Six-Mode Interaction of Panel Flutter With Joint Relaxation Deterministic Analysis

The influence of boundary conditions relaxation on two-dimensional panel flutter is studied in the presence of in-plane loading. The boundary value problem of the panel involves time-dependent boundary conditions that are converted into autonomous form using a special coordinate transformation. Galerkin’s method is used to discretize the panel partial differential equation into six nonlinear ordinary differential equations representing the first six modes. The influence of boundary conditions relaxation on the panel modal frequencies and limit cycle amplitudes in the time and frequency domains is examined through the spectrogram of the generalized coordinate for each mode. The relaxation and system nonlinearity are found to have opposite effects on the time evolution of the panel frequency. Depending on the system damping and dynamic pressure, the panel flutter frequency can increase or decrease with time as the boundary conditions approach the state of simple supports. Bifurcation diagrams are generated by taking the dynamic pressure and relaxation parameter as control parameters. They reveal different regions of periodic, quasi-periodic, and chaotic motions. These regions take place only when the in-plane load exceeds the Euler buckling load.