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On an improved elastic dissipation model for a cantilevered beam
Author(s):
M.
A.
Zarubinskaya;
W.
T.
van Horssen
Journal:
Quart. Appl. Math.
63
(2005),
681-690.
MSC (2000):
Primary 35B05, 35Q72, 74H45
Posted:
September 27, 2005
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Abstract:
In this paper we will study an improved elastic dissipation model for a cantilevered beam, where the damping is assumed to be proportional to the bending rate of the beam. For an earlier formulated dissipation model for the cantilevered beam it has been recently shown that damping will not always be generated. However, for the improved dissipation model it will be shown in this paper that damping will always be generated.
References:
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- 1.
- D.L. Russell, On the positive root of the fourth derivative operator, Quarterly of Applied Mathematics, 16, No. 4, (1988), pp. 751-773. MR 0973388 (90f:47069)
- 2.
- D.L. Russell, A comparison of certain elastic dissipation mechanisms via decoupling and projection techniques, Quarterly of Applied Mathematics, 19, No. 2, (1991), pp. 373-396. MR 1106398 (92e:73029)
- 3.
- D.L. Russell, On mathematical models for the elastic beam with frequency-proportional damping, Chapter 4 in Control and Estimation in Distributed Parameter Systems, edited by H.T. Banks, 11 of Frontiers in Applied Mathematics, SIAM Pubs., (1992).
- 4.
- G. Chen, D.L. Russell, A mathematical model for linear elastic systems with structural damping, Quarterly of Applied Mathematics, 16, No. 1, (1982), pp. 433-454. MR 0644099 (83f:70034)
- 5.
- W.T. van Horssen, M.A. Zarubinskaya, On an elastic dissipation model for a cantilevered beam, Quarterly of Applied Mathematics, 61, No. 3, (2002), pp.565-573. MR 1999837 (2004d:74041)
- 6.
- W.T. van Horssen, On the applicability of the method of separation of variables for partial difference equations, Journal of Difference Equations and Applications, 8, No. 1, (2002), pp. 53-60. MR 1884591 (2003d:39024)
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Additional Information:
M.
A.
Zarubinskaya
Affiliation:
Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands
Email:
maria@dv.twi.tudelft.nl
W.
T.
van Horssen
Affiliation:
Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands
Email:
W.T.vanHorssen@ewi.tudelft.nl
PII:
S0033-569X-05-00979-4
Received by editor(s):
February 2, 2005
Received by editor(s) in revised form:
on March 16, 2005
Posted:
September 27, 2005
Copyright of article:
Copyright
2005,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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