Engineering, 2022, 58(20): 27-45.

References

[1] THOMBRE S，ZHAO Z，RAMM-SCHMIDT H，et al. Sensors and AI techniques for situational awareness in autonomous ships:A review[J]. IEEE Transactions on Intelligent Transportation Systems，2020，23(1):64-83.
[2] 林京. 机器信息学:机械产品智能化的学科支撑[J]. 机械工程学报，2021，57(2):11-20. LIN Jing. Machinery Informatics:A fundamental discipline to intelligent machinery[J]. Journal of Mechanical Engineering，2021，57(2):11-20.
[3] 李江腾，王非. 基于知识嵌入和DNN的工商业用户异常用电检测[J]. 电力工程技术，2020，39(3):158-165. LI Jiangteng，WANG Fei. Non-technical loss detection based on energy measurement knowledge and deep neural network among industrial and commercial customers[J]. Electric Power Engineering Technology，2020，39(3):158-165.
[4] 张政，张波. 移动负载的动态无线供电系统发展及关键技术[J]. 电力工程技术，2020，39(1):21-30. ZHANG Zheng，ZHANG Bo. Development and key technologies of dynamic wireless power transfer system for moving load[J]. Electric Power Engineering Technology，2020，39(1):21-30.
[5] HAN S，KIM J，WON S M，et al. Battery-free，wireless sensors for full-body pressure and temperature mapping[J]. Science Translational Medicine，2018，10(435):4950.
[6] YUAN X，LI L，GOU H，et al. Energy and environmental impact of battery electric vehicle range in China[J]. Applied Energy，2015，157:75-84.
[7] TIAN X，WU Y，HOU P，et al. Environmental impact and economic assessment of secondary lead production:Comparison of main spent lead-acid battery recycling processes in China[J]. Journal of Cleaner Production，2017，144:142-148.
[8] RAGHUNATHAN V，KANSAL A，HSU J，et al. Design considerations for solar energy harvesting wireless embedded systems [C]//IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks，2005. IEEE，2005:457-462.
[9] ROUNDY S，LELAND E S，BAKER J，et al. Improving power output for vibration-based energy scavengers[J]. IEEE Pervasive Computing，2005，4(1):28-36.
[10] 曹自平，王楚，袁明，等. 环境能量采集技术的研究现状及发展趋势[J]. 南京邮电大学学报，2016，36(4):1-10. CAO Ziping，WANG Chu，YUAN Ming，et al. Survey on ambient energy harvesting techniques and its development tendency[J]. Journal of Nanjing University of Posts and Telecommunications，2016，36(4):1-10.
[11] JIA Y. Review of nonlinear vibration energy harvesting:Duffing，bistability，parametric，stochastic and others[J]. Journal of Intelligent Material Systems and Structures，2020，31(7):921-944.
[12] BOUGHALEB J，ARNAUD A，MONFRAY S，et al. Coupling of a bimetallic strip heat engine with a piezoelectric transducer for thermal energy harvesting[J]. Molecular Crystals and Liquid Crystals，2016，628(1):15-22.
[13] WANG J，ZHANG C，GU S，et al. Enhancement of low-speed piezoelectric wind energy harvesting by bluff body shapes:Spindle-like and butterfly-like cross-sections[J]. Aerospace Science and Technology，2020，103:105898.
[14] ARROYO E，BADEL A，FORMOSA F. Energy harvesting from ambient vibrations:Electromagnetic device and synchronous extraction circuit[J]. Journal of Intelligent Material Systems and Structures，2013，24(16):2023-2035.
[15] YANG F，DU L，YU H，et al. Magnetic and electric energy harvesting technologies in power grids:A review[J]. Sensors，2020，20(5):1496.
[16] LIU W，BADEL A，FORMOSA F，et al. A wideband integrated piezoelectric bistable generator:Experimental performance evaluation and potential for real environmental vibrations[J]. Journal of Intelligent Material Systems and Structures，2015，26(7):872-877.
[17] TAO K，TANG L，WU J，et al. Investigation of multimodal electret-based MEMS energy harvester with impact-induced nonlinearity[J]. Journal of Microelectromechanical Systems，2018，27(2):276-288.
[18] KIM D W，KIM S W，JEONG U. Lipids:Source of static electricity of regenerative natural substances and nondestructive energy harvesting[J]. Advanced Materials，2018，30(52):1804949.
