Optimal Design Of A Parallel Beam System With Elastic Supports To Minimize Flexural Response To Harmonic Loading

Abstract

Mechanical systems subject to vibration are prevalent across many industries. Harmonic problems can be especially challenging to optimize due to the likelihood that the response will be multi-modal; influenced by system natural frequencies throughout the design space. Further, analysis of these systems often involves large and complex computer models which require significant resources to execute. A parallel beam system, as evaluated with Finite Element Modeling (FEM), is used as an example in this work to demonstrate a proposed method of identifying an optimum in a constrained, multi-modal response environment with consideration for Expensive Black Box Functions. The presented method leverages benefits of a combined approach where the domain is first surveyed for potential areas of optimal response using a method of Steepest Feasible Descent (SFD), followed by a search in the optimal region using direct search methods. The method of SFD is made useful for constrained models by a penalty system including both deterministic and programmatic methods. A sensitivity-based search vector method also helps to manage situations where significant difference in magnitude exists among the design variables. Evidentiary support for these key program elements is provided using standardized test functions. The effectiveness of the method is also demonstrated by seeking a minimum flexural response for a parallel beam system subject to elastic support and response constraints.