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Research Papers

Linearized Frequencies and Damping in Composite Laminated Beams Subject to Buckling

[+] Author and Article Information
Dimitris I. Chortis

Research Assistant

Dimitris S. Varelis

Postdoctoral Fellow

Dimitris A. Saravanos

Professor
e-mail: saravanos@mech.upatras.gr
Department of Mechanical Engineering and Aeronautics,
University of Patras,
Patras 26500, Greece

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received November 15, 2011; final manuscript received October 3, 2012; published online February 25, 2013. Assoc. Editor: Marco Amabili.

J. Vib. Acoust 135(2), 021006 (Feb 25, 2013) (10 pages) Paper No: VIB-11-1276; doi: 10.1115/1.4023051 History: Received November 15, 2011; Revised October 03, 2012

This paper considers the damped small-amplitude free-vibration of composite laminated strips subject to large in-plane forces and rotations. A theoretical framework is formulated for the prediction of the nonlinear damping of composite laminates subject to large Green–Lagrange axial strains and assuming a Kelvin viscoelastic solid. An extended beam finite element is developed capable of providing the nonlinear stiffness and damping matrices of the system. The linearized damped free-vibration equations associated with the deflected strip shape in the pre- and postbuckling region are presented. Numerical results quantify the strong geometric nonlinear effect of compressive in-plane loads on the modal damping and frequencies of composite strips. Measurements of the modal damping of a cross-ply glass/epoxy beam subject to buckling were also conducted and correlate well with the finite element predictions.

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Figures

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Fig. 1

Laminated composite strip-beam element. (a) Cross-section module; (b) finite element.

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Fig. 2

Experimental setup configuration

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Fig. 3

Transverse midspan displacement of the aluminum clamped-free strip in pre- and postbuckling response under an in-plane compressive displacement along the beam axis

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Fig. 4

Bending modal frequencies of an aluminum clamped-free strip under in-plane compressive displacement. (a) First; (b) second; (c) third mode.

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Fig. 5

Predicted and measured transverse displacement at the midspan of the [02/902]s clamped-free Gl/epoxy plate-strip under in-plane compressive displacement along the beam axis

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Fig. 6

Predicted and measured first bending modal characteristics of a [02/902]s clamped-free Gl/epoxy plate-strip under in-plane compressive displacement. (a) Modal natural frequency; (b) modal loss factor.

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Fig. 9

Predicted free-vibration response for [0 deg + θ/90 deg+ θ/45 deg + θ/−45 deg + θ]s clamped-free Gl/Epoxy plate-strips under in-plane compressive displacement. (a) Transverse displacement; (b) first modal natural frequency; (c) first modal loss factor.

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Fig. 7

Effect of second-order terms on the predicted modal characteristics for the [02/902]s clamped-free Gl/epoxy plate-strip first mode. (a) Modal natural frequency; (b) modal loss factor.

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Fig. 8

[02/902]s and [902/02]s clamped-free Gl/epoxy plate-strips under in-plane compressive displacement. (a) Predicted transverse displacement; (b) predicted first modal natural frequency; (c) predicted first modal loss factor.

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Fig. 10

Comparison of free-vibration characteristics between an asymmetric lamination [04/904] and symmetric laminations [02/902]s and [902/02]s. (a) First modal natural frequency; (b) first modal loss factor.

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