[19] TAO K，CHEN Z，YI H，et al. Hierarchical honeycomb-structured electret / triboelectric nano- generator for biomechanical and morphing wing energy harvesting[J]. Nano-micro letters，2021，13(1):1-16.
[20] WANG Z L，JIANG T，XU L. Toward the blue energy dream by triboelectric nanogenerator networks[J]. Nano Energy，2017，39:9-23.
[21] WANG Z，HU J，HAN J，et al. A novel high-performance energy harvester based on nonlinear resonance for scavenging power-frequency magnetic energy[J]. IEEE Transactions on Industrial Electronics，2017，64 (8):6556-6564.
[22] CARNEIRO P，SOARES DOS SANTOS M P，RODRIGUES A，et al. Electromagnetic energy harvesting using magnetic levitation architectures:A review[J]. Applied Energy，2020，260:114191.
[23] AMBROŻKIEWICZ B，LITAK G，WOLSZCZAK P. Modelling of electromagnetic energy harvester with rotational pendulum using mechanical vibrations to scavenge electrical energy[J]. Applied Sciences，2020，10(2):671.
[24] DĄBROWSKA A，GRESZTA A. Analysis of the possibility of using energy harvesters to power wearable electronics in clothing[J]. Advances in Materials Science and Engineering，2019，2019:1-13.
[25] KAHOULI B. Does static and dynamic relationship between economic growth and energy consumption exist in OECD countries?[J]. Energy Reports，2019，5:104-116.
[26] LEE B，KIM D H，PARK J，et al. Modulation of surface physics and chemistry in triboelectric energy harvesting technologies[J]. Science and Technology of Advanced Materials，2019，20(1):758-773.
[27] SLABOV V，KOPYL S，SOARES DOS SANTOS M P，et al. Natural and eco-friendly materials for triboelectric energy harvesting[J]. Nano-Micro Letters，2020，12(1):1-18.
[28] SUNG C，BAI C，CHEN J，et al. Controllable fuel cell humidification by ultrasonic atomization[J]. Journal of Power Sources，2013，239:151-156.
[29] PUTRA I，SUNU P W，TEMAJA I W，et al. Investigation on application of ultrasonic humidifier for air conditioning system[C]//Journal of Physics:Conference Series. IOP Publishing，2020，1450(1):012050.
[30] AL-ABED M，ANTICH P，WATENPAUGH D E，et al. Phantom study evaluating detection of simulated upper airway occlusion using piezoelectric ultrasound transducers[J]. Computers in Biology and Medicine，2017，89:325-336.
[31] TRESSLER J F. Piezoelectric and acoustic materials for transducer applications[M]. Boston:Springer，2008.
[32] WANG W，JIANG Y，THOMAS P J. Structural design and physical mechanism of axial and radial sandwich resonators with piezoelectric ceramics:A review[J]. Sensors，2021，21(4):1112.
[33] 汪恒，唐荣江，郑伟光，等. 基于非完美声学黑洞的压电能量收集系统[J]. 压电与声光，2020，42(6):859-863. WANG Heng，TANG Rongjiang，ZHENG Weiguang，et al. Piezoelectric energy harvesting system based on imperfect acoustic black hole[J]. Piezoelectrics & Acoustooptics，2020，42(6):859-863.
[34] 黄瑶，万小丹，刘伟群. 基于振动能量发电的自适应机械同步开关[J]. 振动、测试与诊断，2021，41(4):741- 746. HUANG Yao，WAN Xiaodan，LIU Weiqun. Optimized adaptive mechanical switch for vibration energy generator[J]. Journal of Vibration，Measurement & Diagnosis，2021，41(4):741-746.
[35] 郭晓莹，李茂军，李琛. 一种基于压电片的能量转换装置及其优化设计[J]. 压电与声光，2018，40(2):300-303. GUO Xiaoying，LI Maojun，LI Chen. An energy conversion device based on piezoelectric plate and its optimum design[J]. Piezoelectrics & Acoustooptics，2018，40(2):300-303.
[36] OTTMAN G K，HOFMANN H F，LESIEUTRE G A. Optimized piezoelectric energy harvesting circuit using step-down converter in discontinuous conduction mode[J]. IEEE Transactions on Power Electronics，2003，18(2):696-703.
