Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



The associated elastic problems in dynamic visco-elasticity

Author: L. N. Tao
Journal: Quart. Appl. Math. 21 (1963), 215-222
DOI: https://doi.org/10.1090/qam/160386
MathSciNet review: 160386
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Abstract | References | Additional Information

Abstract: The paper is concerned with the associated elastic problems of linear visco-elastic bodies under dynamic conditions. By the introduction of an adjunct problem and the use of Laplace transforms, an associated elastic problem is established. This includes the quasi-static study of Lee as a special case. Also, a modification of the adjunct problem leads to a second associated elastic problem, which is in agreement with the correspondence principle.

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

  • [1] T. Alfrey, Non-homogeneous stresses in visco-elastic media, Quart. Appl. Math. 2, 113-119 (1944) MR 0010499
  • [2] H. S. Tsien, A generalization of Alfrey's theorem for visco-elastic media, Quart. Appl. Math. 8, 104-106 (1950) MR 0034693
  • [3] E. H. Lee, Stress analysis in visco-elastic bodies, Quart. Appl. Math. 13, 183-190 (1955) MR 0069741
  • [4] E. H. Lee, Viscoelastic stress analysis, in Structural Mechanics, Pergamon Press, 1960, pp. 456-482 MR 0114400
  • [5] S. C. Hunter, Viscoelastic waves, in Progress in solid mechanics, vol. I, North-Holland, 1960, pp. 1-57 MR 0115417
  • [6] D. R. Bland, The theory of linear viscoelasticity, Pergamon Press, 1960 MR 0110314
  • [7] W. T. Read, Stress analysis for compressible visco-elastic materials, J. Appl. Phys. 21, 671-674 (1950) MR 0037178
  • [8] R. C. F. Bartels and R. V. Churchill, Resolution of boundary problems by the use of a generalized convolution, Bull. Am. Math. Soc. 48, 276-282 (1942). MR 0005994

Additional Information

DOI: https://doi.org/10.1090/qam/160386
Article copyright: © Copyright 1963 American Mathematical Society

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