Characterization and synthesis of Rayleigh damped elastodynamic networks
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Mathematics Department, University of Utah, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090
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Department of Mathematics, University of Utah, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090
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Received:
01 May 2013
Revised:
01 March 2014
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Primary: 74B05, 35R02.
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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[J]. Networks and Heterogeneous Media, 2014, 9(2): 299-314. doi: 10.3934/nhm.2014.9.299
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Abstract
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.
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