Free vibrations of a stiffened rectangular plate

Free vibration of a thin rectangular plate stiffened by an arbitrary number of stiffeners parallel to a pair of its edges and simply supported on all edges, is considered. The equation of motion for the stiffened plate is derived by considering the stiffeners as producing external line loadings on the plate. Dirac delta functions are used to discretely locate these external loadings at the stiffener locations in the equation of motion. Solutions of the equation of motion are obtained from a system of equations of order R x R, where R is equal to the number of stiffeners. Results for the natural frequencies and associated mode shapes are given for square plates stiffened by one, two, three and ten stiffeners and rectangular plates with two stiffeners. In each case, various stiffener flexural rigidities and linear mass densities were considered.