Optimal location of a cutout in rectangular Mindlin plates for maximum fundamental frequency of vibration

Abstract.

This brief note presents an effective numerical technique for determining the optimal location of a cutout in rectangular Mindlin plates for maximum fundamental frequency of vibration. Instead of adopting the widely-used finite element method for the vibration analysis, we propose that the Ritz method be employed as the latter method avoids the need to remesh and redefine connectivity for a perforated plate at every iteration step of the optimization procedure. The location of a cutout, of a given shape and size, is specified by the coordinates of the geometric centre of the cutout. The optimal values of these coordinates are determined using the Generalized Reduced Gradient (GRG) method. To demonstrate the method, optimal locations of circular and square cutouts in square plates are determined. The sensitivity of the fundamental frequency to the location of the cutout is also investigated.