APPLICATION OF THE METHOD OF KANTOROVICH TO THE SOLUTION OF PROBLEMS OF FREE VIBRATION OF SINGLY CURVED RECTANGULAR PLATES INCLUDING THE PRESENCE OF MEMBRANE STRESSES

摘要

The free vibration characteristics of singly curved rectangular plates are studied. The study includes the presence of tensile membrane stresses. The method of Kantorovich is used to reduce Flugge's exact set of partial differential equations to ordinary differential equations. The ordinary differential equations are then solved, consistent with the given boundary conditions, using (a) exact exponential type of solutions, both in complex and real forms and (b) a modified matrix progression method. The results for the cases without inplane stresses are compared with experimental results and results obtained by other authors.