VIBRATION OF SHALLOW SHELLS WITH 2 ADJACENT EDGES CLAMPED AND THE OTHERS FREE

Considerable information is available in the published literature on t he free vibration frequencies and mode shapes of rectangular flat plat es having two adjacent edges clamped and the other two free. However, no results appear to have been published previously for shallow shells having such edge conditions. The present work uses the Ritz method wi th displacement components in the form of algebraic polynomials to obt ain accurate frequencies. Frequencies are determined for the first eig ht modes of shallow shells having spherical, cylindrical, and hyperbol ic paraboloidal curvatures and square planforms. Beginning with the pl ate, the curvatures are incrementally increased in each case to the li mits of shallow shell theory. Data are presented for moderately thin a nd thicker shells, Contour plots of the corresponding mode shapes are shown for some of the more interesting configuration.