Free vibrations analysis of cracked variable stiffness composite plates by the eXtended Ritz method

Variable stiffness composite laminates show advantageous structural features related to their enlarged design space. They are attractive candidates for advanced engineering applications where the assessment of static and dynamic behavior and strength in the presence of cracks is often required. In the present work, a single-domain extended Ritz formulation is proposed to study the free vibrations of cracked variable stiffness composite plates. The plate model is based on the first-order shear deformation theory whose primary variable, i.e. displacements and rotations, are approximated via a set of orthogonal polynomial trial functions enriched with a set of special crack functions. These functions are able to inherently account for crack opening and crack tip singular fields. The plate governing equations are deduced by the stationarity of the energy functional and the formulation has been implemented in a computer code. The method has been validated by comparing the present results with literature solutions for cracked isotropic plates and uncracked variable stiffness plates as, to the best of author's knowledge, no data on cracked variable stiffness plates free vibrations are available. An explicative and representative study on the free vibrations of variable angle tow composite laminates is finally presented with the aim of illustrating the approach capabilities, providing benchmarck results and identifying distinctive features and opportunities of the variable stiffness concept for the design of advanced damage tolerant structures.