Fundamental equations of certain electromagnetic-acoustic discontinuous fields in variational form

Continuum Mechanics and Thermodynamics

Volumn 16, Issue 1-2, 2004, Pages 53-71

  Altay, G A ^a   Dokmeci M C ^b  

^a BOGAZICI UNIVERSITY   (Turkey)

^b ISTANBUL TECHNICAL UNIVERSITY   (Turkey)

Author keywords

Discontinuous electromagnetic acoustic fields; Uniqueness of solutions; Variational principles

Indexed keywords

EID: 1342263570     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00161-003-0141-5     Document Type: Article

References (57)

1. Maugin, G.A.: Continuum Mechanics of Electromagnetic Solids, North Holland New York (1988)
2. Rumsey, V.H.: Reaction concept in electromagnetic theory. Phys. Rev. 94, 483-491 (1954)
3. Tonti, E.: Variational principles in electromagnetism. Rend. Ist. Lombardo A-102, 845-861 (1968)
4. Gurtin, M.E.: Variational principles in the linear theory of viscoelasticity. Arch. Rational Mech. Anal. 13, 179-191 (1963)
5. Tonti, E.: On the variational formulation for linear initial value problems. Annali di Matem. Pura Appl. 95, 331-359 (1973)
6. Harrington, R.F.: Field Computation by Moment Methods, Krieger New York (1968)
7. Anderson, N., Arthurs, A.M.: A variational principle for Maxwell's equations. Int. J. Electron. 45, 333-334 (1978)
8. Herrera, I.: Variational principles for problems with linear constraints: prescribed jumps and continuation type restrictions. J. Inst. Math. Appl. 25, 67-96 (1980)
9. Toupin, R.A.: The elastic dielectric. J. Rational Mech. Anal. 5, 849-915 (1956)
10. Daher, N., Maugin, G.A.: Virtual power and thermodynamics for electromagnetic continua with interfaces. J. Math. Phys. 27, 3022-3035 (1986)
11. Berk, A.D.: Variational principle for electromagnetic resonators and waveguides. IRE Trans. Antennas Propag. AP-4, 104-110 (1956)
12. Panofsky, W.K.H., Phillips, M.: Classical Electricity and Magnetism, 2nd edn., Addison Wesley London (1962)
13. Nelson, D.F., Chen, B.: Lagrangian treatment of magnetic dielectrics. Phys. Rev. B 50, 1023-1038 (1994)
14. Silvester, P.P., Pelosi, G. (Eds.): Finite Elements for Wave Electromagnetics: Methods and Techniques, IEEE Press New York (1994)
15. Papastavridis, J.G.: A panoramic view of the principles and equations of motion of advanced engineering dynamics. Appl. Mech. Rev. 51, 239-265 (1998)
16. Oden, J.T., Reddy, J.N.: Variational Methods in Theoretical Mechanics, Springer Berlin (1976)
17. English, W.J.: A computer-implemented vector variational solution of loaded rectangular waveguides. SIAM J. Appl. Math. 21, 461-468 (1971)
18. Jeng, S.K., Chen, C.H.: Variational finite element solution of electromagnetic wave propagation in a one-dimensional inhomogeneous anisotropic medium. J. Appl. Phys. 55, 630-636 (1984)
19. Tao, L.N.: On variational principles for electromagnetic theory. J. Math. Phys. 7, 526 (1966)
20. Morosi, C.: Action principles for electromagnetism. Rend. Accad. Naz. Lincei, Serie VIII, LI, 502-510 (1971)
21. Anderson, N., Arthurs, A.M.: Complementary variational principles for Maxwell's equations. Int. J. Electron. 47, 229-236 (1979)
22. Morishita, K., Kumagai, N.: Unified approach to derivation of variational expression for electromagnetic fields. IEEE Trans. MTT-25, 34-40 (1977)
23. Cendra, H., Holm, D.D., Hoyle, M.J.W., Marsden, J.E.: The Maxwell-Vlasov equations in Euler-Poincaré form. J. Math. Phys. 39, 3138-3157 (1988)
24. Biehl, F.J.: Variational principles for general electromagnetic fields in nonmoving media. Arch. Electrotech. 70, 441-449 (1987)
25. Schuler, J., Felippa, C.A.: Electromagnetic finite elements based on a four potential variational principle, Finite Elem. Anal. Des. 6, 321-339 (1990)
26. Mindlin, R.D.: Lecture Notes at Columbia University, New York (1968); The Collected Works of RD Mindlin, Springer Berlin Heidelberg New York (1989)
27. Aşkar, G.A., Dökmeci, M.C.: Certain variational principles of mechanics of continua. BU&ITU R#07 (2000)
