### Reliability-Based Design of a Dynamical Suspension with Random Stiffness under an Imposed Amplitude Response Hull

#### Abstract

This paper deals with the design of a suspension, idealised as a spring-massdamper 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 optimisation. To concentrate in the main ideas, only the stiffness of the system will be considered random. The stiffness is characterised by a uniform random variable, and its mean and standard deviation are the optimisation parameters. The design problem is stated as a two-objective optimisation. The two-objective functions are the mean and the

standard deviation of the stiffness. One searches 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 (NBI) 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 amplituderesponse hull. Despite the simplicity of the example treated here, chosen to highlight the main ideas without distraction, the strategy proposed here can be generalised 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.

standard deviation of the stiffness. One searches 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 (NBI) 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 amplituderesponse hull. Despite the simplicity of the example treated here, chosen to highlight the main ideas without distraction, the strategy proposed here can be generalised 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.

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Güemes 3450

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**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**