Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



The modeling of piezoceramic patch interactions with shells, plates, and beams

Authors: H. T. Banks, R. C. Smith and Yun Wang
Journal: Quart. Appl. Math. 53 (1995), 353-381
MSC: Primary 73R05; Secondary 73K05, 73K10, 73K15
DOI: https://doi.org/10.1090/qam/1330657
MathSciNet review: MR1330657
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: General models describing the interactions between one or a pair of piezoceramic patches and elastic substructures consisting of a cylindrical shell, plate, or beam are presented. In each case, the contributions to the internal moments and forces due to the presence of the patches are carefully discussed. In addition to these material contributions, the input of voltage to the patches produces mechanical strains that lead to external moments and forces. These external loads depend on the material properties of the patch, the geometry of patch placement, and the voltage. The internal and external moments and forces due to the patches are then incorporated into the equations of motion, which yields models describing the dynamics of the combined structure. These models are sufficiently general to allow for potentially different patch voltages, which implies that they can be suitably employed when using piezoceramic patches for controlling system dynamics when both extensional and bending vibrations are present.

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

  • [1] H. T. Banks, Y. Wang, D. J. Inman, and J. C. Slater, Variable coefficient distributed parameter system models for structures with piezoceramic actuators and sensors, Proc. 31st IEEE Conf. Decision and Control, Tucson, AZ, December 16-18, 1992, pp. 1803-1808
  • [2] R. L. Clark, Jr., C. R. Fuller, and A. Wicks, Characterization of multiple piezoelectric actuators for structural excitation, J. Acoustical Soc. Amer. 90, 346-357 (1991)
  • [3] E. F. Crawley and E. H. Anderson, Detailed models of piezoceramic actuation of beams, AIAA Paper 89-1388-CP, 1989
  • [4] E. F. Crawley and J. de Luis, Use of piezoelectric actuators as elements of intelligent structures, AIAA J. 25, 1373-1385 (1987)
  • [5] E. F. Crawley, J. de Luis, N. W. Hagood, and E. H. Anderson, Development of piezoelectric technology for applications in control of intelligent structures, Applications in Control of Intelligent Structures, American Controls Conference, Atlanta, June 1988, pp. 1890-1896
  • [6] E. K. Dimitriadis, C. R. Fuller, and C. A. Rogers, Piezoelectric actuators for distributed noise and vibration excitation of thin plates, J. Vibration and Acoustics 13, 100-107 (1991)
  • [7] C. L. Dym, Introduction to the Theory of Shells, Pergamon Press, New York, 1974
  • [8] C. R. Fuller, G. P. Gibbs, and R. J. Silcox, Simultaneous active control of flexural and extensional power flow in beams, J. Intelligent Materials, Systems and Structures 1, no. 2, April 1990
  • [9] C. R. Fuller, S. D. Snyder, C. H. Hansen, and R. J. Silcox, Active control of interior noise in model aircraft fuselages using piezoceramic actuators, Paper 90-3922, AIAA 13th Aeroacoustics Conf., Tallahassee, FL, October 1990
  • [10] G. P. Gibbs and C. R. Fuller, Excitation of thin beams using asymmetric piezoelectric actuators, Proc. 121st Meeting ASA, Baltimore, MD, April 1991
  • [11] N. J. Hoff, The accuracy of Donnell's equations, J. Appl. Mech. 22, 329-334 (1955)
  • [12] J. Jia and C. A. Rogers, Formulation of a laminated shell theory incorporating embedded distributed actuators, The American Society of Mechanical Engineers, Reprinted from AD-Vol. 15, Adaptive Structures (B. K. Wada, ed.), Book No. H00533, 1989
  • [13] S. J. Kim and J. D. Jones, Optimal design of piezo-actuators for active noise and vibration control, AIAA 13th Aeroacoustics Conf., Tallahassee, FL, October 1990
  • [14] H. Kraus, Thin elastic shells: An introduction to the theoretical foundations and the analysis of their static and dynamic behavior, John Wiley, New York, 1967
  • [15] L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, vol. 7: Theory of Elasticity, Translated from the Russian by J. B. Sykes and W. H. Reid, Pergamon Press, London, 1959
  • [16] A. W. Leissa, Vibration of Shells, NASA SP-288, 1973
  • [17] H. C. Lester and S. Lefebvre, Piezoelectric actuator models for active sound and vibration control of cylinders, Proc. Conf. Recent Advances in Active Control of Sound and Vibration, Blacksburg, VA, 1991, pp. 3-26
  • [18] A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, 4th ed., Cambridge Univ. Press, London, 1927
  • [19] S. Markuš, The Mechanics of Vibrations of Cylindrical Shells, Elsevier, New York, 1988
  • [20] L. S. D. Morley, An improvement of Donnell's approximation for thin-walled circular cylinders, Quart. Mech. and Appl. Math. 12, 89-99 (1959)
  • [21] A. S. Saada, Elasticity Theory and Applications, R. E. Krieger Publ. Co., Malabar, FL, 1987
  • [22] S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed., McGraw-Hill, New York, 1987
  • [23] H. S. Tzou and M. Gadre, Theoretical analysis of a multi-layered thin shell coupled with piezoelectric actuators for distributed vibration controls, J. Sound and Vibration 132, 433-450 (1989)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73R05, 73K05, 73K10, 73K15

Retrieve articles in all journals with MSC: 73R05, 73K05, 73K10, 73K15

Additional Information

DOI: https://doi.org/10.1090/qam/1330657
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society