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Finite Element Analysis of Beams With Constrained Damping Treatment Modeled Via Fractional Derivatives

[+] Author and Article Information
Luis E. Suárez, José Arroyo

Department of Civil Engineering, University of Puerto Rico, Mayaguez PR 00681-5000

Arsalan Shokooh

Department of General Engineering, University of Puerto Rico, Mayaguez PR 00681-5000

Appl. Mech. Rev 50(11S), S216-S224 (Nov 01, 1997) doi:10.1115/1.3101839 History: Online April 20, 2009

Abstract

This paper presents a finite element formulation for the modeling of beams and frames with artificial damping provided by means of a constrained single layer of damping material. The behavior of the damping material is described using the fractional derivative model of viscoelasticity. In this model, the first order derivatives of the strains in the constitutive equations of the viscoelastic materials are replaced by derivatives of order α < 1. The finite element model developed is a one-dimensional beam element with three degrees of freedom per node. The dynamic response is calculated with a procedure involving a transformation of the original equations of motion to the state space and its decoupling with the eigenvectors of a special eigenvalue problem. The accuracy of the modal properties obtained with the beam model is compared with those calculated from a more elaborate plane stress finite element model. It was found that the proposed beam element provides very accurate results and with much lower computational costs than the 2-D model.

Copyright © 1997 by American Society of Mechanical Engineers
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