Nonlinear flutter of 2D variable stiffness curvilinear fibers composite laminates by a higher-order shear flexible beam theory with Poisson’s effect

•Studied the large amplitude flutter behaviour of 2D variable stiffness laminated composite panels with curvilinear fibres.•Integrated beam model with modified constitutive equations due to Poisson's effect in dynamic analysis of general laminates.•Shown limit cycle oscillation effect on flutter boundaries considering geometric nonlinearity and by eigenvalue analysis.•Curvilinear fibre angles in the variable stiffness laminate affect visibly the flutter region with vibration amplitude.•Analysis made layer with straight/curvilinear fibres based on the flutter boundaries forms a benchmark for other studies. In this work, the nonlinear supersonic panel flutter characteristics of two-dimensional variable stiffness curvilinear fibres based laminated composite panels are studied using a higher-order shear flexible theory represented by sine function coupled with first-order approximation leading to quasi-aerodynamic theory. The structural formation takes care of geometric nonlinearity with von Karman’s assumptions. The beam constitutive equation is modified for the laminated beam with general lay-up by accounting for Poisson’s effect. The nonlinear dynamic equilibrium equations developed by Lagrangian equations of motion are solved using finite element approach in conjunction with the direct iterative solution procedure. For limit cycle oscillation, critical dynamic pressure is predicted iteratively through eigenvalue analysis, thereby identifying the first coalescence of vibrational modes. Also, the flutter behavior of two-dimensional panel under static differential pressure is investigated considering nonlinear static equilibrium position of panel obtained by Newton-Raphson’s iterative approach and then followed by modes coalescence approach. These solution procedures are tested against the results in literature. A thorough numerical investigation is done to show the effect of the curvilinear fiber path orientation, limited cycle amplitude, static differential pressure, panel thickness, panel end condition flexibilities and thermal environment on the nonlinear supersonic panel flutter of two-dimensional variable stiffness laminated panels.