Frequency domain

In the frequency domain method, most important part is to calculate the dynamic stiffness matrix at each frequency either from stiffness and mass matrix or directly from spectral formulation. The applied load vector is transformed in the frequency domain by Fourier Transform and solved for structural response at each frequency. After getting responses for each frequency, inverse Fourier Transform provides the time domain responses.

Although majority of investigations into structures under dynamic loading are concerned with obtaining the natural frequencies, and possibly mode shapes of the structure, a much more valuable description of the dynamic behavior of the structure is the Frequency Response Function (FRF), which describes the relationship between a local excitation force applied at one location on the structure and the resulting response at another location. Essentially, the FRF returns information about the behavior of the structure over a range of frequencies. The response at a particular frequency for some forcing and response locations will simply be a complex vector, which is often plotted in terms of real and imaginary parts or in terms of amplitude and phase. The frequency response of a system can be measured by:

1. applying an impulse to the system and measuring its response;
2. sweeping a constant-amplitude pure tone through the bandwidth of interest and measuring the output level and phase shift relative to the input.

Mal et al [2005] have presented a methodology for automatic damage identification and localization using FRF of the structure. Lopes et al [2000] relate the electrical impedance of the piezoelectric material to the FRFs of a structure. The FRFs are extracted from the measured electrical impedance through the electromechanical interaction of the piezo-ceramic material and the structure.