Transverse vibrations of simply supported orthotropic rectangular plates with rectangular and circular cut-outs carrying an elastically mounted concentrated mass

Practicing a hole or an orifice through a plate or a slab constitutes a very frequent engineering situation due to operational reasons imposed on the structural system. From a designer\'s viewpoint it is important to know the effect of this modification of the mechanical system upon its elastodynamic characteristics. The present study deals with the determination of the lower natural frequencies of the structural element described in the title of the paper using a variational approach and expressing the displacement amplitude of the plate in terms of the double Fourier series which constitutes the classical, exact solution when the structure is simply supported at its four edges.