DYNAMIC-RESPONSE ANALYSIS IN THE FREQUENCY-DOMAIN

Analysis in the frequency domain using discrete Fourier transforms is an efficient means of calculating the dynamic response of linear systems. In fact, for systems with frequency dependent parameters and also in those cases where the complex frequency response functions are more easily determined, frequency domain analysis may be the only effective means of determining the dynamic response. The use of discrete transforms along with finite summation requires that the forcing function and the impulse function be converted into periodic forms. This modification may introduce unacceptable errors in the results of analysis, unless appropriate steps are taken to avoid or minimize the effect of aliasing or overlapping. For single-degree-of-freedom systems, procedures that will eliminate the effect of aliasing have already been developed. However, problems related to frequency domain analysis still exist for multi-degree-of-freedom systems with non-proportional damping, in analysis through substructuring and in those cases where a continuum solution is involved. A new procedure which addresses these problems and is applicable to both single- and multi-degree-of-freedom system as well as to analysis through substructuring is presented here.