Chaotic Motion of a Heated Double-Layer Thin Circular Plate
Wang Yonggang(1),Ding Daohong(1),Dai Shiliang(2),Wang Xinzhi(3)
(1 Department of Applied Mechanics, China Agricultural University, Beijing 100083, China)
(2 Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China )
(3 School of Science, Lanzhou University of Technology, Lanzhou 730050, China)

Abstract: Considering the effect of geometric nonlinearity and uniformly distrib uted stationary temperature, the chaotic phenomena of a double-layer thin circular plate under transverse periodic excitation are investigated. The nonlinear dynamic equations for the double-layer plate are established by employing the Galerkin's technique, then the critical condition for occurrence of chaotic motions is discussed theoretically with Melnikov function method. The chaotic motions are searched and simulated numerically for a driving membrane of thermal actuated micropump via Computer Algebra Systems Maple, and the Poincaré map and phase curve along with Lyapunov exponent are used to evaluate if a chaotic motion appears. The results indicate some complex chaotic motions in the heated double-layer plate.
Keywords: double-layer plate, stationary temperature, Melnikov-function, chaotic motion, Poincaré map, Lyapunov exponent.