Vibration of annular sector plates from three-dimensional analysis

Accurate three-dimensional elasticity solutions are presented for the free-vibration analysis of annular sector plates with arbitrary (but continuous) boundary conditions. The Ritz procedure is used to minimize the integral energy functional, which is formulated in a cylindrical polar coordinate system, in the derivation of the governing eigenvalue equation. The vibratory characteristics of annular sector plates with variations in boundary condition, sector angle, and thickness are examined. The accuracy of the method is validated through appropriate convergence and comparison studies. The first known results presented here provide a basis for understanding the physics of vibrations of annular sector plates and can be used to assess numerical results obtained from various refined two-dimensional theories. © 2001 Acoustical Society of America.