FURTHER-STUDIES ON THE VIBRATION OF PLATES WITH CURVED EDGES, INCLUDING COMPLICATING EFFECTS

The Ritz method is used to obtain an eigenvalue equation for the free vibration of a class of thin, flat plates which involve curved boundar ies defined by polynomial expressions. The class of plates is such tha t each plate may be discretized into four 90-degrees sectorial element s allowing it to have up to four sections of outer boundary and up to four sections of inner boundary, each described by polynomials. In the absence of symmetry, or where it is not utilized, the elements are jo ined together through the use of very stiff translational and rotation al springs which enforce the required continuity conditions. A number of complicating effects have been included, such as the presence of in ternal point or line supports, concentrated masses, and stepped thickn ess geometry. Natural frequency parameters are given for several plate s for which comparison results exist and the accuracy of the approach demonstrated. Results are also given for several plates of varying com plexity which have not previously been treated in the open literature.