Exact free vibration study of rectangular Mindlin plates with all-over part-through open cracks

Based on Mindlin plate theory (MPT), a set of exact closed-form characteristic equations incorporating shear deformation and rotary inertia are proposed for the first time to analyze free vibration problem of moderately thick rectangular plates with an arbitrary number of all-over part-through cracks. The proposed rectangular plates have two opposite edges simply supported while six possible combinations of free, simply supported and clamped boundary conditions are taken into account for two other edges. The crack is assumed to be open, non-propagating and perpendicular to two opposite simply supported edges. A continuously distributed line-spring model is used to describe the elastic behavior of an all-over part-through crack. The accuracy of the current approach is investigated through comparing the present exact natural frequencies with those of 3D finite element method obtained by ABAQUS software package. A parametric study is undertaken to show the effect of crack depth, crack location, number of cracks and thickness-to-length ratio on natural frequencies of rectangular moderately thick plates with different boundary conditions in tabular and graphical forms. Finally, the effect of shearing and tearing modes on the modeling of cracks located at the nodal line is shown.