This paper proposes a new iterative approach for the calculation of eigenvalues of single and multiple degree-of-freedom viscoelastic systems. The Biot model of viscoelasticity is assumed. With this model, the viscoelastic forces depend on the past history of motion via convolution integrals over exponentially decaying kernel functions. Current methods to solve this type of problem normally use the state-space approach involving additional internal variables. Such approaches often increase the order of the eigenvalue problem to be solved and can become computationally expensive for large systems. The method proposed in this paper is aimed to address this issue. In total, five iterative algorithms for the real and complex eigenvalues of single and multiple degree-of-freedom systems have been proposed. The results are obtained in terms of explicit closed-form expressions. This enables one to approximately calculate the eigenvalues of complex viscoelastic systems using the eigenvalues of the underlying elastic systems. Representative numerical examples are given to verify the accuracy of the derived expressions.
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April 2011
Research Papers
Iterative Methods for Eigenvalues of Viscoelastic Systems
Sondipon Adhikari,
Sondipon Adhikari
Chair of Aerospace Engineering
School of Engineering,
e-mail: s.adhikari@swansea.ac.uk
Swansea University
, Singleton Park, Swansea SA2 8PP, UK
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Blanca Pascual
Blanca Pascual
School of Engineering,
Swansea University
, Singleton Park, Swansea SA2 8PP, UK
Search for other works by this author on:
Sondipon Adhikari
Chair of Aerospace Engineering
School of Engineering,
Swansea University
, Singleton Park, Swansea SA2 8PP, UKe-mail: s.adhikari@swansea.ac.uk
Blanca Pascual
School of Engineering,
Swansea University
, Singleton Park, Swansea SA2 8PP, UKJ. Vib. Acoust. Apr 2011, 133(2): 021002 (7 pages)
Published Online: March 1, 2011
Article history
Received:
October 10, 2009
Revised:
April 29, 2010
Online:
March 1, 2011
Published:
March 1, 2011
Citation
Adhikari, S., and Pascual, B. (March 1, 2011). "Iterative Methods for Eigenvalues of Viscoelastic Systems." ASME. J. Vib. Acoust. April 2011; 133(2): 021002. https://doi.org/10.1115/1.4002220
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