[1] [1] NG T H,LIAO W H, Sensitivity analysis and energy harvesting for a self-powered piezoelectric sensor[J]. Journal of Intelligent Material Systems and Structures,2005,16(10):785-797,

[2] [2] WANG L,REN B Y,TZOU H S,et al, Distributed sensor signal analysis of double-curvature piezoelectric laminated thin shell based on finite difference［C］// Xiamen,China: proceedings of the 2010 Symposium on Piezoelectricity,Acoustic Waves and Device Applications (SPAWDA),2010,

[3] [3] LI H,ZHANG X F,TZOU H S, Diagonal piezoelectric sensors on cylindrical shells[J]. Journal of Sound and Vibration,2017,400(Suppl, C):201-212,

[4] [4] JIAO P C,EGBE K J I,XIE Y W,et al, Piezoelectric sensing techniques in structural health monitoring:A state-of-the-art review[J]. Sensors,2020,20(13):3730-3750,

[9] [9] WANG Bo,GU Yijia,ZHANG Shujun,et al, Flexoelectricity in solids:Progress,challenges,and perspectives [J]. Progress in Materials Science,2019:100570,

[10] [10] ZENG S,WANG B L,WANG K F, Analyses of natural frequency and electromechanical behavior of flexoelectric cylindrical nanoshells under modified couple stress theory [J]. Journal of Vibration and Control,2019,25(3):559-570,

[11] [11] SU Yaxuan,LIN Xiaohui,HUANG Rui,et al, Analytical electromechanical modeling of nanoscale flexoelectric energy harvesting [J]. Applied Sciences Basel,2019,9(11):2273,

[12] [12] DAEHEE S,SUNGHO K,CHADOL O,et al, Flexoelectric healing of intrinsically more conductive nanochannels in NdNiO3 thin films[J]. Applied Surface Science,2019,497:143727,

[13] [13] HUANG W B,YANG S R,ZHANG N Y,et al, Cracks monitoring and characterization using Ba0, 64Sr0, 36TiO3 flexoelectric strain gradient sensors[J]. Sensors and Smart Structures Technologies for Civil,Mechanical,and Aerospace Systems 2014:906119,

[14] [14] HUANG W B,YANG S R,ZHANG N Y,et al, Direct measurement of opening mode stress intensity factors using flexoelectric strain gradient sensors[J]. Experimental Mechanics,2015,55(2):313-320,

[15] [15] HU S D,LI H,TZOU H S, Distributed flexoelectric structural sensing:Theory and experiment[J]. Journal of Sound and Vibration,2015,348:126-136,

[16] [16] TZOU H, Piezoelectric shells:Sensing,energy harvesting,and distributed control[M]. 2nd ed, Germany:Springer,2019,

[18] [18] SOEDEL W, Vibrations of shells and plates[M]. New York:Marcel Dekker,Inc,1993,