Document Type : Original Article


Department of Mechanical Engineering, University of Bu-Ali Sina, Iran


In this paper, the effect of pre-stress condition on the resonance frequency of the transducer is studied by using numerical and analytical methods. To compare the obtained results, two sandwich-type transducers with nominal frequency of 25 kHz and 30 kHz are considered. Experimental determination of pre-stress value in transducer is described and measured. Then resonance frequency of transducers in the presence of pre-stress is determined by impedance analyser. Numerical analysis is conducted by modelling three-dimensional transducer in details at ABAQUS software. The resonance frequency is determined with and without pre-stress. The FE results show that by applying pre-stress on the transducers, the resonance frequency of transducers decreased. Furthermore, the FE results are very close to experimental results. Furthermore, a systematic analytical solution is presented based on one-dimensional wave propagation. The resultant displacement for each sub-section of the transducer is calculated and then all of them are assembled and solved by considering the continuity conditions of displacement and force components. It is found that pre-load condition that is produced by central bolt reduces resonance frequency of the transducer. The obtained analytical results provide fast and reliable model for predicting resonance frequency of transducer.


[1]     Abdullah, A., Pak, A., Abdullah, M. M., Shahidi, A., and Malaki, M., Study of the Behavior of Ultrasonic Piezo-Ceramic Actuators by Simulations, Electronic Materials Letters, Vol. 10, No. 1, 2014, pp. 37-42. doi:10.1007/s13391-013-3098-y.
[2]     Hoseini, S. M., Drilling of Engineering Ceramics Using Combination of Ultrasonic Vibrations and Diamond Slurry, Advance Design and Manufacturing Technology, Vol. 6, No. 2, 2013.
[3]     Sadegh Amalnik, M., Expert System Approach for Optimization of Design and Manufacturing Process for Rotary Ultrasonic Machining, Advance Design and Manufacturing Technology, Vol. 11, No. 1, 2018, pp. 1-13.
[4]     Amini, S., Nazari, F., Baraheni, and M., Ghasemi A. H., Investigating the Effect of Rotation Speed and Ultrasonic Vibrations in The Incremental Forming Process, Advance Design and Manufacturing Technology, Vol. 11, No. 4, 2018, pp. 91-97.
[5]     Abdi Behnagh, R., Esmaeilzadeh, P., and Agha Mohammad Pour, M., Simulation of Ultrasonic Welding of Al-Cu Dissimilar Metals for Battery Joining, Advance Design and Manufacturing Technology, Vol 13, No. 2, 2020.
[6]     Abdullah, A., Malaki, M., on The Damping of Ultrasonic Transducers’ Components, Aerospace Science and Technology, Vol. 28, No. 1, 2013, pp. 31-39. doi:10.1016/j.ast.2012.10.002.
[7]     Pak, A., Determination of Material Properties Components Used in Fem Modeling of Ultrasonic Piezoelectric Transducer, Advance Design and Manufacturing Technology, Vol. 12, No. 2, 2019, pp. 75-81.
[8]     Arnold, F. J, Mühlen, S. S., Resonance Frequencies on Mechanically Pre-Stressed Ultrasonic Piezotransducers, Ultrasonics, Vol. 39, No. 1, 2001, pp. 1-5. doi:10.1016/s0041-624x(00)00047-0
[9]     Arnold, F. J, Mühlen, S. S., The Influence of the Thickness of Non-Piezoelectric Pieces on Pre-Stressed Piezotransducers, Ultrasonics, Vol. 41, No. 3, 2003, pp. 191-196. doi:
[10]  Adachi, K., Takahashi, T., and Hasegawa, H., Analysis of Screw Pitch Effects on the Performance of Bolt-Clamped Langevin-Type Transducers, the Journal of the Acoustical Society of America, Vol. 116, No. 3, 2004, pp. 1544. doi:10.1121/1.1777852.
[11]  Deangelis, D. A., Schulze, G. W., and Wong, K. S., Optimizing Piezoelectric Stack Preload Bolts in Ultrasonic Transducers, Physics Procedia, Vol. 63, 2015, pp. 11-20. doi:10.1016/j.phpro.2015.03.003.
[12]  Meng, X., Lin, S., Analysis of a Cascaded Piezoelectric Ultrasonic Transducer with Three Sets of Piezoelectric Ceramic Stacks, Sensors (Switzerland), Vol. 19, No. 3, 2019. doi:10.3390/s19030580
[13]  Mančić, D. D., Radmanović, M. D., Design of Ultrasonic Transducers by Means of the Apparent Elasticity Method, Working and Living Environmental Protection, Vol. 2, No. 4, 2004, pp. 293-300.
[14]  Tolstoy, I., On Elastic Waves in Prestressed Solids, Journal of Geophysical Research: Solid Earth, Vol. 87, No. B8, 1982, pp. 6823-6827. doi:
[15]  Singh, I., Madan, D. K., and Gupta, M., Propagation of Elastic Waves in Prestressed Media, Journal of Applied Mathematics, 2010. doi:10.1155/2010/817680
[16]  Sobieszczyk, P., Majka, M., Kuźma, D., Lim, T. C., and Zieliński, P., Effect of Longitudinal Stress on Wave Propagation in Width-Constrained Elastic Plates with Arbitrary Poisson’s Ratio, Physica Status Solidi (B), Vol. 252, No. 7, 2015, pp. 1615-1619. doi:10.1002/pssb.201552256.
[17]  Birch, F., The Effect of Pressure Upon the Elastic Parameters of Isotropic Solids, According to Murnaghan’s Theory of Finite Strain, Journal of Applied Physics, Vol 9, No. 4, 1938, pp. 279-288. doi:10.1063/1.1710417
[18]  Kreyszig, E., Advanced Engineering Mathematics, John Wiley & Sons, 2010.
[19]  Abdullah, A., Shahini, M., and Pak, A., An Approach to Design a High Power Piezoelectric Ultrasonic Transducer, Journal of Electroceramics, Vol. 22, No. 4, 2009, pp. 369-382. doi:10.1007/s10832-007-9408-8.