A Coupled Motion of the Thermally Induced Fluid Convection and the Membrane Motion

Abstract

The present study formulates a model for a coupled oscillation of the convective flow and the solid membrane vibration, which occurs in a 2D domain of a fluid cell. The convection flow is induced by the transient thermal field of the membrane at the bottom of the fluid. The heat conduction in the solid material also causes the membrane to vibrate. This flow motion deviates from the conventional Rayleigh–Benard problem in that a transient thermal field causes the convection flow instead of a constant temperature gradient. A numerical computation reveals the synchronized motion behaviors between the Lorenz-type oscillator for the convection flow and the Duffing oscillator for the membrane motion. The bifurcation conditions from the stability analysis of the model justify the steady-state attractor behaviors and the difference in behavior from the oscillators without coupling.