Despite tremendous advances in modern computational technology, there still remain many engineering problems that do not allow numerical solutions of reasonable accuracy. In many of these problems the main difficulty stems from lack of our ability to accurately model damping. Such examples are simulation of structure-borne noise, stability analysis of dynamic systems and numerical prediction of fatigue failure. In these problems small difference in damping description results in a completely different solution, while the current state of the art of damping modeling cannot provide such accuracy.
A new concept proposed by one of the authors [1,2], which uses the dynamic stiffness matrix (DSM-the inverse of a frequency response function matrix), is studied in this two-part paper. Advantages of the method and practical issues to overcome are discussed in both papers. The method obtains the damping model directly from measured data; and is independent of classical damping models. The method can describe the spatial distribution of damping without additional data conditioning, and has a very simple algorithm. Thus, the effect of numerical and measurement errors are minimized.
This paper contains a numerical study of the algorithm and identifies key properties of input DSM data along with various pre- and post-processing diagnostic tools. Spatial truncation and its effects on the input data and resulting matrices will also be discussed. The second paper examines the advantages, and issues of applying the damping identification method to three simple experimental structures.