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Two potential applications of a dynamic stiffness matrix (DSM) based direct damping matrix identification method are presented in this paper. The method was proposed to identify both the mechanism and spatial distribution of damping as a matrix of general function of frequency. First potential application is the analytical-experimental hybrid structural dynamics modeling, in which the model is constructed by combining analytically formulated mass and stiffness matrices with the experimentally identified damping matrix. Second application is the direct measurement of complex shear modulus of viscoleastic materials. The real and imaginary parts of the dynamic stiffness measured on a test setup that resembles a single degree of freedom system is used to compute the shear modulus and the loss factor of viscoelastic materials.

Theoretical development of a dynamic stiffness matrix (DSM) based direct damping matrix identification method is revisited in this paper. This method was proposed to identify both the mechanism and spatial distribution of damping in dynamic structures as a matrix of general function of frequency. The objective of this paper, in addition to the review of the theoretical development, is to investigate some major issues regarding the feasibility of this method. The first issue investigated is how the errors in measured frequency response functions (FRF) affect the accuracy of the DSM. It was already known that the DSM is highly sensitive to errors that are present in the FRF. A detailed analytical and computational study is conducted, which finally leads to a sound physical explanation of the high sensitivity of the DSM to measurement errors. A new and also important conclusion is that the leakage error drastically affects the accuracy of the computed DSM.

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.