FREE-VIBRATION OF AN L-SHAPED PLATE - THE GENERAL-SOLUTION AND AN EXAMPLE OF A SIMPLY-SUPPORTED PLATE WITH A CLAMPED CUTOUT

This study develops a new accurate method for finding the natural vibr ations frequency of plates with cutouts. The method is based on replac ing the plate with a cutout by a rectangular plate. This is achieved b y filling the cutout with a ''dummy'' plate made of the same material, and of the same thickness as the original from which it is separated by an infinitesimal gap. Thanks to this device it is possible to apply finite Fourier transformation of discontinuous functions in a rectang ular domain. The expression for the deflection now depends on the unkn own quantities along the boundary and across the gap. Subsequent appli cation of the available boundary conditions leads to a system of bound ary integral equations. An L-shaped plate simply supported along the p erimeter and fixed along the cutout, is analyzed as an example. The fr equencies of natural vibration are calculated and compared with the re sults obtained using the finite element method. The method presented h ere is also applicable to two- and three-dimensional problems of solid s with holes or cavities and to similar thermoelastic problems. Applic ation to plates with curved boundaries is also possible.