Fundamental variational equations of discontinuous thermopiezoelectric fields

International Journal of Engineering Science

Volumn 34, Issue 7, 1996, Pages 769-782

  Askar Altay G ^a,b   Dökmeci, M Cengiz ^b  

^a BOGAZICI UNIVERSITY   (Turkey)

^b ISTANBUL TECHNICAL UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000316890     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/0020-7225(95)00133-6     Document Type: Article

References (66)

1. W. P. MASON, Crystal Physics of Interaction Processes. Academic Press, New York (1966).
2. R. D. MINDLIN, Problems of Continuum Mechanics: N. I. Muskhelishvili 70th Birthday Volume, pp. 282-290. SIAMS, Philadelphia (1961).
3. C. LANCZOS, The Variational Principles of Mechanics. University of Toronto Press, Toronto (1960).
4. S. G. MIKHLIN, Variational Methods in Mathematical Physics. Macmillan, New York (1964).
5. L CARIO and T. KAHAN, Variational Techniques in Electromagnetism. Gordon and Breach, New York (1965).
6. J. M. JIN, The Finite Element Method in Electromagnetics. Wiley, New York (1993).
7. P. B. ZHOU, Numerical Analysis of Electromagnetic Fields. Springer, New York (1963).
8. M. M. VAINBERG, Variational Methods for the Study of Nonlinear Operators. Holden-Day, San Francisco (1964).
9. M. E. GURTIN, in Encyclopedia of Physics, vol. VI a/2 pp. 1-295. Springer, Berlin (1972).
10. I. A. VEKOVISHCHEVA, Sov. Appl. Mechs. 7, 1049 (1974); Prikl. Mekh. 7, 129 (1971).
11. I. A. VEKOVISHCHEVA, Sov. Appl. Mechs. 7, 1049 (1974); Prikl. Mekh. 7, 129 (1971).
12. H. F. TIERSTEN and R. D. MINDLIN, Q. Appl. Math. 20, 107 (1962).
13. E. P. EERNISSE, IEEE Trans. Sonics Ultrason. SU-14, 153 (1967).
14. E. P. EERNISSE and R. HOLLAND, IEEE Trans. Sonics Ultrason. SU-15, 119 (1968).
15. M. C. DÖKMECI, L. II. Nuovo Cimento 7, 449 (1973).
16. M. C. DÖKMECI, J. Math. Phys. 19, 109 (1978).
17. M. C. DOKMECI, Int. Engng Sci. 18, 431 (1980).
18. V. A. MOL'KOV, Mech. Solids 27, 102 (1992).
19. H. F. TIERSTEN, Proc. IEEE 55, 1523 (1967).
20. H. F. TIERSTEN, Linear Piezoelectric Plate Vibrations. Plenum Press, New York (1969).
21. W. NOWACKI, J. Thermal Stresses 1, 171 (1978).
22. W. NOWACKI, Theory of Asymmetric Elasticity. Pergamon Press, New York (1968).
23. D. S. CHANDRASEKHARAIAH, J. Thermal Stresses 7, 293 (1984).
24. Z. HAILAN, Chin. J. Acoust. 4, 223 (1985).
25. M. C. DÖKMECI, Proc. Int. Symp. on Strength of Materials and Components at Sonic Ultrasonic Frequency (in Russian) Academy Science USRR and Ukraine SSR, Kiev pp. 203-208 (1987).
26. M. C. DÖKMECI, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. UFFC-35, 775 (1988).
27. M. C. DÖKMECI, IEEE Trans. Ultrason. Ferrolec. Freq. Contr. UFFC-37, 369 (1990).
28. R. S. SANDHU and K. S. PISTER, Int. J. Solids Struct. 7, 639 (1971).
29. G. R. BUCHANAN Comput. Mech. 2, 163 (1987).
30. M. A. BIOT, J. Appl. Phys. 27, 240 (1956).
31. R. D. MINDLIN, Int. J. Solids Struct. 10, 625 (1974).
32. J. T. ODEN and J. N. REDDY, Variational Methods in Theoretical Mechanics. Springer, Berlin (1976).
