A reverse receptance approach for analysis of vibration of grooved plates

A reverse receptance approach is proposed to solve eigenvalues of a plate with two orthogonally connected through grooves, two parallel through grooves and two parallel internal grooves. The procedure is a modification of the well-known receptance method commonly used to study vibrations of combined structures. In the present paper, vibrations of rectangular plates with grooves in different sizes and boundary conditions are studied analytically to illustrate the approach. A through groove is simulated by a simply supported beam, while an internal groove is simulated by a free–free beam. The accuracy is evaluated by comparing the percent differences between the natural frequencies solved using the reverse receptance method and the standard finite element method.It is verified that the reverse receptance method with both force and moment connections at the interface of each plate–groove pair and with sufficient interaction points is adequate and accurate for solving vibration characteristics of a plate with either through or internal grooves. Parametric study reveals that the percent differences are directly proportional to the length, the width and the depth of the grooves on the plate. It is found that, for good accuracy, the groove width should not exceed 3.6% of the plate width, while the groove depth should not exceed half of the plate thickness. This report demonstrates the potential of reverse receptance concept in the engineering practice of machine design, as a simple numerical or analytical approach to study dynamics of structures with complex geometries.