[37] LEFEUVRE E，BADEL A，RICHARD C，et al. Piezoelectric energy harvesting device optimization by synchronous electric charge extraction[J]. Journal of Intelligent Material Systems and Structures，2005，16(10):865-876.
[38] LALLART M，GUYOMAR D. Piezoelectric conversion and energy harvesting enhancement by initial energy injection[J]. Applied Physics Letters，2010，97(1):014104.
[39] LIU W，ZHAO C，BADEL A，et al. Compact self-powered synchronous energy extraction circuit design with enhanced performance[J]. Smart Materials and Structures，2018，27(4):47001.
[40] CHEN Z，XIA Y，HE J，et al. Elastic-electro-mechanical modeling and analysis of piezoelectric metamaterial plate with a self-powered synchronized charge extraction circuit for vibration energy harvesting[J]. Mechanical Systems and Signal Processing，2020，143:106824.
[41] LEFEUVRE E，BADEL A，BRENES A，et al. Power and frequency bandwidth improvement of piezoelectric energy harvesting devices using phase-shifted synchronous electric charge extraction interface circuit[J]. Journal of Intelligent Material Systems and Structures，2017，28(20):2988-2995.
[42] LIU W Q，BADEL A，FORMOSA F，et al. Wideband energy harvesting using a combination of an optimized synchronous electric charge extraction circuit and a bistable harvester[J]. Smart Materials and Structures，2013，22(12):125038.
[43] BABAYO A A，ANISI M H，ALI I. A Review on energy management schemes in energy harvesting wireless sensor networks[J]. Renewable and Sustainable Energy Reviews，2017，76:1176-1184.
[44] CARREON-BAUTISTA S，HUANG L，SANCHEZ-SINENCIO E. An autonomous energy harvesting power management unit with digital regulation for IoT applications[J]. IEEE Journal of Solid-State Circuits，2016，51(6):1457-1474.
[45] 刘轩，王越，吴义鹏. 基于超级电容的储能模块自放电分析[J]. 电力工程技术，2021，40(3):2-6. LIU Xuan，WANG Yue，WU Yipeng. Self-discharge analysis of energy storage module based on super- capacitor[J]. Electric Power Engineering Technology，2021，40(3):2-6.
[46] WILLIAMS C B，YATES R B. Analysis of a micro-electric generator for microsystems[J]. Sensors and Actuators A:Physical，1996，52:8-11.
[47] WU Y，BADEL A，FORMOSA F，et al. Piezoelectric vibration energy harvesting by optimized synchronous electric charge extraction[J]. Journal of Intelligent Material Systems and Structures，2012，24(12):1445-1458.
[48] BADEL A，LEFEUVRE E. Nonlinearity in energy harvesting systems[M]. Cham:Springer，2016.
[49] ARROYO E，BADEL A，FORMOSA F，et al. Comparison of electromagnetic and piezoelectric vibration energy harvesters:Model and experiments[J]. Sensors and Actuators A:Physical，2012，183:148-156.
[50] 刘丽兰，钟声，吴子英. 雨滴冲击下双稳态压电悬臂梁俘能装置动力学特性及试验研究[J]. 振动与冲击，2021，40(11):182-189. LIU Lilan，ZHONG Sheng，WU Ziying. Dynamic characteristics study and tests of bistable piezoelectric cantilever beam energy harvester under raindrop impact[J]. Journal of Vibration and Shock，2021，40(11):182-189.
[51] 阚君武，唐可洪，王淑云，等. 压电悬臂梁发电装置的建模与仿真分析[J]. 光学精密工程，2008，16(1):71-75. KAN Junwu，TANG Kehong，WANG Shuyun，et al. Modeling and simulation of piezoelectric cantilever generators[J]. Optics and Precision Engineering，2008 16(1):71-75.
[52] ERTURK A，INMAN D J. An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations[J]. Smart Materials and Structures，2009，18(2):25009.
[53] 刘琪，李波，梅杰，等. 基于PVDF的压电悬臂梁非线性动力学分析[J]. 武汉理工大学学报，2021，43(6):69-75. LIU Qi，LI Bo，MEI Jie，et al. Nonlinear dynamic analysis of piezoelectric cantilever based on PVDF[J]. Journal of Wuhan University of Technology，2021，43(6):69-75.
