Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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

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.

References [Enhancements On Off] (What's this?)

  • [1] 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)
  • [2] 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)
  • [3] 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)
  • [4] E. P. EerNisse, Variational method for electroelastic vibration analysis, IEEE Trans. Sonics and Ultrasonics (SU) 14, 153-160 (1967)
  • [5] H. F. Tiersten, Linear Piezoelectric Plate Vibrations, Plenum Press, New York, 1969, pp. 34-36
  • [6] 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

DOI: https://doi.org/10.1090/qam/1315450
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society