Chaotic Behavior of a Symmetric Laminate With Transient Thermal Field

[+] Author and Article Information
Xiaoling He

 University of Wisconsin, 3200 N Cramer Street, P. O. Box 784, Milwaukee, WI 53201xiaoling@uwm.edu

J. Vib. Acoust 128(4), 429-438 (May 27, 2005) (10 pages) doi:10.1115/1.2128646 History: Received August 03, 2004; Revised May 27, 2005

A symmetric isotropic laminate in a simply supported boundary condition is analyzed for its nonlinear dynamic response subjected to a nonuniform transient thermal field. The equation of motion of a modified Duffing type in a decoupled modal form is obtained for both orthotropic and isotropic symmetric laminate from the reduction of the governing equation of motion by using a Galerkin-type method. Thermally induced nonlinear response and thermal mechanically induced response are investigated in a multimode analysis. The influence of the transient thermal field is found to cause drastically different modal response from that due to the steady-state thermal field. Chaos is found being induced by the transient in-plane thermal field, or by both transient in-plane and transverse thermal fields. Unique bifurcation behavior is observed with different thermal frequencies. Different loading levels can cause transition between chaos and quasi-periodic oscillations.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 2

Modes I and II thermal frequency response: (a) j=[010] and (b) j=[0100]

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Figure 3

Mode-I Poincaré map subject to a constant transverse thermal load. (a) j=3, N=50, T=8.6ms; and (b) j=2, N=1000, T=18μs.

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Figure 4

Mode-II response subject to a constant transverse thermal load. (a) Temporal response at j=2, k=0, t=0.1s, and (b) Phase diagram at j=1, k=0, t=0.1475s.

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Figure 5

Mode-I response with both in-plane and transverse transient thermal sources. (a) Temporal response at j=1, k=1.8, and (b) Phase diagram at j=3, k=2

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Figure 6

Frequency response. (a) Mode-II thermal mechanical response with k=[010], j=0, 3,4,5,6,7, Q=2.4N∕cm2, and (b) Mode-I thermal response, k=[0100], j=0,1,2,3,7, Q=0.

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Figure 7

Mode-II transition with constant load in thermal mechanical response Qmn=Q+QmnT. (a) j=2, k=0, Q=2.4N∕cm2, and (b) j=2, k=0, Q=0N∕cm2.

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Figure 8

Mode-II transition with constant external load Qmn=Q+QmnTcos(kω12t). (a) j=2.2, k=1, Q=0, (b) j=2.2, k=1, Q=0.24N∕cm2, and (c) j=2.2, k=1, Q=24N∕cm2

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Figure 9

Transition with harmonic load in thermal mechanical response Qmn=(Q+QmnT)cos(ωt),ω=kωmn. (a) Mode I with j=3, k=2, Q=0.048N∕cm2, (b) Mode II with j=3, k=2, Q=0.048N∕cm2, and (c) Mode II with j=3, k=2, Q=19.2N∕cm2.




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