A reduced second-order approach for linear viscoelastic oscillators

Adhikari, S. (2010) A reduced second-order approach for linear viscoelastic oscillators. Journal of Applied Mechanics, Transactions of the ASME, 77(4), 041003. (doi: 10.1115/1.4000913)

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Abstract

This paper proposes a new approach for the reduction in the model-order of linear multiple-degree-of-freedom viscoelastic systems via equivalent second-order systems. The assumed viscoelastic forces depend on the past history of motion via convolution integrals over 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. Here, an approximate reduced second-order approach is proposed for this type of problems. The proposed approximation utilizes the idea of generalized proportional damping and expressions of approximate eigenvalues of the system. A closed-form expression of the equivalent second-order system has been derived. The new expression is obtained by elementary operations involving the mass, stiffness, and the kernel function matrix only. This enables one to approximately calculate the dynamical response of complex viscoelastic systems using the standard tools for conventional second-order systems. Representative numerical examples are given to verify the accuracy of the derived expressions.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Adhikari, Professor Sondipon
Authors: Adhikari, S.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Journal of Applied Mechanics, Transactions of the ASME
Publisher:ASME
ISSN:0021-8936
ISSN (Online):1528-9036
Published Online:31 March 2010

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