In this paper, a procedure for the optimal design of multi-parametric nonlinear systems is presented which makes use of a parametric continuation strategy based on simple shooting method. Shooting method is used to determine the periodic solutions of the nonlinear system and multi-parametric continuation is then employed to trace the change in the system dynamics as the design parameters are varied. The information on the variation of system dynamics with the value of the parameter vector is then used to find out the exact parameter values for which the system attains the required response. This involves a multi-parametric optimisation procedure which is accomplished by the coupling of parameter continuation with different search algorithms. Genetic Algorithm as well as Gradient Search methods are coupled with parametric continuation to develop an optimisation scheme. Furthermore, in the coupling of continuation and Genetic Algorithm, a ``norm-minimising'' strategy is developed and made use of minimising the use of continuation. The optimisation procedure developed is applied to the Duffing oscillator for the minimisation of the system acceleration with nonlinear stiffness and damping coefficient as the parameters and the results are reported. It is also briefly indicated how the proposed method can be successfully used to tune nonlinear vibration absorbers.
B. Balaram, Narayanan, M. D., and Rajendrakumar, P. K., “Optimal design of multi-parametric nonlinear systems using a parametric continuation based Genetic Algorithm approach”, Nonlinear Dynamics, vol. 67, pp. 2759–2777, 2012.