Vibration of circular and annular Mindlin plates with internal ring stiffeners

Abstract

The first-known investigation is reported for free vibration of circular and annular Mindlin plates with intermediate concentric ring stiffeners. The total potential energy functional is first derived for the stiffened circular and annular plates. The Mindlin first-order shear deformation plate theory is used to account for the effects of plate shear deformation and rotary inertia, while the Engesser theory is used to consider the shear deformation and torsional effects in stiffeners. A set of trial functions is proposed for the displacement fields to satisfy the geometric boundary conditions of the plate at outset. Minimizing the energy functional by applying the Ritz procedure, the governing eigenvalue equation is derived. Solving the eigenvalue equation, first-known sets of vibration solutions are obtained for circular and annular Mindlin plates with concentric ring stiffeners. The accuracy of the results is tested using convergence studies. The significant influences of boundary conditions, plate thickness ratio, cut-out ratio and locations of ring stiffeners are highlighted.