A comprehensive review on dual approach to the vibration analysis: Some dual techniques and application

This paper reviews key ideas of the researches on the dual approach to the vibration analysis. Three types of dual techniques, namely, forward - return dual technique, global-local dual technique, weighted averaging dual technique for the problem of equivalent replacement are summarized. Different implements and realizations of dual techniques to nonlinear vibration analysis and design of dynamic absorbers are reviewed. Finally, the challenging issues based on the dual techniques are discussed. A number of possibilities for developing analytical techniques related to dual techniques are proposed. The review shows that the dual approach is an appropriate one and the dual techniques are effective tools for studying random and deterministic nonlinear vibrational systems.