[54] 马天兵，丁永静，杜菲，等. 变截面三角形压电振动能量收集器的特性研究[J]. 传感器与微系统，2021，40(6):27-29. MA Tianbing，DING Yongjing，DU Fei，et al. Study on characteristics of variable section triangle piezoelectric vibration energy harvester[J]. Transducer and Micro- system Technologies，2021，40(6):27-29.
[55] 赵娟，刘伟群，刘永斌，等. 压电等应变梁能量回收装置研究[J]. 压电与声光，2010，32(3):406-409. ZHAO Juan，LIU Weiqun，LIU Yongbin，et al. Research on uniform-strain piezoelectric energy harvesting mechanism[J]. Piezoelectrics & Acoustooptics，2010，32 (3):406-409.
[56] ARROYO E，JIA Y，DU S，et al. Experimental and theoretical study of a piezoelectric vibration energy harvester under high temperature[J]. Journal of Microelectromechanical Systems，2017，26(6):1216-1225.
[57] CHEN R，REN L，XIA H，et al. Energy harvesting performance of a dandelion-like multi-directional piezoelectric vibration energy harvester[J]. Sensors and Actuators A:Physical，2015，230:1-8.
[58] 亓有超，赵俊青，张弛. 微纳振动能量收集器研究现状与展望[J]. 机械工程学报，2020，56(13):1-15. QI Youchao，ZHAO Junqing，ZHANG Chi. Review and prospect of micro-nano vibration energy harvesters[J]. Journal of Mechanical Engineering，2020，56(13):1-15.
[59] 吴义鹏，季宏丽，裘进浩，等. 共振频率可调式非线性压电振动能量收集器[J]. 振动与冲击，2017，5:12-16. WU Yipeng，JI Hongli，QIU Jinhao，et al. A nonlinear piezoelectric vibration energy harvesting device with tunable resonance frequencies[J]. Journal of Vibration and Shock，2017，5:12-16.
[60] LI H，DAI F，DU S. Broadband energy harvesting by exploiting nonlinear oscillations around the second vibration mode of a rectangular piezoelectric bistable laminate[J]. Smart Materials and Structures，2015，24(4):45024.
[61] LI H，LI A. Potential of a vibro-impact nonlinear energy sink for energy harvesting[J]. Mechanical Systems and Signal Processing，2021，159:107827.
[62] WU X，LIN J，KATO S，et al. A frequency adjustable vibration energy harvester[C]//Proceedings of PowerMEMS，2008:245-248.
[63] TANG L，YANG Y，SOH C. Improving functionality of vibration energy harvesters using magnets[J]. Journal of Intelligent Material Systems and Structures，2012，23(13):1433-1449.
[64] PILLATSCH P，MILLER L M，HALVORSEN E，et al. Self-tuning behavior of a clamped-clamped beam with sliding proof mass for broadband energy harvesting[C]//Journal of Physics:Conference Series. IOP Publishing，2013，476(1):012068.
[65] LAN C，CHEN Z，HU G，et al. Achieve frequency-self-tracking energy harvesting using a passively adaptive cantilever beam[J]. Mechanical Systems and Signal Processing，2021，156:107672.
[66] CHENG Y，WU N，WANG Q. An efficient piezoelectric energy harvester with frequency self-tuning[J]. Journal of Sound and Vibration，2017，396:69-82.
[67] LALLART M，ANTON S R，INMAN D J. Frequency self-tuning scheme for broadband vibration energy harvesting[J]. Journal of Intelligent Material Systems and Structures，2010，21(9):897-906.
[68] SHAHRUZ S M. Design of mechanical band-pass filters for energy scavenging[J]. Journal of sound and vibration，2006，292(3-5):987-998.
[69] ZHU D，TUDOR M J，BEEBY S P. Strategies for increasing the operating frequency range of vibration energy harvesters:A review[J]. Measurement Science and Technology，2010，21(2):22001.
[70] CHEN L，XUE J，PAN S，et al. Study on cantilever piezoelectric energy harvester with tunable function[J]. Smart Materials and Structures，2020，29(7):75001.
[71] YUAN Z，LIU W，ZHANG S，et al. Bandwidth broadening through stiffness merging using the nonlinear cantilever generator[J]. Mechanical Systems and Signal Processing，2019，132:1-17.
