The vibration of an elastic dielectric with piezoelectromagnetism
Authors:
J. S. Yang and X. Y. Wu
Journal:
Quart. Appl. Math. 53 (1995), 753-760
MSC:
Primary 73R05; Secondary 73D30
DOI:
https://doi.org/10.1090/qam/1359509
MathSciNet review:
MR1359509
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: This paper presents a few results on the free vibration of a finite elastic dielectric with linear piezoelectromagnetism. Following the proof of selfadjointness, the orthogonality of modes corresponding to different frequencies is proved. A variational principle is given in Rayleigh quotient form for the natural frequency. The variational principle is mixed in the sense that all field variables can be varied independently, and it can be used to generate other variational principles.
D. Iesan, Reciprocity, uniqueness and minimum principles in the linear theory of piezoelectricity, Internat. J. Engrg. Sci. (28) 11, 1139–1149 (1990)
R. D. Mindlin, Electromagnetic radiation from a vibrating quartz plate, Internat. J. Solids Structures 9, 697–702 (1973)
P. C. Y. Lee, Electromagnetic radiation from an AT-cut quartz plate under lateral field excitation, J. Appl. Phys. (65) 4, 1395–1399 (1989)
P. C. Y. Lee, Y.-G. Kim, and J. H. Prevost, Electromagnetic radiation from doubly rotated piezoelectric crystal plates at thickness frequencies, J. Appl. Phys. (67) 11, 6633–6642 (1990)
P. C. Y. Lee, A variational principle for the equations of piezoelectromagnetism in elastic dielectric crystals, J. Appl. Phys. (69) 11, 7470–7473 (1991)
J. S. Yang, A generalized variational principle for piezoelectromagnetism in an elastic medium, Arch. Mech. (43) 6, 795–798 (1991)
H.-Y. Yee, An Investigation of Microwave Dielectric Resonators, Internal Memorandum, Microwave Laboratory, W. W. Hansen Laboratories of Physics, Stanford University, Stanford, California, 1963
J. S. Yang, Variational formulations for the vibration of a piezoelectric body, Quart. Appl. Math. 53, 95–104 (1995)
A. D. Berk, Variational principles for electromagnetic resonators and waveguides, IRE Trans, on Antennas and Propagation, AP-4, 1956, pp. 104–111
D. Iesan, Reciprocity, uniqueness and minimum principles in the linear theory of piezoelectricity, Internat. J. Engrg. Sci. (28) 11, 1139–1149 (1990)
R. D. Mindlin, Electromagnetic radiation from a vibrating quartz plate, Internat. J. Solids Structures 9, 697–702 (1973)
P. C. Y. Lee, Electromagnetic radiation from an AT-cut quartz plate under lateral field excitation, J. Appl. Phys. (65) 4, 1395–1399 (1989)
P. C. Y. Lee, Y.-G. Kim, and J. H. Prevost, Electromagnetic radiation from doubly rotated piezoelectric crystal plates at thickness frequencies, J. Appl. Phys. (67) 11, 6633–6642 (1990)
P. C. Y. Lee, A variational principle for the equations of piezoelectromagnetism in elastic dielectric crystals, J. Appl. Phys. (69) 11, 7470–7473 (1991)
J. S. Yang, A generalized variational principle for piezoelectromagnetism in an elastic medium, Arch. Mech. (43) 6, 795–798 (1991)
H.-Y. Yee, An Investigation of Microwave Dielectric Resonators, Internal Memorandum, Microwave Laboratory, W. W. Hansen Laboratories of Physics, Stanford University, Stanford, California, 1963
J. S. Yang, Variational formulations for the vibration of a piezoelectric body, Quart. Appl. Math. 53, 95–104 (1995)
A. D. Berk, Variational principles for electromagnetic resonators and waveguides, IRE Trans, on Antennas and Propagation, AP-4, 1956, pp. 104–111
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73R05,
73D30
Retrieve articles in all journals
with MSC:
73R05,
73D30
Additional Information
Article copyright:
© Copyright 1995
American Mathematical Society
