Vibration of annular sector mindlin plates with internal radial line and circumferential arc supports

Abstract

An energy approach is presented for the free vibration analysis of thick annular sector plates with internal line/arc supports. This has been a topic of practical interest, but there appears to have been no previous work reported. Based on the stationary energy principle and the recently proposed pb-2 Rayleigh-Ritz method, the governing eigenvalue equation is derived for internally supported thick annular sector plates of different radii, relative thickness ratios, sector angles, and with various end conditions along the radial and circumferential edges. The proposed solution algorithm involves (1) sets of mathematically complete two-dimensional polynomials (p - 2) used as the admissible displacement and rotational functions, and (2) a basic function (b) formed from the piecewise expressions for the boundary and internal line/arc supports. These functions automatically satisfy all the kinematic boundary conditions of the four edges and internal supports. The numerical procedure has been demonstrated by several example plate problems. Convergence and comparison studies for simple examples are used to verify the accuracy of the present method.