Design Optimization of a Random Suspension Device Considering a Reliability Constraint on the Frequency Response Function

Abstract This work deals with the design of a suspension device, idealized as a spring-mass-damper system. The amplitude of a nominal system is constrained to satisfy certain limitations in a given frequency band and the design is to be done as a reliability-based optimization. This constitutes a major difficulty since the constraint becomes a random process. To concentrate in the main ideas, only the stiffness of the system will be considered random. The stiffness is characterized by a uniform random variable, and its mean and standard deviation are the optimization parameters. The design problem is stated as a two-objective optimization. They are the mean and the standard deviation of the stiffness: one search for the lowest stiffness and the greatest standard deviation, while the amplitude response must be within the acceptable domain of vibration, which is prescribed. To generate the Pareto front, the Normal Boundary Intersection method is used in the RFNM algorithm. Results show that a not-connected Pareto curve can be obtained for some choice of constraint. Hence, in this simple example, one shows that difficult situations can occur in the design of dynamic systems when prescribing an amplitude-response hull. Despite the simplicity of the example treated here, chosen to highlight the main ideas without distraction, the strategy proposed here can be generalized for more complex cases and give valuable results, able to help designers to choose for the best compromise between the mean and the standard deviation in reliability-based designs.