Dimensionality and Spatial Coherency in the Dynamics Flexible Impact Oscillators

摘要

Several new experimental methods for studying nonlinear behavior in structuraldynamics have been developed. Control software for automated bifurcation data acquisition system which can be used to generate high resolution experimental bifurcation diagrams is proving to be useful in identifying critical dynamical regimes for specific systems and to provide an important source of model validation data. A stochastic interrogation method for studying global dynamics and basins of attraction experimentally has been developed and applied. Data obtained with this technique has been used to find basins of attraction, identify global bifurcations, and generate nonlinear models. The same procedure has been used to obtain the first experimental image of homoclinic bifurcation before any stable chaotic solutions are present in the system, and to perform damping measurements in a new way. It has also been shown how spatial correlation measurements and the proper orthogonal decomposition allow the relationship between spatial and temporal complexity to be examined and provide shape functions which describe the observed dynamics, even when linear normal modes are not well defined. On the theoretical front, a new numerical method for studying nonlinear modal interactions based on the calculation of Lyapunov exponents has also been developed. The method splits the modes into active and passive sets: the active modes interact to contain the attractor, and hence can be considered more important in formulating a low-dimensional model. (MM).