NATURAL FREQUENCIES FOR CANTILEVERED DOUBLY-CURVED LAMINATED COMPOSITE SHALLOW SHELLS

The Ritz method with algebraic polynomial displacement functions is used to analyze free vibrations of thin cantilevered laminated plates and shallow shells having rectangular planforms. Convergence studies are made which demonstrate that accurate results are obtained using 192 displacement terms for spherical, circular cylindrical, hyperbolic paraboloidal shallow shells and 64 terms for plates. Results are compared with those obtained experimentally and by finite element methods. It is found that the present method needs considerably less degrees of freedom than the finite element method to obtain the same accuracy and compares well with results from experiment. The effect of various parameters (material, number of layers, fiber orientation, curvature) upon the frequencies is studied.