Non-linear vibrations and stability of a periodically supported rectangular plate in axial flow

In the present study, the geometrically non-linear vibrations of thin infinitely long rectangular plates subjected to axial flow and concentrated harmonic excitation are investigated for different flow velocities. The plate is assumed to be periodically simply supported with immovable edges and the flow channel is bounded by a rigid wall. The equations of motion are obtained based on the von Karman non-linear plate theory retaining in-plane inertia and geometric imperfections by employing Lagrangian approach. The fluid is modeled by potential flow and the flow perturbation potential is derived by applying the Galerkin technique. A code based on the pseudo-arc-length continuation and collocation scheme is used for bifurcation analysis. Results are shown through bifurcation diagrams of the static solutions, frequency-response curves, time histories, and phase-plane diagrams. The effect of system parameters, such as flow velocity and geometric imperfections, on the stability of the plate and its geometrically non-linear vibration response to harmonic excitation are fully discussed and the convergence of the solutions is verified.