28. Morishita, K., Kumagai, N.: Systematic derivation of variational expressions for electromagnetic and/or acoustic waves. IEEE Trans. MTT-26, 684-689 (1978)
29. Lee, P.C.Y.: A variational principle for the equations of piezoelectromagnetism in elastic dielectric crystals. J. Appl. Phys. 69, 7470-7473 (1991)
30. Hadjigeorgiou, E.P., Kalpakides, V.K., Massalas, C.V.: A general theory for elastic dielectrics. II. the variational approach. Int. J. Non-linear Mech. 34, 967-980 (1999)
31. Duvaut, G., Lions, P.L.: Inequations in Physics and Mechanics, Springer Berlin (1979)
32. Auld, B.A.: Acoustic Fields and Waves in Solids, 2nd edn., Krieger New York (1990)
33. Mason, W.P.: Crystal Physics of Interaction Processes, Academic Press New York (1966)
34. Fichera, G.: Existence theorems in elasticity. In: Encyclopedia of Physics, vol. VIa/2, pp. 347-424, Springer Berlin Heidelberg New York (1972)
35. Gurtin, M.E.: The linear theory of elasticity. In: Encyclopedia of Physics, vol. VIa/2, pp. 1-295, Springer Berlin Heidelberg New York (1972)
36. Jones, D.S.: Methods in Electromagnetic Wave Propagation, Oxford University Press Oxford (1995)
37. Santos, J.E., Sheen, D.: On the existence and uniqueness of solutions to Maxwell's equations in bounded domains with application to magnetotellurics. Math. Models Methods Appl. Sci. 10, 615-628 (2000)
38. Kirchhoff, G.: Über das Gleichgewicht und die Bewegung eines unendlich dünnen elastischen Stabes. J. Reine Angew. Math. 56, 285-313 (1859)
39. Neumann, F.: Vorlesungen über die Theorie der elastischen, der festen Körper und das Lichtathers, Teubner Leipzig (1885)
40. Weiner, J.H.: A uniqueness theorem for the coupled thermoelastic problem. Q. Appl. Math. 15, 102-105 (1957)
41. Aşkar Altay, G., Dökmeci, M.C.: A uniqueness theorem in Biot's poroelasticity theory. Z. Angew Math. Phys. 49, 838-846 (1998)
42. Knops, R.J., Payne, L.E.: Uniqueness theorems in linear elasticity. Springer Berlin (1972)
43. Aşkar Altay, G., Dökmeci, M.C.: Coupled thermoelastic shell equations with second sound for high-frequency vibrations of temperature-dependent materials. Int. J. Solids Struct. 38 2737-2768 (2001)
44. Morse, M., Feshbach, H.: Methods of Theoretical Physics, McGraw-Hill New York (1953)
45. Biot, M.A.: New variational-Lagrangian irreversible thermodynamics with application to viscous flow, reaction-diffusion, and solid mechanics. In: Advances in Applied Mechanics, vol. 24, pp. 1-91, Academic Press New York (1984)
46. Rosen, P.: Use of restricted variational principles for solution of differential equations. J. Appl. Phys. 25, 336-338 (1954)
47. Friedrichs, K.O.: Ein Verfahren der Variationsrechung das Minimum eines Integrals als das Maximum eines anderen Ausdruckes darzustellen. Math. Phys. (Ges. Wiss. Göttingen, Nachrichten) 1, 13-20 (1929)
48. Fraeijs de Veubeke, B.M.: Dual principles of elastodynamics-finite element applications. In: Lecture on Finite Element Methods in Continuum Mechanics, pp. 357-377, University of Alabama Press Huntsville (1973)
49. Dökmeci, M.C.: Certain integral and differential types of variational principles in nonlinear piezoelectricity. IEEE Trans. UFFC-35, 775-787 (1988)
50. Lanczos, C.: The Variational Principles of Mechanics, 4th edn., Dover New York (1986)
51. Tiersten, H.F.: Natural boundary and initial conditions from a modification of Hamilton's principle. J. Math. Phys. 9, 1445-1451 (1968)
52. Kellogg, O.D.: Foundations of Potential Theory, F. Ungar New York (1946)
53. Christoffel, E.B.: Untersuchungen über die mit dem Fortbestehen linearer partieller. Differentialgleichungen vertraglichen Unstetigkeiten. Ann. Math. 8, 81-113 (1877)
54. Harrington, R.F.: Time-Harmonic Electromagnetic Fields, McGraw Hill New York (1961)
55. Tiersten, H.F.: Linear Piezoelectric Plate Vibrations, Plenum Press New York (1969)
56. He, J.-H.: Coupled variational principles of piezoelectricity. Int. J. Eng. Sci. 39, 323-341 (2001)
57. Cannarozzi, A.A., Ubertini, F.: Some hybrid variational methods for linear electroelasticity problems. Int. J. Solids Struct. 38, 2573-2596 (2001)