Stochastic Optimization for Vibrational Systems of Multi-degrees of Freedom

A prohahilistic approach to design variables optimization of mechanical systems of multi ~ degrees of freedom is presented. The proposed method is based on the mathematical modelling of the systems, Optimization is understood as a calculation of the mean values and standard deviations of the random parameters chosen from the set of all design variables, which in the feasible domain minimize the objective function. Feasible domain is defined by probabilistic constraints. The method is illustrated on the optimization of torsinal discrete linear system parameters and applied to the design of dynamic absorber. The optimal standard de viations of the random design parameters are obtained as well as the optimal mean values. The numerical rem suits are compared with those ohtained by deterministic optimization. In addition, effects of the standard deviations of the random design variables on the results of the optimization are also discussed. INTRODUCTION Structural optimization has made remarkable progress in recent years and it is now recognized as a practical design tool. Deterministic optimization has heen successfully applied to a large range of structural prohlems[“. Hcwever, because of the properties of the eigineering materials, manufacturing and installing errors. the structural parameters of the complex strum tures are random. The produced structures will have uncertain dynamic characteristics. So, the structural problems are often non deterministic, and consquently, decisions must be made in the presence of uncertainties. That give birth. in the last one two decades, to systematic procedures for decisions making under uncertainties, through the concept of reliability. A formulation suggested by Charnes and Coop@‘, in which the stochastic optimization problem is converted into an equivala~t deterministic optimize-~ tion, is known as the chance constraint programming technique. The idea hehind this techniqw is to express the constraints, associated with the structural safety. in terms of the probabilities of violating the corre spending constratints of the deterministic optimization problem. Other applications of the same approach can he found in Ra+“, Rae showed that the weight of a structure which constituted the deterministic problem WE satisfied with a higher probability. The chance constraint programming technique hased on reliability has been also applied to design some frame structures such as platforms (Theft ~ Christenswl and Murotsuc5j) L. Prasek and V. Zeman‘61propos?d a stochastic optimization technique for dynamic mechani-