Ritz-Legendre approach for capturing the mode jumping phenomena in variable-stiffness composite fuselage panels

In this work, a semi-analytical model is proposed for addressing the mode jumping phenomenon in variable-stiffness composite fuselage panels. The Ritz approach is implemented for obtaining the analytical geometrically nonlinear response. A composite skin is modelled using the von Kármán strain–displacement relationships. Legendre orthogonal polynomials are adopted for defining the displacement field. The panel is loaded in two consecutive steps. In the first step the panel is loaded by pressure and in-plane tensile loads leading to an initial mode shape. In the second step, the panel is loaded by an in-plane axial compressive load which triggers an abrupt mode-shape change in the initial mode resulting in a mode jumping event. In order to investigate the effects of the stiffness variation on the mode jumping response, the fibre orientation angles are varied along two main directions, perpendicular and parallel to the direction of the load that causes the mode jumping. The accuracy of the semi-analytical results is verified using Abaqus. It is demonstrated that the mode jumping of the variable-stiffness laminates can be captured successfully. It is concluded that by varying the stiffness, the configuration of the mode after jumping can be tailored and its occurrence can be delayed.