Refined models for free vibration analysis of elastic plates with part-through surface cracks

Abstract

In this paper, two refined models are proposed for the vibration analysis of isotropic and orthotropic thin plates with part-through surface cracks. The governing equations of cracked plates are formulated via the refined models. Like in the conventional model, crack terms are incorporated in the governing equations. All-over and finite-length cracks (i.e., central and edge cracks) can be directly handled by the new models and their modified forms, respectively. The matched interface and boundary method is then applied to formulate eigenvalue equations. A series of parametric studies for investigating the effects of crack depth and crack length are presented. Numerical results of the proposed models are compared with the existing and finite element solutions to validate their performance and accuracy. The salient feature of the refined models is to complement the deficiency of the conventional model for the analysis of crack depth problems. Several illustrative examples are provided to demonstrate the superior performance of the refined models over the conventional one. The present models are effective for predicting the natural frequencies of thin plates with part-through surface cracks.