The effects of in-plane loading on vibration and buckling of the grooved plates

This paper presents an analytical study on the influence of in-plane forces on the dynamic characteristics of a plate with grooves in different sizes. A sub-structuring approach, the reverse receptance method, is applied to solve the eigenvalues of an in-plane forces loaded plate with two parallel grooves and two orthogonal grooves, respectively. On considering coupling and interaction between two orthogonally connected grooves, the point receptance arrays are employed. Accuracy is evaluated by comparing the analytical solutions with numerical results obtained from the finite element model.Parametric study reveals, the deeper the groove, the lower the natural frequencies and buckling loads of the grooved plate will be. With in-plane tensions applied and increased linearly, the grooved plate is stiffened gradually and its natural frequencies increase accordingly. With equal bi-axial tensions, the natural frequencies of the grooved plates increase twice as much as those with uni-axial tension do. With in-plane compressive forces on the plate, the situations are reversed. The lowest natural frequency of a grooved plate with sufficient tensions can be higher than that of a non-grooved unloaded plate. When the groove size and the loading condition are the same, the orthogonal grooves decrease the natural frequencies and the buckling loads of a plate more than the parallel grooves do. The in-plane forces do not affect the mode shapes of the grooved plate; but the grooves do.The analytical evaluation demonstrates the accuracy and applicability of the proposed approach.

► Reverse receptance method solves natural frequencies and buckling loads of grooved plates with in-plane loads.
► In-plane tensions stiffen a grooved plate and increase its natural frequencies.
► In-plane compressions weaken a grooved plate and decrease its natural frequencies.
► Neither the in-plane tensions nor the in-plane compressions affect the mode shapes of the grooved plate.
► The orthogonal grooves reduce the natural frequencies and the buckling loads of the plate more than the parallel grooves do.