X-Ritz Solution for Nonlinear Free Vibrations of Plates with Embedded Cracks

Abstract

The analysis of large amplitude vibrations of cracked plates is considered in this study. The problem is addressed via a Ritz approach based on the first-order shear deformation theory and von Kármán’s geometric nonlinearity assumptions. The trial functions are built as series of regular orthogonal polynomial products supplemented with special functions able to represent the crack behaviour (which motivates why the method is dubbed as eXtended Ritz); boundary functions are used to guarantee the fulfillment of the kinematic boundary conditions along the plate edges. Convergence and accuracy are assessed to validate the approach and show its efficiency and potential. Original results are then presented, which illustrate the influence of cracks on the stiffening effect of large amplitude vibrations. These results can also serve as benchmark for future solutions of the problem.