Optimal design of linear and nonlinear vibration absorbers for damped systems

Nonlinear programming techniques are applied to obtain optimal tuning and damping parameters for dynamic absorbers. The optimization has been carried out for damped as well as undamped primary systems. It is found that optimal tuning parameters, obtained with the goal of minimizing the main mass maximum displacement, undergo small changes as damping is introduced into the main system. The use of other objective functions, such as minimizing maximum velocity, or mean-squared motion to white noise excitation lead to more significant changes in optimal parameter values. It is shown, on the basis of approximate solutions to the nonlinear absorber problem, that only small improvements in steady state response are obtained using hardening or softening coupling springs.