Document Type : Original Article


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


Ultrasonic transducers have found new applications such as ultrasonic assisted micromachining, micro forming, surface treatment, welding, etc. Apart from the transducer’s shape and size, the resonant frequencies and amplitude are seriously affected by materials properties used for transducer components. A further problem with the material is that their properties may vary from batch to batch and may also depend on the size of the raw stock. In this work using modal analysis, the material properties are calculated based on the frequency response method, which is more accurate than the nominal one. The finite element modelling was employed for both 2D and 3D FEM analysis to observe the behaviour of the cylindrical test rods and two sandwich-type piezoelectric transducers with the nominal frequency of 20 kHz and 30 kHz to find the validity of these properties. The obtained results showed that the modal analysis method could accurately determine the bar speed, Poisson's ratio and elastic modulus of the ultrasonic transducer components. The accuracy of this method increases by considering more vibration mode. Based on the results, obtained errors for FEM modelling of two ultrasonic transducers with the frequency of 20 kHz and 30 kHz are 0.15% and 0.33%, respectively.


Main Subjects

[1]    Frederick, R., Ultrasonic Engineering, John Wiley and Sons, New York, USA, 1965.
[2]    Kumar, S., Wu, C. S., Padhy, G. K., and Ding, W., Application of Ultrasonic Vibrations in Welding and Metal Processing: A Status Review, Journal of Manufacturing Processes, Vol. 26, 2017, pp. 295-322.
[3]    Langevin, P., French Patent, Application No. FR575435D filed 27, December 1923.
[4]    Mason, W. P., Electromechanical Transducers and Wave Filters, Van Nostrand, New York, USA, 1942.
[5]    Krimholtz, R., Leedom, D. A., and Mattaei, G. L., New Equivalent Circuits for Elementary Piezoelectric Transducer, Electron, Vol. 6, 1970, pp. 398–399.
[6]    Redwood, M., Experiments With the Electrical Analog of a Piezoelectric Transducer, Journal of the Acoustical Society of America, Vol. 36, No. 1, 1964, pp. 1872–1880.
[7]    Al-Budairi, H., Lucas, M., and Harkness, P., A Design Approach for Longitudinal–Torsional Ultrasonic Transducers, Sensors and Actuators A: Physical, Vol. 198, 2013, pp. 99-106.
[8]    Kagawa, Y., Yamabuchi, T., Finite Element Simulation of a Composite Piezoelectric Ultrasonic Transducer, IEEE Transactions on Sonics and Ultrasonics, Vol. 26, No. 2, 1979, pp. 81 – 87.
[9]    Jian, S. W., Dale, F. O., A Finite Element-Electric Circuit Coupled Simulation Method for Piezoelectric Transducer, IEEE Ultrasonics Symposium, Caesars Tahoe, NV, USA, 1999, pp. 1105 – 1108.
[10] Cunningham, P. M., Use of the Finite Element Method in Ultrasonic Applications, Ultrasonic Industry Association Symposium, Ohio, USA, 2000.
[11] Kocbach, J., Finite Element Modeling of Ultrasonic Piezoelectric Transducers- Influence of Geometry and Material Parameters on Vibration, Response Functions and Radiated Field, Ph.D. dissertation, Department of Physics, University of Bergen, Bergen, 2000.
[12] Moreno, E., Acevedo, P.,. Fuentes, M., Sotomayor, A. Borroto, L., Villafuerte, M. E., and Leija, L., Design and Construction of a Bolt-Clamped Langevin Transducer, 2nd International Conference on Electrical and Electronics Engineering, Mexico City, Mexico, 2005, pp. 393 – 395.
[13] A. I. Fernando, M. Pappalardo, and J. Gallego, Finite Element Three-Dimensional Analysis of the Vibrational Behavior of the Langevin-Type Transducer, Ultrasonics, Vol. 40, 2002, pp. 513-517.
[14] Abdullah, A., Pak, A., Correct Prediction of the Vibration Behavior of a High Power Ultrasonic Transducer by FEM Simulation, The International Journal of Advanced Manufacturing Technology, Vol. 39, 2008, pp. 21–28.
[15] 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.
[16] Culp., D. R., Ultrasonic Resonator Design Using Finite Element Analysis, Available, 2002:, [2002].
[17] Lundberg, B., Blanc, R. H., Determination of Mechanical Material Properties From the Two-Point Response of an Impacted Linearly Viscoelastic Rod Specimen, Journal of Sound and Vibration, Vol. 126, No. 1, 1988, pp. 97-108.
[18] Hillstrom, L., Mossberg, M., and Lundberg, B., Identification of Complex Modulus From Measured Strains on an Axially Impacted Bar Using Least Squares., Journal of Sound and Vibration, Vol. 230, No. 3, 2000, pp. 689-707.
[19] Mousavi, S., Nicolas, D. F., and Lundberg, B., Identification of Complex Moduli and Poisson's ratio From Measured Strains on an Impacted Bar, Journal of Sound and Vibration, Vol. 277, No. 4–5, 2004, pp. 971-986.
[20] Mousavi, S., Hillström, L., and Lundberg, B., Identification of Complex Shear Modulus From Measured Shear Strains on a Circular Disc Subjected to Transient Torsion at Its Centre, Journal of Sound and Vibration, Vol. 313, No. 3-5, 2008, pp. 567-580.
[21] Graff, K. F., Wave Motion in Elastic Solids, London, UK, Oxford University Press, 1975.
[22] Hen, S., Resonant Frequency Method for the Measurement and Uncertainty Analysis of Acoustic and Elastic Properties, Ultrasonics, Vol. 38, 2000, pp. 206–221.
[23] TAMURA Co., Piezoelectric Ceramics for High Power Applications Data Sheet, Available:, 2017.