Variational formulations for the vibration of a piezoelectric body
Author:
J. S. Yang
Journal:
Quart. Appl. Math. 53 (1995), 95-104
MSC:
Primary 73R05; Secondary 73D30, 73V25
DOI:
https://doi.org/10.1090/qam/1315450
MathSciNet review:
MR1315450
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: This paper presents a systematic discussion on the variational principles for the vibration of a piezoelectric body. It is shown that there exist four types of variational formulations depending on the internal energy, electric enthalpy, mechanical enthalpy, and enthalpy, respectively. The one depending on the internal energy is in a positive-definite form which immediately leads to a few important properties of the lowest resonant frequency.
H. M. Westergaard, On the method of complementary energy and its application to structures stressed beyond its proportional limit, to buckling and vibrations, and to suspension bridges, Proc. Amer. Soc. Civil Engrs. 67, 199–227 (1941)
K. Washizu, Note on the principle of stationary complementary energy applied to free vibration of an elastic body, Internat. J. Solids and Structures 2, 27–35 (1966)
G. M. L. Gladwell and G. Zimmermann, On energy and complementary energy formulations of acoustic and structural vibration problems, J. Sound Vibration 3, 233–241 (1966)
E. P. EerNisse, Variational method for electroelastic vibration analysis, IEEE Trans. Sonics and Ultrasonics (SU) 14, 153–160 (1967)
H. F. Tiersten, Linear Piezoelectric Plate Vibrations, Plenum Press, New York, 1969, pp. 34–36
R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. 1, Interscience, New York, 1953, p. 407
H. M. Westergaard, On the method of complementary energy and its application to structures stressed beyond its proportional limit, to buckling and vibrations, and to suspension bridges, Proc. Amer. Soc. Civil Engrs. 67, 199–227 (1941)
K. Washizu, Note on the principle of stationary complementary energy applied to free vibration of an elastic body, Internat. J. Solids and Structures 2, 27–35 (1966)
G. M. L. Gladwell and G. Zimmermann, On energy and complementary energy formulations of acoustic and structural vibration problems, J. Sound Vibration 3, 233–241 (1966)
E. P. EerNisse, Variational method for electroelastic vibration analysis, IEEE Trans. Sonics and Ultrasonics (SU) 14, 153–160 (1967)
H. F. Tiersten, Linear Piezoelectric Plate Vibrations, Plenum Press, New York, 1969, pp. 34–36
R. Courant and D. Hilbert, Methods of Mathematical Physics, vol. 1, Interscience, New York, 1953, p. 407
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73R05,
73D30,
73V25
Retrieve articles in all journals
with MSC:
73R05,
73D30,
73V25
Additional Information
Article copyright:
© Copyright 1995
American Mathematical Society
