Investigation of nonlinear aero-elastic of isotropic cracked plate in supersonic flow

In the present study, an analytical model was presented for investigating the nonlinear aero-elastic response of cracked plate in supersonic flow. In this context, two-dimensional equations of cracked induced isotropic plate were proposed considering pure bending loading and simply support boundary condition. To form this equation, plate modeling based on the classical plate theory (CPT) and the von-Karman nonlinear relations. Also, the Line-Spring Model (LSM) and linear piston theory were considered for crack location and aerodynamic effect, respectively. Applying the Galerkin's method and plate assume modes, the partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs). Then, by using Runge-Kutta numerical solution method, these equations (PDEs) were solved and the results were investigated. Eventually, some of effective aero-elastic parameters like flow condition and crack size were prescribed within the limit cycle oscillation (LCO) in flutter status. Results demonstrate that the presence of crack was leading early flutter, increasing the maximum amplitude of the limit cycle oscillations and aero-elastic instability that can ultimately reduce the structural performance.