Chaotic motion of a bimetallic circular plate

Considering the effect of geometric nonlinearity and uniformly distributed time-varying temperature, the bifurcation behaviors and chaotic phenomena of a bimetallic thin circular plate are investigated. First of all, the nonlinear dynamic equation for bimetallic plate is established and further reduced to Duffing equation of harmonic parametric excitation, from which the pitchfork bifurcation problem is discussed. Secondly, the critical conditions for occurrence of homoclinic and subharmonic bifurcations as well as chaos are studied theoretically by means of Melnikov function method. Finally, the chaotic motions are searched and simulated numerically with the application of Computer Algebra Systems Maple, and the Poincaré map and phase portrait are used to evaluate if a chaotic motion appears. The results indicate that there exist some chaotic motions in a heated bimetallic plate.