Vibrations of mindlin sectorial plates using the ritz method considering stress singularities

Abstract

This paper reports very accurate vibration frequencies of moderately thick sectorial plates with various boundary conditions and vertex angles (alpha = 90 degrees, 180 degrees, 270 degrees, 300 degrees, 330 degrees, and 355 degrees) based on Mindlin plate theory, and provides the nodal patterns of their vibration modes for the first time in the published literature. Most of the extensive frequencies presented are exact to the four digits shown. The classical Ritz method is employed, using corner functions and algebraic trigonometric functions as the admissible functions. Because the corner functions properly describe the singularity behaviors of moments and shear forces in the vicinity of the vertex of a sectorial plate, they substantially enhance the convergence and accuracy of the numerical results, which is shown by convergence studies.