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
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 2

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

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
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.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In