Application of Three Bioinspired Optimization Methods for the Design of a Nonlinear Mechanical System

The present work focuses on the optimal design of nonlinear mechanical systems by using heuristic optimization methods. In this context, the nonlinear optimization problem is devoted to a two-degree-of-freedom nonlinear damped system, constituted of a primary mass attached to the ground by a linear spring and a secondary mass attached to the primary system by a nonlinear spring. This arrangement forms a nonlinear dynamic vibration absorber (nDVA), which is used in this contribution as a representative example of a nonlinear mechanical system. The sensitivity analysis of the suppression bandwidth, namely, the frequency range over which the ratio of the main mass displacement amplitude to the amplitude of the forcing function is less than unity, with respect to the design variables that characterize the nonlinear system based on the first order finite differences is presented. For illustration purposes the optimization problem is written as to maximize the suppression bandwidth by using three recent bioinspired optimization methods: Bees Colony Algorithm, Firefly Colony Algorithm, and Fish Swarm Algorithm. The results are compared with other evolutionary strategies.