Theoretical and experimental studies of steady state nonlinear localization and energy pumping in systems of coupled oscillators

In this work, theoretical and experimental methods are applied to the study of nonlinear localization and energy pumping phenomena in systems of coupled oscillators with essential (non-linearizable) stiffness nonlinearities. A basic aim of the work is to show that systems of coupled oscillators can be designed to passively confine steady state vibrations in a priori determined subsystems; in turn, such motion confinement phenomena enhance the capacity of these systems to act as efficient and robust vibration isolators of unwanted disturbances generated at their boundaries. In contrast to earlier studies where linearizable stiffnesses were considered, the motion confinement was done by introducing essentially nonlinear stiffnesses to the system. Apart from passive motion confinement capability, certain of the systems considered possess additional interesting dynamical features: such as complete elimination of linearized-type resonances over broad frequency ranges; dual-mode vibration isolation capability (that is, they can effectively localize and isolate unwanted vibrations generated at different locations on their boundaries); and nonlinear hysteresis phenomena caused by ‘jumps’ of the steady state responses between co-existing branches of solutions.; In particular, a theoretical study is undertaken of a nonlinear vibration isolation system with essential stiffness nonlinearities capable of simultaneously (a) isolating its upper part from periodic disturbances generated at its base, and (b) isolating its base from periodic disturbances generated at its upper part.; In a second study, the steady state dynamics of a weakly coupled system composed of a linear primary oscillator coupled to a nonlinear attachment is investigated. Both theoretical and experimental investigations are undertaken to study the effect of the NES on the steady state dynamics of the coupled system.; Finally, the dynamics of a coupled system with high degree of essential odd stiffness nonlinearity is studied. A comparison is made of the steady state response of this highly nonlinear system with the non-smooth system that results when the high-order nonlinearity is replaced by nonlinearity of the clearance type.; Based on the results of this work it can be concluded that using essentially nonlinear stiffness elements for passive vibration control can provide relatively simple, modular vibration isolation designs for engineering structures.