Mixed electroelastic waves and CFL stability conditions in computational piezoelectricity

Applied Numerical Mathematics

Volumn 48, Issue 1, 2004, Pages 41-62

  Melnik, R V N ^a   Zotsenko, K N ^b  

^a UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

^b Electronic Data Systems Australia   (Australia)

Author keywords

Coupled dynamics; Courant Friedrichs Lewy condition; Discrete conservation laws; Mixed electroelastic waves

Indexed keywords

ELASTICITY; ELECTRIC FIELDS; ELECTROSTATICS; MATHEMATICAL MODELS; PIEZOELECTRIC MATERIALS; SYSTEM STABILITY; THEOREM PROVING; VIBRATIONS (MECHANICAL);

COUPLED DYNAMICS; DISCRETE CONSERVATION LAWS; ELECTRIC LOADINGS; ELECTROSTATIC WAVES;

PIEZOELECTRICITY;

EID: 0347985397     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2003.06.002     Document Type: Article

References (49)

1. Auricchio F., Bisegna P., Lovadina C. Finite element approximation of piezoelectric plates. Internat. J. Numer. Methods Engrg. 50:2001;1469-1499.
2. Ballato A. Piezoelectricity: Old effect, new thrusts. IEEE Trans. Ultrason. Ferroelectr. 42:(5):1995;916.
3. Berlincourt D.A., Curran D.R., Jaffe H. Piezoelectric and piezomagnetic materials and their function in transducers. Mason W.P. Physical Acoustics, Vol. 1A. 1964;204-236 Academic Press, New York.
4. Buchanan R.C. Ceramic Materials for Electronics: Processing, Properties, and Applications. 1991;Marcel Dekker, New York.
5. Chen W.-Q. Problems of radially polarized piezoelectric bodies. Internat. J. Solids Structures. 36:1999;4317-4332.
6. R. Courant, K. Friedrichs, H. Lewy, On partial differential equations of mathematical physics, Technical Report NYO-7689, AEC Computing Facility, Institute of Mathematical Sciences, New York University, September, 1956 (English translation of the original paper, published in Math. Annalen 100 (1928) 32-74).
7. R. Courant, K. Friedrichs, H. Lewy, On partial differential equations of mathematical physics, Technical Report NYO-7689, AEC Computing Facility, Institute of Mathematical Sciences, New York University, September, 1956 (English translation of the original paper, published in Math. Annalen 100 (1928) 32-74).
8. Crawley E.F. Intelligent structures for aerospace: A technology overview ans assessment. AIAA J. 32:1994;1689-1699.
9. Davi G., Milazzo A. Multidomain boundary integral formulation for piezoelectric materials fructure mechanics. Internat. J. Solids Structures. 38:2001;7065-7078.
10. Denda M., Lua J. Development of the BEM for 2D piezoelectricity. Composites: Part B. 30:1999;699-707.
11. Dieulesaint E., Royer D. Elastic Waves in Solids: Applications to Signal Processing. 1980;Wiley, New York. (or Vols. I and II by the same authors, Springer, 2000).
12. Ding H.J., Liang J.A. The fundamental solutions for transversly isotropic piezoelectricity and boundary element method. Comput. Structures. 71:1999;447-455.
13. Ebenezer D.D., Abraham P. Piezoelectric thin shell theoretical model and eigenfunction analysis of radially polarized ceramic cylinders. J. Acoust. Soc. Amer. 105:(1):1999;154-163.
14. Fielding J.T. Jr, Smith D., Meyer R. Jr, Trolier-McKinstry S., Newnham R.E. Characterization of PZT hollow-sphere transducers. Proceedings of the IX IEEE International Symposium on Applications of Ferroelectrics. 1994;202-205.
15. Fukada E. Poiseuille Medal Award Lecture: Piezoelectricity of biopolymers. Biorheology. 32:1995;593.
16. Furihata D. Finite-difference schemes for nonlinear wave equation that inherit energy conservation property. J. Comput. Appl. Math. 134:2001;37-57.
17. Gururaja T.R. Piezoelectric transducers for medical ultrasonic imaging. Amer. Ceramic Soc. Bull. 73:(5):1994;50-55.
18. Heylinger P. A note on the static behaviour of simply-supported laminated piezoelectric cylinders. Internat. J. Solids Structures. 34:(29):1997;3781-3794.
19. Hornsby J.S., Das-Gupta D.K. Finite-difference modeling of piezoelectric composite transducers. J. Appl. Phys. 87:(1):2000;467-473.
20. Ikeda T. Fundamentals of Piezoelectricity. 1990;Oxford University Press, Oxford.
21. Kagawa Y., Tsuchiya T., Kawashima T. FE simulation of piezoelectric vibrator gyroscopes. IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 43:(4):1996;509-520.