33. B. A. FINLAYSON, The Method of Weighted Residuals and Variational Principles. Academic Press, New York (1972).
34. B. A. FINLAYSON and L. E. SCRIVEN, Int. J. Heat Mass Transfer. 10, 799 (1967).
35. K. WASHIZU, Variational Methods in Elasticity and Plasticity. 3rd Edn. Pergamon Press, New York (1982).
36. R. HOLLAND and E. P. EERNISSE, Design of Resonant Piezoelectric Devices, Vol. 56. M.I.T. Press, Cambridge, MA (1969).
37. G. K. MIKHAILOV and V. Z. PARTON, Applied Mechanics: Soviet Reviews, Vol. 2: Electromagnetoelasticity. Hemisphere, New York (1990).
38. M. C. DÖKMECI, A dynamic analysis of piezoelectric strained elements. U.S.A.R.D.S.G., F.R., June (1992).
39. R. D. MINDLIN, Theory of beams and plates. Lecture notes at Columbia University, New York (1968).
40. R. A. Toupin, J. Rational Mech. Anal. 5, 849 (1956).
41. J. A. SCHOUTEN, Tensor Analysis for Physicists. Oxford University Press, London (1951).
42. O. D. KELLOGG, Foundations of Potential Theory. F. Ungar, New York (1946).
43. G. VENKATARAMAN, L. A. FELDKAMP and V. C. SAHNI, Dynamics of Perfect Crystals. M.I.T. Press, Cambridge, MA (1975).
44. G. FICHERA, Handbuch der Physik. Vol. Vla/2, pp. 347-389. Springer, Berlin (1972).
45. N. DAHER and G. A. MAUGIN, Acta Mech. 60, 217 (1986).
46. M. A. BIOT, in Advances Applied Mechanics, Vol. 24, pp. 1-91. Academic Press, New York (1984).
47. G. BATRA, J. Elasticity 21, 131 (1989).
48. C. TRUESDELL and R. A. TOUPIN, The Classical Field Theories, Encyclopedia of Physics, Vol. III/1, pp. 226-793. Springer, Berlin (1960).
49. M. GERADIN, ed., B. M. Fraeijs De Veubeke Memorial Volume of Selected Papers, pp. 295-319. Sijthoff and Noordhoff, Rockville, Maryland (1980).
50. K. O. FRIEDRICHS, Math. Phys. 1, 13 (1929).
51. P. M. MORSE and H. FESHBACH, Methods of Theoretical Physics, Part II. McGraw-Hill, New York (1953).
52. P. ROSEN, J. Appl. Phys. 25, 336 (1954).
53. M. A. BIOT, Variational Principles in Heat Transfer: A Unified Lagrangian Analysis of Dissipative Phenomena. Clarendon Press, London (1970).
54. R. COURANT and D. HILBERT, Methods of Mathemical Physics, Vol. 1. Interscience, New York (1953).
55. M. C. DÖKMECI, Meccanica 8, 252 (1973).
56. G. ALTAY and M. C. DÖKMECI, On variational principles for thermopiezoelectric discontinuous fields. TÜBİTAK/EEE-AG, TR., July (1994).
57. H. F. TIERSTEN, J. Math. Phys. 9, 1445 (1968).
58. G. CHEN, Int. J. Engng Sci. 28, 875 (1990).
59. T. E. SIMKINS, AIAA J. 16, 559 (1978).
60. J. W. WU and T. E. SIMKINS, J. Sound Vibr. 72, 491 (1980).
61. J. J. WU, J. Sound Vibr. 53, 341 (1977).
62. R. F. HARRINGTON, Harmonic Elecgromagnetic Fields. McGraw-Hill, New York (1961).
63. W.-Z. CHIEN, in Advances in Applied Mechanics, Vol. 24, pp. 93-153. Academic Press, New York (1984).
64. B. A. BOLEY and J. H. WEINER, Theory of Thermal Stresses. Wiley New York (1967).
65. G. A. AŞKAR and M. C. DÖKMECI, J. Acoust. Soc. Am. 95, 3007 (1994).
66. P. PENFIELD Jr, Phys. Fluids 9, 1184 (1966).