Vibrations of rectangular plates
Ballal, Bhalchandra Y
Veletsos, Anestis S.
Master of Science
In this thesis, numerical data is presented for the natural frequencies of vibrations of rectangular plates of uniform thickness having all possible combinations of simply supported, fixed and free edges. A vide range of side ratios and Poisson's ratios are considered and the results are presented in the form of tables and graphs. The solutions for plates with two opposite edges simply supported are obtained by employing Levy's Method and those for plates having two opposite edges not simply supported are obtained by employing Rayleigh-Ritz, procedure using the natural modes of vibrating beams as approximating deflection functions of the plates. The first six natural modes of clapped-clamped and free-free beams and the first five natural modes of clamped-free beams were used in the analysis. Some results are also presented for plates with two opposite edges simply supported and the others supported on flexible beams. All the data is based on the ordinary theory of flexure of plates which neglects the shear deformation and rotatory inertia.