[1] Wang Y，Lin B，Wang S，et al．Study on the system matching of ultrasonic vibration assisted grinding for hard and brittle materials processing[J]．International Journal of Machine Tools and Manufacture，2014，77：66-73．
[2] Gallego-Juárez J A, Graff K F. Power ultrasonics: applications of high-intensity ultrasound[M]．Amsterdam：Elsevier，2014．
[3] Campos-Pozuelo C，Vanhille C，Gallego-Juarez J A．Comparative study of the nonlinear behavior of fatigued and intact samples of metallic alloys[J]．IEEE transactions on ultrasonics, ferroelectrics, and frequency control，2006，53(1)： 175-184．
[4] Barone A，Gallego Juarez J A．Flexural Vibrating Free-Edge Plates with Stepped Thicknesses for Generating High Directional Ultrasonic Radiation[J]．The Journal of the Acoustical Society of America，1972，51(3B)：953-959．
[5] Gallego-Juarez J A．High-power ultrasonic processing: recent developments and prospective advances[J]．Physics Procedia，2010，3(1)：35-47．
[6] Gallego-Juárez J A，Rodriguez G，Acosta V，et al．Power ultrasonic transducers with extensive radiators for industrial processing[J]．Ultrasonics Sonochemistry，2010，17(6)：953-964．
[7] He X，Yao J，Zhang H，et al．Effects of excitation area of longitudinal transducer on the flexural vibration characteristics of a rectangular plate in stripe mode[J]．Ultrasonics，2015，58：104-110．
[8] Ning J，He X，Zhao G．Effects of driving frequency of longitudinal transducer on the vibration characteristics of a stepped plate[J]．Applied Acoustics，2014，79：164-168．
[9] Yamamoto M，Shiba H，Fujii T，et al．Tonpilz piezoelectric transducer with a bending piezoelectric disk on the radiation surface[J]．Japanese journal of applied physics，2003，42(5S)：3221-3224．
[10] Kim H，Roh Y．Design and fabrication of a wideband Tonpilz transducer with a void head mass[J]．Sensors and Actuators A: Physical，2016，239：137-143．
[11] Yongrae R，Hyunki K．Design and Fabrication of a Wideband Tonpilz Transducer with a Cavity-type Head Mass[C]// Pak- Kon Choi．Processing of Symposium on Ultrasonic Electronics．Tsukuba：Steering committee of symposium on ultrasonic electronics，2015．1P6-5-1-1P6-5-2．
[12] Lin S．Radiation impedance and equivalent circuit for piezoelectric ultrasonic composite transducers of vibrational mode-conversion[J]．IEEE transactions on ultrasonics, ferroelectrics, and frequency control，2012，59(1)：139-149．
[13] 王时英，吕明，轧刚．基于力耦合的非谐振单元组成的超声变幅器设计[J]．振动与冲击，2012，31(11)：104-107．
WANG Shiying, LV Ming, YA Gang. Design of an ultrasonic transducer with non-resonant units based on force coupling [J]. Journal of Vibration and Shock, 2012, 31(11): 104-107.
[14] 吕明，王时英，秦慧斌．非谐振设计理论与齿轮超声加工[M]．北京：科学出版社，2014．
LV Ming，WANG Shiying，QIN Huibin．Nonresonant Design Theory and Ultrasonic Gear Machining[M]．Beijing：Science Press，2014．
[15] Hosseini-Hashemi S，Bedroud M，Nazemnezhad R．An exact analytical solution for free vibration of functionally graded 
circular/annular Mindlin nanoplates via nonlocal elasticity[J]．Composite Structures，2013，103：108-118．
[16] Wang S，Lv M，Ya G，et al．Theoretical and Experimental Research on Design of Non-Resonant Gear Transformer[C]// Assimina Pelegri. Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition. Montreal：American Society of Mechanical Engineers，2014．
[17] 佘银柱．超声珩齿非谐振单元变幅器的设计理论与实验研究[D]．太原：太原理工大学，2012．
SHE Yinzhu．Theoretical and experimental research on transformer with non-resonance structure in ultrasonic gear honing[D]．Taiyuan：Taiyuan University of Technology，2012．