Numerical experiments on dynamic stiffening of beams and plates

By introducing continuous or discontinuous variations in the thickness of beams, arches and plates, it is possible in many practical situations to raise the value of the fundamental frequency and, at the same time, to lower the weight of the structural element. This is a beneficial situation, especially in those cases where weight reduction and large dynamic stiffness are of interest. The present paper surveys some recent practical accomplishments in this area.The rigorous procedure consists, from a general structural optimization viewpoint, of minimizing an objective function (for instance, total volume) subject to constraints on the geometry and behavior (natural frequencies, buckling loads, etc.). In many instances it is convenient to reverse the problem: one fixes or limits the weight or volume and constructs some quantity which describes the desired behavior of the system e.g. the fundamental frequency.The problems under study in the present paper are considerably more modest in scope, since the procedure is performed by numerical experiments.