1 Abstract The aim of this contribution is to extend the techniques of composite materials design to non-linear material behaviour and apply it for design of new materials for passive vibration control. As a first step a computational tool allowing determination of macroscopic optimized one-dimensional isolator behaviour was developed. Voigt, Maxwell, standard and more complex material models can be implemented. Objective function considers minimization of the initial reaction and/or displacement peak as well as minimization of the steady-state amplitude of reaction and/or displacement. The complex stiffness approach is used to formulate the governing equations in an efficient way. Material stiffness parameters are assumed as non-linear functions of the displacement. The numerical solution is performed in the complex space. The steady-state solution in the complex space is obtained by an iterative process based on the shooting method which imposes the conditions of periodicity with respect to the known value of the period. Extension of the shooting method to the complex space is presented and verified. Non-linear behaviour of material parameters is then optimized by generic probabilistic meta-algorithm, simulated annealing. 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. Procedure is programmed in MATLAB environment. Keywords: composite materials, passive vibration control, non-linear visco-elastic behaviour, optimization, shooting method, simulated annealing, cost functional. 1 Introduction The latest developments in computational mechanics have lead to integrated methodologies that permit not only the structural design and shape optimization of the mechanical component but also the tailoring of the material properties and Paper 166 Design of New Materials for Passive Vibration Control Z. Dimitrovová 1 and H.C. Rodrigues 2 1 UNIC, Department of Civil Engineering New University of Lisbon, Portugal 2 IDMEC, Department of Mechanical Engineering Technical University of Lisbon, Portugal ©Civil-Comp Press, 2009 Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing, B.H.V. Topping, L.F. Costa Neves and R.C. Barros, (Editors), Civil-Comp Press, Stirlingshire, Scotland