22. Kim J., Varadan V.V., Varadan V.K. Finite element modelling of structures including piezoelectric active devices. Internat. J. Numer. Methods Engrg. 40:1997;817-832.
23. Lee J.S. Boundary element method for electroelastic interaction in piezoceramics. Engrg. Anal. Boundary Elements. 15:(4):1995;321-328.
24. Liu Y., Fan H. Analysis of thin piezoelectric solids by the boundary element method. Comput. Methods Appl. Mech. Engrg. 191:2002;2297-2315.
25. Lu P., Mahrenholtz O. A variational boundary element formulation for piezoelectricity. Mech. Res. Comm. 21:(6):1994;605-615.
26. Matsuo T., et al. Spatially accurate dissipative or conservative finite difference schemes derived by the discrete variational method. Japan J. Ind. Appl. Math. 19:(3):2002;311-330.
27. Maugin G.A., Pouget J., Drouot R., Collet B. Nonlinear Electromechanical Couplings. 1992;Wiley, New York.
28. Melnik R.V.N. Existence and uniqueness theorems of the generalized solution for a class of nonstationary problems of coupled electroelasticity. Soviet Math. (Izv. VUZ). 35:(4):1991;23-30.
29. Melnik R.V.N. The stability condition and energy estimate for nonstationary problems of coupled electroelasticity. Math. Mech. Solids. 2:(2):1997;153-180.
30. Melnik R.V.N. Convergence of the operator-difference scheme to generalized solutions of a coupled field theory problem. J. Difference Equations Appl. 4:1998;185-212.
31. Melnik R.V.N., Melnik K.N. A note on the class of weakly coupled problems of nonstationary piezoelectricity. Comm. Numer. Meth. Engrg. 14:1998;839-847.
32. Melnik R.V.N. Generalised solutions, discrete models and energy estimates for a 2D problem of coupled field theory. Appl. Math. Comput. 107:2000;27-55.
33. Melnik R.V.N. Discrete models of coupled dynamic thermoelasticity for stress-temperature formulations. Appl. Math. Comput. 122:2001;107-132.
34. Melnik R.V.N. Computational analysis of coupled physical fields in piezothermoelastic media. Comput. Phys. Comm. 142:2001;231-237.
35. Melnik R.V.N. Numerical analysis of dynamic characteristics of coupled piezoelectric systems in acoustic media. Math. Comput. Simulation. 61:2003;497-507.
36. Meyer R. Jr, Weitzing H., Xu Q., Zan Q., Newnham R.E. Lead zerconate titanate hollow-sphere transducers. J. Amer. Cer. Soc. 77:1994;1669-1672.
37. Nam C., Kim Y., Weisshaar T.A. Optimal sizing and placement of piezo-actuators for active flutter suppression. Smart Mater. Struct. 5:1996;216-224.
38. Rahmoune M., Latour M. Application of mechanical waves induced by piezofilms to marine foulding protection of oceanographic sensors. Smart Mater. Struct. 4:1995;195-201.
39. Rogacheva N.N. The dependence of the electromechanical coupling coefficient of piezoelectric elements on the position and size of the electrodes. PMM J. Appl. Math. Mech. 65:2001;317-326.
40. Romero M.J., Al-Jassim M.M. Advantages of using piezoelectric quantum structures for photovoltaics. J. Appl. Phys. 93:2003;626-631.
41. Rosen C.Z., Hiremath B.V., Newnham R. Piezoelectricity. 1992;Springer, New York.
42. Samarskii A.A. The Theory of Difference Schemes. 2001;Marcel Dekker, New York.
43. Samarskii A.A., Nikolaev E.S. Numerical Methods for Grid Equations. 1989;Birkhäuser, Basel.
44. Samarskii A.A., Gavrilyuk I.P., Makarov V.L. Stability and regularization of three-level difference schemes with unbounded operator coefficients in Banach spaces. SIAM J. Numer. Anal. 39:2001;708-723.
45. Shulga N.A., Bolkisev A.M. Oscillations of Piesoelectric Bodies. 1990;Naukova Dumka, Kiev.
46. Strikwerda J.C. Finite Difference Schemes and Partial Differential Equations. 1989;Wadsworth & Brooks, Pacific Grove, CA.
47. Tauchert T.R., et al. Developments in thermopiezoelasticity with relevance to smart composite structures. Composite Structures. 48:2000;31-38.
48. Uchino K. Piezoelectric actuators/ultrasonic motors: Their developments and markets. Proceedings of the IX IEEE International Symposium on Applications of Ferroelectrics. 1994;319-324.
49. Vatulyan A.O., Kublikov V.L. Boundary element method in electroelasticity. Boundary Elements Comm. 6:(2):1995;59-61.