[72] HUANG H，YUAN Z，LIU W. Design strategy for optimizing the bandwidth of the hardening vibration generator with customized response[J]. Sensors and Actuators A:Physical，2021，332:113197.
[73] WU H，TANG L，YANG Y，et al. Development of a broadband nonlinear two-degree-of-freedom piezoelectric energy harvester[J]. Journal of Intelligent Material Systems and Structures，2014，25(14):1875-1889.
[74] DECHANT E，FEDULOV F，FETISOV L，et al. Bandwidth widening of piezoelectric cantilever beam arrays by mass-tip tuning for low-frequency vibration energy harvesting[J]. Applied Sciences，2017，7(12):1324.
[75] UPADRASHTA D，YANG Y. Trident-shaped multimodal piezoelectric energy harvester[J]. Journal of Aerospace Engineering，2018，5(31):4018070.
[76] TOYABUR R M，SALAUDDIN M，PARK J Y. Design and experiment of piezoelectric multimodal energy harvester for low frequency vibration[J]. Ceramics International，2017，43:675-681.
[77] YANG L，ZHANG H. A wide-band piezoelectric energy harvester with adjustable frequency through rotating the angle of the jointed beam[J]. Ferroelectrics，2017，520(1):237-244.
[78] ZHAO N，YANG J，YU Q，et al. Three-dimensional piezoelectric vibration energy harvester using spiral-shaped beam with triple operating frequencies[J]. Review of Scientific Instruments，2016，87(1):15003.
[79] WEI X，ZHAO H，YU J，et al. A Tower-shaped three-dimensional piezoelectric energy harvester for low-level and low-frequency vibration[J]. International Journal of Precision Engineering and Manufacturing-Green Technology，2021，8(5):1537-1550.
[80] DENG H，DU Y，WANG Z，et al. A multimodal and multidirectional vibrational energy harvester using a double-branched beam[J]. Applied Physics Letters，2018，112(21):213901.
[81] 杨涛，周生喜，曹庆杰，等. 非线性振动能量俘获技术的若干进展[J]. 力学学报，2021，53(11):2895-2909. YANG Tao，ZHOU Shengxi，CAO Qingjie，et al. Some advances in nonlinear vibration energy harvesting technology[J]. Chinese Journal of Theoretical and Applied Mechanics，2021，53(11):2895- 2909.
[82] MEI X，ZHOU S，YANG Z，et al. Enhancing energy harvesting in low-frequency rotational motion by a quad-stable energy harvester with time-varying potential wells[J]. Mechanical Systems and Signal Processing，2021，148:107167.
[83] LU Z，SHAO D，FANG Z，et al. Integrated vibration isolation and energy harvesting via a bistable piezo-composite plate[J]. Journal of Vibration and Control，2020，26(9-10):779-789.
[84] YAN Z，SUN W，HAJJ M R，et al. Ultra-broadband piezoelectric energy harvesting via bistable multi-hardening and multi-softening[J]. Nonlinear Dynamics，2020，100(2):1057-1077.
[85] CHEN Y，CHEN L，XU X，et al. Chaotic motion in a nonlinear car model excited by multi-frequency road surface profile[J]. Chinese Journal of Mechanical Engineering，2017，30(3):689-697.
[86] LI X，KEFU L. Development and validation of a piecewise linear nonlinear energy sink for vibration suppression and energy harvesting[J]. Journal of Sound and Vibration，2021，503:116104.
[87] FAN K，TAN Q，ZHANG Y，et al. A monostable piezoelectric energy harvester for broadband low-level excitations[J]. Applied Physics Letters，2018，112(12):123901.
[88] LAN C，LIAO Y，HU G，et al. Equivalent impedance and power analysis of monostable piezoelectric energy harvesters[J]. Journal of Intelligent Material Systems and Structures，2020，31(14):1697-1715.
[89] ZHAO D，WANG X，CHENG Y，et al. Analysis of single-degree-of-freedom piezoelectric energy harvester with stopper by incremental harmonic balance method[J]. Materials Research Express，2018，5(5):55502.
[90] HARNE R L，WANG K. A review of the recent research on vibration energy harvesting via bistable systems[J]. Smart Materials and Structures，2013，22:023001.
[91] FAN Y，GHAYESH M H，LU T. A broadband magnetically coupled bistable energy harvester via parametric excitation[J]. Energy Conversion and Management，2021，244:114505.
