While modal analysis theory has not changed over the last century, the application of the theory to experimentally measured data has changed significantly. The advances of recent years with respect to measurement and analysis capabilities have caused a reevaluation of what aspects of the theory relate to the practical world of testing. Thus, the aspect of transform relationships has taken on renewed importance since digital forms of the integral transforms are in constant use. The theory from the vibrations point of view involves a more thorough understanding of how the structural parameters of mass, damping, and stiffness relate to the impulse-response function (time domain), the frequency response function (Fourier or frequency domain), and the transfer function (Laplace domain) for single and multiple degree-of-freedom systems.

SINGLE DEGREE-OF-FREEDOM SYSTEMS

In order to understand modal analysis, complete comprehension of single degree-of-freedom systems is necessary. In particular, complete familiarity with single degree-of-freedom systems as presented and evaluated in the time, frequency (Fourier), and Laplace domains serves as the basis for many of the models that are used in modal parameter estimation. This single degree-of-freedom approach is trivial from a modal analysis perspective since no modal vectors exist. The true importance of this approach results from the fact that the multiple degree-of-freedom case can be viewed as simply a linear superposition of single degree-of-freedom systems.

The general mathematical representation of a single degree-of-freedom system is expressed by

where

m	= mass constant
c	= damping constant
k	= stiffness constant

This differential...