Natural frequencies of stiffened rectangular plates

The natural frequencies of the first symmetric and first antisymmetric modes of a simplysupported rectangular plate are determined. The plate is reinforced by a single integral stiffener placed along one of its centre lines, the dimensions of the plate and stiffener cross-section being chosen so that the mass of the plate-stiffener combination remains constant. Two forms of stiffener cross-section are studied, namely, rectangular sections and T-sections. The ratio (frequency of stiffened plate/frequency of unstiffened plate of equal mass) is determined by the Ritz method using a two-term solution, for a wide range of ratios of ( a/b ) and (stiffener depth/plate thickness). The frequencies obtained by the Ritz method for the symmetric mode are compared with those found from the exact solution and are found to agree closely. The results show a maximum increase in frequency for the symmetric mode of about three times, whereas the frequency of the antisymmetric mode is generally lower than that of the unstiffened plate. An increase in the symmetric mode frequency and a decrease in the antisymmetric mode frequency, makes it possible for both modes to possess equal frequencies for a particular ( a/b ) ratio and a certain size of stiffener.