VIBRATION ANALYSIS OF CANTILEVERED SHALLOW SHELLS WITH TRIANGULAR AND TRAPEZOIDAL PLANFORMS

Abstract The Ritz method with algebraic polynomials is used to present the first known natural frequencies for cantilevered shallow shells having triangular and trapezoidal planforms. Detailed convergence studies showed that relatively accurate results can be obtained. Comparisons with experimental and analytical frequencies available in the literature for cantilevered triangular plates are made. These comparisons show that the present method is superior to many other analytical methods used previously in plate vibration analysis. The lowest six frequencies are then obtained for various sets of shapes and curvatures of right triangular and trapezoidal thin shallow shells.