Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



A mathematical model for linear elastic systems with structural damping

Authors: G. Chen and D. L. Russell
Journal: Quart. Appl. Math. 39 (1982), 433-454
MSC: Primary 70J20; Secondary 34C28, 34C35
DOI: https://doi.org/10.1090/qam/644099
MathSciNet review: 644099
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Abstract: We present a mathematical model exhibiting the empirically observed damping rates in elastic systems. The models studied are of the form ($ A$ the relevant elasticity operator)

$\displaystyle \ddot x + B\dot x + Ax = 0$

with $ B$ related in various ways to the positive square root, $ {A^{1/2}}$, of $ A$. Comparison with existing ``ad hoc'' models is made.

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

  • [1] R. P. Boas, A trigonometric moment problem, J. London Math. Soc. 14, 242-244 (1939)
  • [2] N. Dunford and J. T. Schwartz, Linear operators, Interscience, New York, 1957
  • [3] Y. C. Fung, Foundations of solid mechanics, Prentice-Hall, Englewood Cliffs, 1965
  • [4] W. C. Hurty and M. F. Rubinstein, Dynamics of structures, Prentice-Hall, Englewood Cliffs, 1964 MR 0177532
  • [5] T. Kato, Perturbation theory for linear operators, Springer-Verlag, New York, 1966 MR 0203473
  • [6] J. L. Lions, Optimal control of systems governed by partial differential equations, Springer-Verlag, New York, 1971 MR 0271512
  • [7] R. S. Phillips, Dissipative operators and hyperbolic systems of partial differential equations, Trans. Amer. Math. Soc. 90, 123-254 (1959) MR 0104919
  • [8] D. L. Russell, Controllability and stabilizability theory for linear partial differential equations, SIAM Review 20, 639-739 (1978) MR 508380
  • [9] R. H. Scanlon and R. Rosenbaum, Introduction to the theory of aircraft vibration and flutter, Macmillan, New York, 1951
  • [10] J. Zabczyk, On decomposition of generators, SIAM J. Cont. Opt. 16, 523-534 (1978) MR 0512915

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Additional Information

DOI: https://doi.org/10.1090/qam/644099
Article copyright: © Copyright 1982 American Mathematical Society

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