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June  2014, 9(2): 299-314. doi: 10.3934/nhm.2014.9.299

Characterization and synthesis of Rayleigh damped elastodynamic networks

1. 

Mathematics Department, University of Utah, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, United States

2. 

Department of Mathematics, University of Utah, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090

Received  May 2013 Revised  March 2014 Published  July 2014

We consider damped elastodynamic networks where the damping matrix is assumed to be a non-negative linear combination of the stiffness and mass matrices (also known as Rayleigh or proportional damping). We give here a characterization of the frequency response of such networks. We also answer the synthesis question for such networks, i.e., how to construct a Rayleigh damped elastodynamic network with a given frequency response. Our analysis shows that not all damped elastodynamic networks can be realized when the proportionality constants between the damping matrix and the mass and stiffness matrices are fixed.
Citation: Alessandro Gondolo, Fernando Guevara Vasquez. Characterization and synthesis of Rayleigh damped elastodynamic networks. Networks & Heterogeneous Media, 2014, 9 (2) : 299-314. doi: 10.3934/nhm.2014.9.299
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show all references

References:
[1]

Journal of Applied Physics, 20 (1949), 816.  Google Scholar

[2]

Math. Models Methods Appl. Sci., 12 (2002), 1153-1176. doi: 10.1142/S0218202502002069.  Google Scholar

[3]

Arch. Ration. Mech. Anal., 170 (2003), 211-245. doi: 10.1007/s00205-003-0272-7.  Google Scholar

[4]

Math. Comp., 78 (2009), 293-313. doi: 10.1090/S0025-5718-08-02128-5.  Google Scholar

[5]

Cambridge University Press, Cambridge, 2007.  Google Scholar

[6]

Linear Algebra Appl., 283 (1998), 115-150. doi: 10.1016/S0024-3795(98)10087-3.  Google Scholar

[7]

The Bell System Technical Journal, 3 (1924), 259-267. doi: 10.1002/j.1538-7305.1924.tb01358.x.  Google Scholar

[8]

The Bell System Technical Journal, 3 (1924), 651-685. doi: 10.1002/j.1538-7305.1924.tb00944.x.  Google Scholar

[9]

Computer Science and Applied Mathematics, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1982.  Google Scholar

[10]

J. Elasticity, 102 (2011), 31-54. doi: 10.1007/s10659-010-9260-y.  Google Scholar

[11]

Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 464 (2008), 967-986. doi: 10.1098/rspa.2007.0345.  Google Scholar

[12]

Netw. Heterog. Media, 5 (2010), 335-360. doi: 10.3934/nhm.2010.5.335.  Google Scholar

[13]

Proceedings of the Eighth International Conference on Electrical Transport and Optical Properties of Inhomogeneous Media, ETOPIM-8, Physica B: Condensed Matter, 405 (2010), 2935-2937. Google Scholar

[14]

SIAM Rev., 43 (2001), 235-286. doi: 10.1137/S0036144500381988.  Google Scholar

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