A case study on frequency response optimization

This paper presents an application of structural synthesis techniques to the design of an exhaust system belonging to a heavy truck. The system is excited by the vehicleʹs powertrain over a wide frequency range, containing ®ve resonant peaks. Through the optimization procedure, the ®nite element method model is modi®ed, and the pro®le of the supporting beams is automatically redesigned to achieve superior performance: ®rst, obtaining optimum values for the natural frequencies and later minimizing the dynamic displacements. It is important to mention that structural synthesis software as the one employed in this study (VMA/GENESIS version 3.0) usually cannot deal with entities that present di€erent values at the various analysis steps as is the case of frequency dependent displacement. It means that such physical terms cannot be computationally expressed as objective functions or constraints for optimization purposes. This problem is overcome by means of a mathematical arti®ce, the ``Beta Methodʹʹ. This scheme relies on an auxiliary design variable for optimization and minimizes the maximum value assumed by a certain entity. The rules for expressing the optimization problem better in terms of the ``Betaʹʹ variable will also be outlined