The Nonlinear Behaviors of a Symmetric Isotropic Laminate in a Mixed Boundary Condition Subject to an Arbitrary Thermal Field Coupled with Mechanical Loading

[+] Author and Article Information
Xiaoling He

 University of Wisconsin, Milwaukee, WI 53211xiaoling@uwm.edu

J. Comput. Nonlinear Dynam 1(2), 168-177 (Dec 10, 2005) (10 pages) doi:10.1115/1.2166118 History: Received April 10, 2005; Revised December 10, 2005

This paper investigates the nonlinear dynamics of a symmetric isotropic rectangular laminated structure by using the method of weighted residuals with total energy conservation. We obtain the equation of motion in a decoupled form Duffing equation for the laminate deflection subject to both thermal and mechanical loading while confined in a mixed boundary condition of simply supported and clamped edges at the boundaries. The Duffing equation incorporates both the steady-state and transient state for the in-plane and transverse thermal fields, which allows for investigation of the thermal field influence on the laminate buckling and vibration behaviors.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

The laminate (dimension 154×154×1.54mm)

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Figure 2

The Duffing equation modal parameters with respect to the aspect ratio for SSCC. (a) The natural frequency without thermal effect ωmn. (b) The system frequency with the in-plane thermal effect ωmnT with Tmno=65°C. (c) The Duffing equation stiffness rmn. (d) The Duffing equation thermal load qmnT with Tmn1=10°C.

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Figure 3

SSCC resonance with a steady-state temperature rise T110=65°C and T111=10°C. (a) Modal frequency response with and without the in-plane thermal effect. (b) Velocity-deflection diagram at resonance k=1 with thermal effect.

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Figure 4

Intermittency chaos with a steady state in-plane temperature rise. (a) Temporal response with T110=130°C and T111=10°C, ω=3ω110. (b) Velocity-deflection diagram with T110=130°C, and T111=10°C, ω=3ω110.

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Figure 5

Thermal vibration with a transient in-plane temperature decline in heat conduction. T0=T110exp−λt, λ=100, T110=65°C, and T1=T111cos(kω11), k=2, T111=−10°C. (a) Temporal response. (b) Velocity-deflection diagram.

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Figure 6

Instability in thermal vibration with a transient in-plane temperature rise in heat conduction, with T0=T110exp−λt, λ=−100, T110=65°C, and T1=T111cos(kω11), k=2, T111=10°C. (a) Temporal response. (b) Velocity-deflection diagram.

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Figure 7

Oscillation transition subject to thermal and mechanical load. (a) Instability with a transient temperature rise with T0(t)=T110exp−λt, λ=−100, T110=65°C, and T1(t)=T111cos(kω11t), k=2, T111=10°C, Q11=24N∕cm2. (b) Phase diagram with a transient temperature rise with T0(t)=T110exp−λt, λ=−100, T110=65°C, and T1(t)=T111cos(kω11t), k=2, T111=10°C, Q11=12N∕cm2. (c) Quasiperiodic oscillation with a transient temperature decline T0(t)=T110exp−λt, λ=100, T110=65°C, and a constant external and thermal load Q11=24N∕cm2. (d) Intermittency chaotic oscillation with a steady state temperature rise T110=130°C and T1(t)=T111cos(kω11t), k=3, T111=−10°C, and an external load Q11=2.4N∕cm2.




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