Analysis of longitudinal and torsional resonance vibrations of a piezoelectrically excited bar by introducing piezoelectric loss coefficients

Abstract

In this study, a method to develop a resonance vibration model of a piezo-bar with slanted ceramics is presented by considering piezoelectric loss coefficients. The vibration model reported here predicts natural frequencies and mode shapes for longitudinal and torsional modes. Analytical results for the longitudinal and torsional vibration displacements were formulated as a function of material and geometric properties. Parametrical analysis of the resonance vibration modes and the explicit solution of the vibration displacement provide a tool for improving the design and developing control schemes for devices such as ultrasonic motors that utilize this structure. Model calculations were compared with ATILA™ finite element analysis simulations and good agreements were found. The model and the formulas to find the resonance frequencies and to calculate the vibration displacement were verified for different design parameters. Although the model was developed for a slanted ceramic stator of a multimode ultrasonic motor, the method to develop the model can be utilized for other single-degree-of-freedom piezoelectric ceramic applications.

Keywords

piezoelectric loss modeling vibration resonance longitudinal torsional

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References

ATILA V6.0.0 Operational Manual (2007) Micromechatronics Inc. State College, PA, USA.

Banks

Inman

(1991) On damping mechanisms in beams. Journal of Applied Mechanics 58: 716–723.

Bendary

Elshafei

Riad

(2010) Finite element model of smart beams with distributed piezoelectric actuators. Journal of Intelligent Material Systems and Structures 21: 747–758.

Bondarenko

Karas

Ulitko

(1982) Methods for determining the vibrational dissipation characteristics of piezoceramic structural elements. International Applied Mechanics 18: 175–179.

Bonello

Rafique

(2011) Modeling and analysis of piezoelectric energy harvesting beams using the dynamic stiffness and analytical modal analysis methods. Journal of Vibration and Acoustics 133: 011009–011011.

Brissaud

(2010) Three-dimensional modeling of piezoelectric materials. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 57: 2051–2065.

Chang

Huang

Wang

(2010) Research on PZT bimorph microgripper system. Proceedings of the 8th World Congress on intelligent control and automation, Intelligent Control and Automation (WCICA), 2010 8th World Congress on, vol., no., pp.5498-5502, 7-9 July 2010, doi: 10.1109/WCICA.2010.555413210.1109/WCICA.2010.5554132.

Ebenezer

Ravichandran

Ramesh

(2005) Forced responses of solid axially polarized piezoelectric ceramic finite cylinders with internal losses. Journal of the Acoustical Society of America 117: 3645–3656.

Erturk

Inman

(2008) On mechanical modeling of cantilevered piezoelectric vibration energy harvesters. Journal of Intelligent Material Systems and Structures 19: 1311–1325.

10.

Ferreira

Agnus

Chaillet

. (2004) A smart microrobot on chip: Design, identification, and control. IEEE/ASME Transactions on Mechatronics 9: 508–519.

11.

Gaudenzi

(2009) Smart Structures: Physical Behaviour, Mathematical Modelling and Applications. John Wiley: Chippenham, Great Britain ISBN: 978-0-470-05982-1.

12.

Holland

(1967) Representation of dielectric, elastic, and piezoelectric losses by complex coefficients. IEEE Transactions on Sonics and Ultrasonics 14: 18–20.

13.

IEEE (1978) IEEE Standard on Piezoelectricity: IEEE Std. 176-1978. New York: The Institute of Electrical and Electronics Engineers, Inc.

14.

Ikeda

(1996) Fundamental of Piezoelectricity. New York: Oxford University Press.

15.

(2011) Recent development of micromachined biosensors. IEEE Sensors Journal 11: 305–311.

16.

Liu

DKC

Friend

Leo

(2010) A brief review of actuation at the micro-scale using electrostatic, electromagnetic and piezoelectric ultrasonics. Acoustical Science and Technology 31: 115–123.

17.

Low

Guo

(1995) Modeling of a three-layer piezoelectric bimorph beam with hysteresis. Journal of Microelectromechanical Systems 4: 230–237.

18.

Maleki

Naeia

Hosseiniana

. (2011) Exact three-dimensional analysis for static torsion of piezoelectric rodsnext term. International Journal of Solids and Structures 48: 217–226.

19.

Park

Y-M

Kim

K-J

(2011) The dynamic modeling and design improvement of a piezoelectric exciter of a touch screen device for efficient tactile feedback. Smart Materials and Structures 20, doi:10.1088/0964-1726/20/5/05500810.1088/0964-1726/20/5/055008.

20.

Rakotondrabe

Haddab

Lutz

(2009) Quadrilateral modelling and robust control of a nonlinear piezoelectric cantilever. IEEE transactions on Control Systems Technology 17: 528–539.

21.

Rao

(2007) Vibration of Continuous Systems. Hoboken, NJ: John Wiley.

22.

Roy

(2009) Dimensional reduction of a piezoelectric composite rod. European Journal of Mechanics—A/Solids 28: 368–376.

23.

Tuncdemir

Ural

Koc

. (2011) Design of translation rotary ultrasonic motor with slanted ceramics. Japanese Journal of Applied Physics 50, doi: 10.1143/JJAP.50.02730110.1143/JJAP.50.027301.

24.

Uchino

Giniewicz

(2003) Micromechatronics. New York: CRC/Dekker.

25.

Watson

Friend

Yeo

(2009) Piezoelectric ultrasonic micro/milli-scale actuators. Sensors and Actuators A: Physical 152: 219–223.

26.

Zhuang

Ural

Rajapurkar

. (2009) Derivation of piezoelectric losses from admittance spectra. Japanese Journal of Applied Physics 48, doi: 10.1143/JJAP.48.04140110.1143/JJAP.48.041401.