Optimal design criteria for isolation devices in vibration control

Vibration control and mitigation is an open issue in many engineering applications. Passive strategies was widely studied and applied in many contests, such as automotive, aerospatial, seismic and similar. One open question is how to choose opportunely devices parameters to optimize performances in vibration control. In case of isolators, whose the main scope is decoupling structural elements from the vibrating support, optimal parameters must satisfy both vibration reduction and displacement limitation. This paper is focused on the a multi-objective optimization criterion for linear viscous-elastic isolation devices, utilised for decreasing high vibration levels induced in mechanical and structural systems, by random loads. In engineering applications base isolator devices are adopted for reducing the acceleration level in the protected system and, consequently, the related damage and the failure probability in acceleration sensitive contents and equipment. However, since these devices act by absorbing a fraction of input energy, they can be subjected to excessive displacements, which can be unacceptable for real applications. Consequently, the mechanical characteristics of these devices must be selected by means of an optimum design criterion in order to attain a better performance control. The proposed criterion for the optimum design of the mechanical characteristics of the vibration control device is the minimization of a bi-dimensional objective function, which collects two antithetic measures: the first is the index of device efficiency in reducing the vibration level, whereas the second is related to system failure, here associated, as in common applications, to the first exceeding of a suitable response over a given admissible level. The multi-objective optimization will be carried out by means of a stochastic approach: in detail, the excitation acting at the support of the protected system will be assumed to be a stationary stochastic coloured process. The design variables of optimization problem, collected in the design vector (DV), are the device frequency and the damping ratio. As cases of study, two different problems will be analysed: the base isolation of a rigid mass and the tuned mass damper positioned on a MDoF structural system, subject to a base acceleration. 20