Vibration of plates with sub-structural deduction: a reverse receptance approach

A reverse receptance approach is proposed to find approximate dynamic characteristics of structures with sub-structural deductions. The procedure is a modification of the well-known receptance method commonly used to study vibrations of combined structures. In the paper, vibrations of circular plates with circular central cutouts are studied analytically to illustrate the approach. Numerical results of the frequencies and mode shapes are compared with the available exact solutions and finite element calculations to evaluate the accuracy and the range of applicability. It is found that for a ratio of radii less than 0.3, the errors of approximate solutions are generally less than 1%. The analytical study demonstrates the potential of the 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.