On the thickness expansion of the electric potential in the determination of two-dimensional equations for the vibration of electroded piezoelectric plates

Journal of Applied Physics

Volumn 91, Issue 3, 2002, Pages 2277-2283

  Tiersten, H F ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT CONDITIONS; DIFFERENT ORDER; EDGE CONDITIONS; INTEGRAL CONDITIONS; PIEZOELECTRIC PLATE; PLATE EQUATIONS; REDUCED SYSTEMS; SURFACE ELECTRODE; TWO-DIMENSIONAL EQUATIONS; VARIATIONAL EQUATIONS;

ELECTRODES; LAGRANGE MULTIPLIERS; PIEZOELECTRIC DEVICES; TWO DIMENSIONAL; VIBRATIONS (MECHANICAL);

ELECTRIC POTENTIAL;

EID: 33845414702     PISSN: 00218979     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1426242     Document Type: Article

References (12)

1. R. D. Mindlin, J. Appl. Phys. 23, 83 (1952).
2. H. F. Tiersten and R. D. Mindlin, Quarterly Appl. Math. 20, 107 (1962).
3. R. D. Mindlin, Int. J. Solids Struct. 8, 895 (1972).
4. R. D. Mindlin, Int. J. Solids Struct. 10, 453 (1974).
5. N. Bugdayci and D. B. Bogy, Int. J. Solids Struct. 17, 1159 (1981).
6. H. F. Tiersten, Mechanics of Electromagnetic Materials and Structures, AMD-Vol. 161 (The American Society of Mechanical Engineers, (AIME), New York, 1993), pp. 21-34, No. G00784-1993.
7. H. F. Tiersten, Proc. SPIE 2427, 326 (1995).
8. F. B. Hildebrand, Methods of Applied Mathematics (Prentice-Hall, Englewood Cliffs, New Jersey, 1965), Chap. 2, Sec. 2.7.
9. H. F. Tiersten, Linear Piezoelectric Plate Vibrations (Plenum, New York, 1969), Eqs. (6.20), (5.5), (5.4), (5.19), and (5.20).
10. R. D. Mindlin, Quarterly Appl. Math. 19, 515 (1961).
11. 3, the expressions for the currents through the top and bottom electrodes may be obtained.
12. (1), exactly the same conditions would be obtained and Eqs. (4.6) would be used in the equations. Clearly, the elimination procedure employed was simpler and more direct.