Numerical methods for modal analysis of stepped piezoelectric beams

Journal of Sound and Vibration

Volumn 298, Issue 4-5, 2006, Pages 918-933

  Maurini, C ^a   Porfiri, M ^b   Pouget, J ^a  

^a SORBONNE UNIVERSITÉ   (France)

^b POLYTECHNIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; NUMERICAL METHODS; PROBLEM SOLVING;

BEAM THEORY; DISCRETIZATION; INFINITE DIMENSIONAL SYSTEM; PIEZOELECTRIC BEAMS;

PIEZOELECTRIC DEVICES;

EID: 33748766081     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2006.05.041     Document Type: Article

References (33)

1. Chopra I. Review of state of art of smart structures and integrated systems. AIAA Journal 40 (2002) 2145-2187
2. Crawley E.F., and de Luis J. Use of piezoelectric actuators as elements of intelligent structures. AIAA Journal 25 (1987) 1373-1385
3. Hagood N.W., and von Flotow A. Damping of structural vibrations with piezoelectric materials and passive electrical networks. Journal of Sound and Vibration 146 (1991) 243-268
4. dell'Isola F., Maurini C., and Porfiri M. Passive damping of beam vibrations through distributed electric networks and piezoelectric transducers: prototype design and experimental validation. Smart Materials and Structures 13 (2004) 299-308
5. Zhou K., Doyle J., and Glover K. Robust and Optimal Control (1996), Prentice-Hall, New Jersey
6. Kagawa Y., and Gladwell G.L.M. Finite element analysis of flexure-type vibrators with electrostrictive transducers. IEEE Transactions on Sonics and Ultrasonics 17 (1970) 41-49
7. Kusculuoglu Z.K., Fallahi B., and Royston T.J. Finite element model of a beam with a piezoceramic patch actuator. Journal of Sound and Vibration 276 (2004) 27-44
8. Lin C.C., and Huang H.N. Vibration control of beam-plates with bonded piezoelectric sensor and actuators. Computers and Structures 73 (1999) 239-248
9. Park C.H. Dynamics modelling of beams with shunted piezoelectric elements. Journal of Sound and Vibration 268 (2003) 115-129
10. Yang S.M., and Lee Y.J. Modal analysis of stepped beams with piezoelectric materials. Journal of Sound and Vibration 176 (1994) 289-300
11. Yang S.M., and Lee Y.J. Interaction of structure vibration and piezoelectric actuation. Smart Materials and Structures 3 (1994) 494-500
12. Maxwell N.D., and Asokanthan S.F. Modal characteristics of a flexible beam with multiple distributed actuators. Journal of Sound and Vibration 269 (2004) 19-31
13. Lee U., Kim J., Shin J., and Leung A.Y.T. Development of a Wittrick-Williams algorithm for the spectral element model of elastic-piezoelectric two-layer active beams. International Journal of Mechanical Sciences 44 (2002) 305-318
14. Wittrick W.H., and Williams F.W. An automatic computational procedure for calculating natural frequencies of skeletal structures. International Journal of Mechanical Sciences 12 (1970) 781-791
15. Wittrick W.H., and Williams F.W. A general algorithm for computing natural frequencies of elastic structures. Quarterly Journal of Mechanics and Applied Mathematics 24 (1971) 263-284
16. Zhaohui Q., Kennedy D., and Williams F.W. An accurate method for transcendental eigenproblems with a new criterion for eigenfrequencies. International Journal of Solids and Structures 41 (2004) 3225-3242
17. Batra R.C., Porfiri M., and Spinello D. Treatment of material discontinuity in two Meshless Local Petrov-Galerkin (MLPG) formulations of axisymmetric transient heat conduction. International Journal for Numerical Methods in Engineering 61 (2004) 2461-2479
18. R.C. Batra, M. Porfiri, D. Spinello, Free and forced vibrations of a segmented bar by a meshless local Petrov-Galerkin MPLG formulation, Computational Mechanics, in press, DOI:10.007/s00466-006-00496-6.
19. Zhang N., and Kirpitchenko I. Modelling the dynamics of a continuous structure with a piezoelectric sensor/actuator for passive structural control. Journal of Sound and Vibration 249 (2002) 251-261
20. Saravanos D.A., and Heyliger P.R. Mechanics and computational models for laminated piezoelectric beams, plates, and shells. Applied Mechanics Review 52 (1996) 305-320
21. Gopinathan S.V., Varadan V.V., and Varadan V.K. A review and critique of theories for piezoelectric laminates. Smart Materials and Structures 9 (2000) 24-48
22. Maurini C., Pouget J., and dell'Isola F. On a model of layered piezoelectric beams including transverse stress effect. International Journal of Solids and Structures 41 (2004) 4473-4502
23. Maurini C., Pouget J., and dell'Isola F. Extension of the Euler-Bernoulli model of piezoelectric laminates to include 3D effects via a mixed approach. Computers and Structures 84 (2006) 1438-1458
24. Sze K.Y., Yang X.M., and Fan H. Electric assumptions for piezoelectric laminate analysis. International Journal of Solids and Structures 41 (2004) 2363-2382
25. Beckert W., and Pfundtner G. Analysis of the deformational behaviour of a bimorph configuration with piezoelectric actuation. Smart Materials and Structures 11 (2002) 599-609
26. Maurini C., dell'Isola F., and Del Vescovo D. Comparison of piezoelectronic networks acting as distributed vibration absorbers. Mechanical Systems and Signal Processing 18 (2004) 1243-1271
27. Andreaus U., dell'Isola F., and Porfiri M. Piezoelectric passive distributed controllers for beam flexural vibrations. Journal of Vibration and Control 10 (2004) 625-659
28. Meirovitch L. Elements of Vibration Analysis (1986), McGraw-Hill, New York
29. Press W.H., Flannery B.P., Teukolsky S.A., and Vetterling W.T. Numerical Recipes in Fortran (1992), Cambridge University Press, Cambridge
30. Blevins R.D. Formulas for Natural Frequency and Mode Shape (1995), Krieger, Malabar
31. Alessandroni S., Andreaus U., dell'Isola F., and Porfiri M. Piezo-electromechanical (PEM) Kirchhoff-Love plates. European Journal of Mechanics-A/Solids 23 (2004) 689-702
32. Alessandroni S., Andreaus U., dell'Isola F., and Porfiri M. A passive electric controller for multimodal vibrations of thin plates. Computers and Structures 83 (2005) 1236-1250
33. ANSI/IEEE std 176-1987, IEEE Standard on Piezoelectricity, 1988.