Keywords: cellular materials design, passive vibration control, non-linear visco-elastic behaviour, optimization, simulated annealing, cost functional.

The contribution of computational mechanics has been essential to the more recent and remarkable developments in structural design and optimization. Now the same impact and influence can be predicted in its application to new materials design, within the framework of micromechanics. The latest developments in these areas have lead to integrated computational methodologies that permit not only the structural design of the mechanical component but also the design of the material used in its fabrication. This is particularly evident in the area of cellular-composite materials where the unit cell geometry (characterizing the composite or cellular material) is a key factor in its effective mechanical properties and thus can significantly improve the structural response of the mechanical component.

The objective of this contribution is to extend the models of cellular-composite material design to nonlinear material behaviour and apply it to the design of materials for passive vibration control.

As a first step a computational tool allowing determination of macroscopic optimized one-dimensional isolator behaviour was developed. In order to characterize non-linear elastic behaviour, fixed parts of the static curve were identified and variable parts were estimated using piece-wise cubic hermit polynomial expressions with a flexible number of divisions. The algorithm assures positive stiffness at any instant, in order to avoid unstable behaviour. Damping is assessed by a linear viscous contribution. Optimal isolator behaviour to a given set of loads is obtained using a generic probabilistic meta-algorithm, simulated annealing. Cost functional involves minimization of the maximum response amplitude in a set of predefined time intervals and a maximization of the total energy absorbed in the first loop. Dependence of the global optimum on several combinations of leading parameters of the simulated annealing procedure, like neighbourhood definition and annealing schedule, is also studied and analyzed. The results obtained facilitate the design of elastomeric cellular materials with improved behaviour in terms of dynamic stiffness for passive vibration control. All computational tools are developed in Matlab.

Future research will be directed to the design of cellular and composite viscoelastic materials with improved behaviour identified by the procedure presented in this contribution. This application will have a direct and immediate impact on product design and development, especially in the design of new mechanical components such as engine mounts and new suspension systems.

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