Research in Structural Dynamics
Final rept. 1 Mar 94-28 Feb 97
GEORGIA INST OF TECH ATLANTA SCHOOL OF AEROSPACE ENGINEERING
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This report addresses truncation in structural dynamics, energy thresholds in nonlinear vibration, dynamic potential of vibrating systems, and high temperature diffusional creep. Study of the dynamics of elastic structures is usually based on structural models with a few degrees of freedom. In this connection it is important to understand how these degrees of freedom should be chosen and how the neglected degrees of freedom affect the accuracy of the model. It is shown that there is an energy threshold beyond which the laws of statistical mechanics become valid, requiring the consideration of all degrees of freedom. For excitation which is moderate but below this threshold methods are presented which show how to capture the leading degrees of freedom and how to take into account the neglected modes. The value of the energy threshold is driven by the specifics of models used so that small changes in the model can strongly increase the value of the threshold. The dynamic potential makes use of an analogy between thermodynamical energy and structural vibration. The existence of the dynamical potential reduces the number of experimentally determined functions to one. It is shown, and confirmed experimentally, how this leads to simple relations between excitations and responses of nonlinear vibrating systems. Finally, a nonlinear theory of diffusional plasticity is presented.
- Statistics and Probability