The influence of corner stress singularities on the vibration characteristics of rhombic plates with combinations of simply supported and free edges
This study is devoted to an accurate calculation of flexural eigenvibrations of elastic rhombic plates whose individual sides are either simply supported or free, respectively (five combinations are considered). It is shown that the occurring stress singularities at two opposite corners with obtuse angles become significant for the solution for highly skewed plates. Therefore the authors use in the numerical approximation (based on the Ritz method) as admissible functions, in addition to the complete algebraic polynomials, the so-called ``corner functions'' which account for the stress singularities and are shown to accelerate the solutions essentially. Detailed results for eigenfrequencies and mode shapes are presented for illustration.
scientific article; zbMATH DE number 1389043