Generalised solutions, discrete models and energy estimates for a 2D problem of coupled field theory

Applied Mathematics and Computation

Volumn 107, Issue 1, 2000, Pages 27-55

  Melnik, R V N ^a  

^a UNIVERSITY OF SOUTHERN QUEENSLAND   (Australia)

Author keywords

Discrete conservation laws for coupled systems; Electro mechanical interactions; Generalised solutions; Piezoelectrics

Indexed keywords

EID: 0002957297     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(98)10143-1     Document Type: Article

References (33)

1. E.E. Antonova, P.P. Silvester, Finite elements for piezoelectric vibrations with open electric boundaries, IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 44 (3) (1997) 548-556.
2. A. Ballato, Piezoelectricity: Old effect, new thrusts, IEEE Trans. Ultrason., Ferroelect. 42 (5) (1995) 916.
3. D.A. Berlincourt, D.R. Curran, H. Jaffe, Piezoelectric and piezomagnetic materials and their function in transducers, in: W.P. Mason (Ed.), Physical Acoustics, vol. 1A, Academic Press, New York and London, 1964, pp. 204-236.
4. L.F. Brown, Ferroelectric polymers: Current and future ultrasonic applications, Proceedings of the IEEE Ultrasonic Symposium, 1992, pp. 539-550.
5. G.R. Buchanan, J. Peddieson Jr., Vibration of infinite piezoelectric cylinders with anisotropic properties using cylindrical finite elements, IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 38 (3) (1991) 291-301.
6. R.C. Buchanan (Ed.), Ceramic Materials for Electronics: Processing, Properties, and Applications, Marcel Dekker, New York, 1991.
7. Long-Qing Chen et al. (Eds.), Mathematics of Microstructure Evolution, Proceedings in Applied Mathematics, vol. 90, SIAM and MMMS, Philadelphia, 1996.
8. E. Dieulesaint, D. Royer, Elastic Waves in Solids: Applications to Signal Processing, Wiley, Chichester, New York, 1980.
9. J.T. Fielding et al., Characterization of PZT hollow-sphere transducers, Proceedings of the IX IEEE International Symposium on Applications of Ferroelectrics, 1994, pp. 202-205.
10. E. Fukada, Poiseuille medal award lecture: Piezoelectricity of biopolymers, Biorheology 32 (1995) 1995.
11. S.K. Godunov, Equations of Mathematical Physics, Nauka, Moscow, 1980.
12. T.R. Gururaja, Piezoelectric transducers for medical ultrasonic imaging, American Ceramic Society Bulletin 73 (5) (1994) 50-55.
13. T. Ikeda, Fundamentals of Piezoelectricity, Oxford University Press, Oxford, 1990.
14. Y. Kagawa, T. Tsuchiya, T. Kawashima, Finite element simulation of piezoelectric vibrator gyroscopes, IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 43 (4) (1996) 120-509.
15. Y. Kawawa, T. Tsuchiya, G. Furukawa, Finite element simulation of dynamic responses of piezoelectric actuators, J. Sound and Vibration 191 (4) (1996) 519-528.
16. J.S. Lee, Boundary element method for electroelastic interaction in piezoceramics, Eng. Anal. with Boundary Elements 15 (4) (1995) 321-328.
17. R. Le Letty, F. Claeyssen, R. Bossut, Combined finite element-normal mode expansion methods in electroelasticity and their application to piezoactive motors, Int. J. Numer. Methods Eng. 40 (18) (1997) 3385-3395.
18. R. Lerch, Simulation of piezoelectric devices by two- and three-dimensional finite elements, IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 37 (3) (1990) 233-243.
19. P. Lu, O. Mahrenholtz, A variational boundary element formulation for piezoelectricity, Mech. Res. Commun. 21 (6) (1994) 605-615.
20. R.V.N. Melnik, Existence and uniqueness theorems of the generalised solutions for a class of non-stationary problems of coupled electroelasticity, S. Mathematics (Iz. VUZ), Allerton Press 35 (4) (1991) 24-32.
21. R.V.N. Melnik, M.N. Moskalkov, Difference schemes for and analysis of approximate solutions of two-dimensional nonstationary problems in coupled electroelasticity, Differential Equations 27 (7) (1991) 1220-1230 (from Plenum Publishing Corporation/Consultants Bureau, New York, 1992, pp. 860-867).
22. R.V.N. Melnik, The stability condition and energy estimate for non-stationary problems of coupled electroelasticity, Math, and Mech. of Solids 2 (2) (1997) 153-180.
23. R.V.N. Melnik, Intelligent structures and coupling in mathematical models: examples from dynamic electroelasticity, Proceedings of the IEEE ICPADM '97, Seoul, Korea, 1997, Vol. 2, 995-998.
24. R.V.N. Melnik, Convergence of the operator-difference scheme to generalized solutions of a coupled field theory problem, Journal of Difference Equations and Applications, to be published.
25. M.N. Moskalkov, Investigation of a difference scheme for the solution of the sound radiator problem for cylindric piezovibrators, Differential Equations 22 (7) (1986) 1220-1226.
26. W. Nowacki, Electromagnetic Effects in Solids, Mir Publishers, Moscow, 1986.
27. C.Z. Rosen, B.V. Hiremath, R. Newnham (Eds.), Piezoelectricity, N.Y. American Institute of Physics, 1992.
28. A.A. Samarskii, Theorie der Differenzenverfahren, (Series: Mathematik und ihre Anwendungen in Physik und Technik), Aufl. Leipzig: Academische Verlagsgesellschaft Geest and Portig, 1984.
29. A.A. Samarskii, E.S. Nikolaev, Numerical Methods for Grid Equations, Birkhauser, Basel, 1989.
30. M. Shashkov, S. Steinberg, Conservative Finite Difference Methods on General Grids, CRC Press, Boca Raton, 1995.
31. S. Takahashi, Ferroelectric Ceramics, in: N. Setter, E.L. Colla (Eds.), Birkhauser, Basel, 1993, pp. 349-362.
32. V.A. Trenogin, Functional Analysis, Nauka, Moscow, 1993.
33. A.O. Vatulyan, V.L. Kublikov, Boundary element method in electroelasticity, Boundary Elements Commun. 6 (2) (1995) 59-61.