Alexander F Vakakis
Analytical and experimental study of nonlinear mode localization and passive motion confinement in a flexible structure
In the proposed work, a new analytical methodology will be used to study the localized nonlinear modes (NNMs) of a system of coupled nonlinear beams, representative of flexible components often encountered in engineering applications. Localized NNMs are spatially confined, synchronous periodic oscillations of all points of the structure, and lead to confinement of motions generated by external impulses. To test the validity of the analytical results, a series of experiments will be performed. The experimental fixture consists of two cantilever beams coupled by means of a linear stiffness. Nonlinearities in the system are actively generated through a feedback control set-up consisting of six controllers with nonlinear gain laws. Input signals are measured by displacement transducers whereas output control forces are applied to the system by control actuators. Experimental modal testing will be conducted to measure the nonlinear resonances of the flexible structure. In addition, impulsive excitations will be applied to the structure in order to detect experimentally the theoretically predicted passive motion confinement phenomenon. It is believed that these experiments will be the first to confirm the existence of localized NNMs and motion confinement in a practical flexible structure. Nonlinear motion confinement phenomena have important implications on the vibration isolation of flexible systems, since structures whose inherent dynamics lead to spatial confinement of motions generated by external disturbances are expected to be more amenable to active or passive vibration suppression than structures with no such properties. The research proposed is expected to extend the present state-of-the-art in the field of the nonlinear dynamics of flexible periodic structures, and to be the first step towards developing a new design principle for robust passive or active vibration isolation of flexible structures.