Effects of constraint, circular cutout and in-plane loading on vibration of rectangular plates

The paper studies the influences of boundary conditions, cutouts and in-plane loading on the vibration of a rectangular plate with a circular hole. To study the interactions between the plate and the hole, the receptance approach is adopted. While a receptance reduction is used at the plate–hole interface, a receptance addition is used for the plate stiffeners at the clamped edge.The study shows that for a free-edge hole, a minimum value of the first natural frequency exists, corresponding to a critical radius of the hole, regardless of the plate boundary constraints. However, a similar result is only found when the edges of the plate and the cutout are both simply supported. Plates with other types of constraints show a monotonically increasing frequency as the radius of the hole is increased. This information can be used by designers while engineering rectangular plates with stiffened circular cutouts.Parts of the analytical results are verified by the finite element solutions. It shows that the receptance approach, both addition and reduction, provides a convenient tool with adequate accuracy for this type of vibrational studies.

► Reverse receptance method solves the natural frequencies of plates with cutouts with adequate accuracy.
► A minimum first natural frequency corresponding to a critical radius of a free hole on a constrained plate.
► In-plane tensions compensate the lost stiffness of the plate due to cutouts.
► The constraints on the edges of the cutouts affect the mode shapes of the plate.