A case study on frequency response optimization

This paper presents an application of structural synthesis techniques to th e design of an exhaust system belonging to a heavy truck. The system is exc ited by the vehicle's powertrain over a wide frequency range, containing fi ve resonant peaks. Through the optimization procedure, the finite element m ethod model is modified, and the profile of the supporting beams is automat ically redesigned to achieve superior performance: first, obtaining optimum values for the natural frequencies and later minimizing the dynamic displa cements. It is important to mention that structural synthesis software as t he one employed in this study (VMA/GENESIS version 3.0) usually cannot deal with entities that present different values at the various analysis steps as is the case of frequency dependent displacement. It means that such phys ical terms cannot be computationally expressed as objective functions or co nstraints for optimization purposes. This problem is overcome by means of a mathematical artifice, the "Beta Method". This scheme relies on an auxilia ry design variable for optimization and minimizes the maximum value assumed by a certain entity. The rules for expressing the optimization problem bet ter in terms of the "Beta" variable will also be outlined. (C) 2001 Elsevie r Science Ltd. All rights reserved.