Nonlinear thermo-fluid–structure interactions of two interacting flexible cantilever plates in a differentially heated cavity

This study investigates the thermo-fluid–structure interaction dynamics of two flexible cantilever plates in a two-dimensional differentially heated square cavity. A fully coupled fluid–structure interaction framework resolves the interplay between buoyancy-driven convection, vortex dynamics, and structural deformation. The effects of Rayleigh number (Ra), geometric confinement, structural asymmetry, and plate thermal boundary conditions on nonlinear bifurcation behavior are systematically examined. The results show that the coupled system remains in a stable steady state at low Ra, while increasing thermal forcing produces self-sustained periodic oscillations, followed by amplitude-modulated multi-frequency dynamics and, at high Ra, a chaotic response supported by a positive largest Lyapunov exponent. For symmetric fixed-cavity configurations, decreasing the inter-plate spacing narrows the flow passage and increases the plate length and structural compliance. Fixed-flexible-span control calculations reveal a non-monotonic dependence on tip-to-tip distance (Ds), showing that the earlier instability of smaller-gap configurations cannot be attributed to geometric confinement alone. Structural asymmetry redistributes hydrodynamic forcing between the plates and suppresses synchronized motion; however, its influence is non-monotonic, with the intermediate asymmetric configuration producing the strongest structural response. Plate thermal boundary conditions also strongly affect the route to unsteadiness. Adiabatic, cold-isothermal, strongly cooled, and heated plates exhibit distinct transitions between regular and chaotic responses, with representative chaotic states supported by positive largest Lyapunov exponents. The mean upper-wall Nusselt number increases with Ra, while its temporal fluctuations become pronounced in the irregular high-Ra regime. Overall, variations in plate geometry and thermal condition provide practical means of modifying the nonlinear response of confined natural convection systems.