NATURAL FREQUENCIES OF VARIABLE THICK NESS BEAMS AND PLATES

摘要

Use of the perturbation method for approximating the fundamental frequencies and mode shapes of variable thickness, simply supported, square plates was expanded to include more specific problems such as higher order frequencies and mode shapes; the discretely stiffened beam and plate; and the simply supported, stepped plate. Perturbation theory is dependent upon representing the thickness of the plate as a continuous function with continuous first derivatives. This presents a problem in using the perturbation method for the discretely stiffened beam and plate, since the area of the stiffener is generally small in comparison to the overall area of the plate, and a reasonable approximation for the combined thickness is difficult to model mathematically as a continuous function. To satisfy these conditions a truncated Fourier series was used to approximate the thickness.