Nonlinear free vibrations of composite structures via the X-Ritz method

The analysis of large amplitude vibrations of thin-walled cracked structures build as plate assemblyis considered in this study. The problem is addressed via a Ritz approach, called X-Ritz, basedon the first order shear deformation theory and von K´arm´an’s geometric nonlinearity assumptions.The trial functions are expressed as series of regular orthogonal polynomial products supplementedwith special functions able to represent the crack behaviour; boundary functions are used to guaranteethe fulfillment of the kinematic boundary conditions. Results are presented, which illustratethe influence of cracks on the stiffening effect due to large amplitude vibrations.