[92] REZAEI M，TALEBITOOTI R，LIAO W. Exploiting bi-stable magneto-piezoelastic absorber for simultaneous energy harvesting and vibration mitigation[J]. International Journal of Mechanical Sciences，2021，207:106618.
[93] ANDÒ B，BAGLIO S，BULSARA A R，et al. A bistable buckled beam based approach for vibrational energy harvesting[J]. Sensors and Actuators A:Physical，2014，211:153-161.
[94] MASANA R，DAQAQ M F. Relative performance of a vibratory energy harvester in mono- and bi-stable potentials[J]. Journal of Sound and Vibration，2011，330(24):6036-6052.
[95] YANG T，CAO Q. Time delay improves beneficial performance of a novel hybrid energy harvester[J]. Nonlinear Dynamics，2019，96(2):1511-1530.
[96] JIANG W，CHEN L. Snap-through piezoelectric energy harvesting[J]. Journal of Sound and Vibration，2014，333(18):4314-4325.
[97] 芮小博，李一博，曾周末. 压电悬臂梁振动能量收集器研究进展[J]. 振动与冲击，2020，39(17):112-123. RUI Xiaobo，LI Yibo，ZENG Zhoumo. Research progress of piezoelectric cantilever vibration energy collector[J]. Journal of Sound and Vibration，2020，39(17):112-123.
[98] LI H，QIN W，LAN C，et al. Dynamics and coherence resonance of tri-stable energy harvesting system[J]. Smart materials and structures，2015，25(1):15001.
[99] WANG G，ZHAO Z，LIAO W，et al. Characteristics of a tri-stable piezoelectric vibration energy harvester by considering geometric nonlinearity and gravitation effects[J]. Mechanical Systems and Signal Processing，2020，138:106571.
[100] LENG Y，TAN D，LIU J，et al. Magnetic force analysis and performance of a tri-stable piezoelectric energy harvester under random excitation[J]. Journal of Sound and Vibration，2017，406:146-160.
[101] ZHOU Z，QIN W，ZHU P. A broadband quad-stable energy harvester and its advantages over bi-stable harvester:Simulation and experiment verification[J]. Mechanical Systems and Signal Processing，2017，84:158-168.
[102] YUAN Z，LIU W，YE M. A mapping method of dynamic response and stiffness characteristics for realizing a customized nonlinear oscillator[J]. Nonlinear Dynamics，2020，102(4):2531-2548.
[103] CHANDRASEKHAR A，VIVEKANANTHAN V. A fully packed spheroidal hybrid generator for water wave energy harvesting and self-powered position tracking[J]. Nano Energy，2020，69:104439.
[104] LAI Z，WANG S，ZHU L，et al. A hybrid piezo-dielectric wind energy harvester for high-performance vortex-induced vibration energy harvesting[J]. Mechanical Systems and Signal Processing，2021，150:107212.
[105] CAI M，YANG Z，CAO J，et al. Recent Advances in Human Motion Excited Energy Harvesting Systems for Wearables[J]. Energy Technology，2020，8(10):2000533.
[106] HUANG M，HOU C，LI Y，et al. A Low-frequency MEMS piezoelectric energy harvesting system based on frequency up-conversion mechanism[J]. Micromachines，2019，10(10):639.
[107] POZZI M，ZHU M. Advances in energy harvesting methods[M]. New York:Springer，2013.
[108] ZOU H，ZHANG W，LI W，et al. Magnetically coupled flextensional transducer for wideband vibration energy harvesting:Design，modeling and experiments[J]. Journal of Sound and Vibration，2018，416:55-79.
[109] HAN D，YUN K. Piezoelectric energy harvester using mechanical frequency up conversion for operation at low-level accelerations and low-frequency vibration[J]. Microsystem Technologies，2015，21(8):1669-1676.
[110] WU Y，QIU J，ZHOU S，et al. A piezoelectric spring pendulum oscillator used for multi-directional and ultra-low frequency vibration energy harvesting[J]. Applied Energy，2018，231:600-614.
[111] WU Y，LI S，FAN K，et al. Investigation of an ultra-low frequency piezoelectric energy harvester with high frequency up-conversion factor caused by internal resonance mechanism[J]. Mechanical Systems and Signal Processing，2022，162:108038.
