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Proceedings Paper

The analysis of distributed systems with nonlocal damping
Author(s): Yongjun Lei; Michael I. Friswell; Sondipon Adhikari
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Paper Abstract

This paper considers the analysis of structures with nonlocal damping, where the reaction force at any point is obtained as a weighted average of state variables over a spatial domain. The model yields an integro-differential equation, and obtaining closed form solutions is only possible for a limited range of boundary conditions by the transfer function method. Approximate solutions using the Galerkin method for beams are presented for typical spatial kernel functions, for a nonlocal viscoelastic foundation model. This requires the approximation of the displacement to be defined over the whole domain. To treat more complicated problems with variable damping parameters, non-uniform section properties, intermediate supports or arbitrary boundary conditions, a finite element method for beams is developed. However, in nonlocal damping models, nodes remote from the element do have an effect on the energy expressions, and hence the damping matrix is no longer block diagonal. The expressions for these direct and cross damping matrices are obtained for separable spatial kernel functions. The approach is demonstrated on a range of examples.

Paper Details

Date Published: 17 March 2006
PDF: 8 pages
Proc. SPIE 6169, Smart Structures and Materials 2006: Damping and Isolation, 61690V (17 March 2006); doi: 10.1117/12.658025
Show Author Affiliations
Yongjun Lei, National Univ. of Defense Technology (China)
Michael I. Friswell, Univ. of Bristol (United Kingdom)
Sondipon Adhikari, Univ. of Bristol (United Kingdom)

Published in SPIE Proceedings Vol. 6169:
Smart Structures and Materials 2006: Damping and Isolation
William W. Clark; Mehdi Ahmadian; Arnold Lumsdaine, Editor(s)

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