Hybrid Optimization and Anti-Optimization of a Stochastically Excited Beam

Random vibrations of the damped Bernoulli–Euler beam with two supports and subjected to a stationary random excitation are studied. The supports are symmetrically placed with respect to the middle cross-section of the beam. We investigate the mean square displacement of the beam with the goal of determining the optimum location of supports in order to minimize the maximum probabilistic response. This study falls in the category of hybrid optimization and anti-optimization, since we are looking for the worst maximum response, constituting the anti-optimization process; subsequently, we are looking for optimization of the structure to make the maximum response minimal by properly the spacing supports.