TY - GEN
T1 - Stability and bifurcations in a model of phase transitions with order parameter
AU - Sikora, Janusz
AU - Cusumano, Joseph P.
AU - Jester, William A.
N1 - Funding Information:
The authors gratefully acknowledge the support of this work by the Office of Naval Research, grant # N0014-95-1-0461.
Publisher Copyright:
© 1997 American Society of Mechanical Engineers (ASME). All rights reserved.
PY - 1997
Y1 - 1997
N2 - A one-dimensional model of phase transitions with convex strain energy is investigated within the limits of nonlinear bar theory. The model is a special case of a coupled field theory that has been developed by Fried and Gurtin to study the nucleation and propagation of phase boundaries. The system of governing equations studied here consists of a wave equation coupled to a nonlinear reaction-diffusion equation. Using phase plane methods, the equilibria of the system have been constructed in order to obtain the macroscopic response of the bar and the bifurcation diagram. It is demonstrated that a large number of coexisting spatially periodic, inhomogeneous solutions can occur, with the number of these solutions being inversely proportional to the diffusion coefficient in the reaction-diffusion subsystem. A stability analysis of the equilibria is presented.
AB - A one-dimensional model of phase transitions with convex strain energy is investigated within the limits of nonlinear bar theory. The model is a special case of a coupled field theory that has been developed by Fried and Gurtin to study the nucleation and propagation of phase boundaries. The system of governing equations studied here consists of a wave equation coupled to a nonlinear reaction-diffusion equation. Using phase plane methods, the equilibria of the system have been constructed in order to obtain the macroscopic response of the bar and the bifurcation diagram. It is demonstrated that a large number of coexisting spatially periodic, inhomogeneous solutions can occur, with the number of these solutions being inversely proportional to the diffusion coefficient in the reaction-diffusion subsystem. A stability analysis of the equilibria is presented.
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U2 - 10.1115/DETC97/VIB-4106
DO - 10.1115/DETC97/VIB-4106
M3 - Conference contribution
AN - SCOPUS:85101906694
T3 - Proceedings of the ASME Design Engineering Technical Conference
BT - 16th Biennial Conference on Mechanical Vibration and Noise
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 1997 Design Engineering Technical Conferences, DETC 1997
Y2 - 14 September 1997 through 17 September 1997
ER -