[112] LIU H，LEE C，KOBAYASHI T，et al. Investigation of a MEMS piezoelectric energy harvester system with a frequency-widened-bandwidth mechanism introduced by mechanical stoppers[J]. Smart materials and structures，2012，21(3):35005.
[113] HALIM M A，PARK J Y. Theoretical modeling and analysis of mechanical impact driven and frequency up-converted piezoelectric energy harvester for low-frequency and wide-bandwidth operation[J]. Sensors and Actuators A:Physical，2014，208:56-65.
[114] KATHPALIA B，TAN D，STERN I，et al. An experimentally validated model for geometrically nonlinear plucking-based frequency up-conversion in energy harvesting[J]. Smart Materials and Structures，2018，27(1):15024.
[115] FU X，LIAO W. Modeling and analysis of piezoelectric energy harvesting with dynamic plucking mechanism[J]. Journal of Vibration and Acoustics，2019，141(3):031002.
[116] TRAN N，GHAYESH M H，ARJOMANDI M. Ambient vibration energy harvesters:A review on nonlinear techniques for performance enhancement[J]. International Journal of Engineering Science，2018，127:162-185.
[117] FAN K，LIU S，LIU H，et al. Scavenging energy from ultra-low frequency mechanical excitations through a bi-directional hybrid energy harvester[J]. Applied Energy，2018，216:8-20.
[118] KUANG Y，YANG Z，ZHU M. Design and characterization of a piezoelectric knee-joint energy harvester with frequency up-conversion through magnetic plucking[J]. Smart materials and structures，2016，25(8):85029.
[119] XUE T，ROUNDY S. On magnetic plucking configurations for frequency up-converting mechanical energy harvesters[J]. Sensors and Actuators A:Physical，2017，253:101-111.
[120] XIE Z，KITIO KWUIMY C A，WANG Z，et al. A piezoelectric energy harvester for broadband rotational excitation using buckled beam[J]. AIP Advances，2018，8(1):15125.
[121] SPECIALE A，ARDITO R，BAÙ M，et al. Snap-through buckling mechanism for frequency up-conversion in piezoelectric energy harvesting[J]. Applied Sciences，2020，10(10):3614.
[122] CAO D X，LEADENHAM S，ERTURK A. Internal resonance for nonlinear vibration energy harvesting[J]. The European Physical Journal Special Topics，2015，224(14):2867-2880.
[123] WU Y，JI H，QIU J，et al. A 2-degree-of-freedom cubic nonlinear piezoelectric harvester intended for practical low-frequency vibration[J]. Sensors and Actuators A:Physical，2017，264:1-10.
[124] 黄玲璐，毛晓晔，丁虎，等. 内共振作用下轴向运动黏弹性梁横向受迫振动[J]. 振动与冲击，2017，36 (17):69-73. HUANG Linglu，MAO Xiaoye，DING Hu，et al. Transverse non-linear forced vibration of an axially moving viscoelastic beam with an internal resonance[J]. Journal of Sound and Vibration，2017，36(17):69-73.
[125] 冯志华，胡海岩. 直线运动柔性梁非线性动力学直线运动柔性梁非线性动力学——组合参数共振与内共振联合激励[J]. 振动工程学报，2004，17(3):253-257. Feng Zhihua，Hu Haiyan. Nonlinear dynamics of flexible beams undergoing a large linear motion of basement:Combinational parametric and Internal resonances[J]. Journal of Vibration Engineering，2004，17(3):253-257.
[126] WU Y，QIU J，KOJIMA F，et al. Design methodology of a frequency up- converting energy harvester based on dual-cantilever and pendulum structures[J]. AIP Advances，2019(9):045312.
[127] WU Y，JI H，QIU J，et al. An internal resonance based frequency up-converting energy harvester[J]. Journal of Intelligent Material Systems and Structures，2018，29(13):2766-2781.
[128] KAN B，YUE W，XUEWEN H，et al. Equivalent stiffness of metal clip-like piezoelectric spring structure[J]. Transactions of Nanjing University of Aeronautics and Astronautics，2020，6(37):963-970.
[129] XU J，TANG J. Modeling and analysis of piezoelectric cantilever-pendulum system for multi-directional energy harvesting[J]. Journal of Intelligent Material Systems and Structures，2017，28(3):323-338.