Modal domain

Since modal parameters depend on the material property and geometry, the change in natural frequencies, mode shapes and modal curvature etc. can be used to locate the damage in structures without the knowledge of excitation force. The extent of the literature pertaining to the various methods for SHM based on modal domain is quite large. Lakshminarayana and Jebaraj [1999] have used first four bending and torsion modes and corresponding changes in natural frequencies to estimate the location of a crack in a beam. It is reported that if the crack is located at the peak / trough positions of the strain-mode shapes, then percentage changes in frequencies would be higher for corresponding modes. It is also found that if the crack is located at the nodal points of the strain-mode shapes, then the percentage change in frequency values would be lower for corresponding modes.

Tracy and Pardoen [1989] have also found that if the delamination is in a region of mode shape where the shear force is very high, there will be considerable degradation in natural frequency which is otherwise not significant. Hence, by studying the mode shapes and the corresponding natural frequencies, estimation on the location of delamination can be made.

The anti-resonance frequencies are the frequencies at which the magnitude of the frequency response at measured degrees of freedom approaches zero. To calculate anti-resonance frequencies of a dynamic system, He and Li [2002] have developed an accurate and efficient method for undamped systems. The reasons for looking to the anti-resonance frequencies are that these anti-resonance frequencies can be easily and accurately measured in a similar way as for the natural frequencies. Furthermore, a system can have much greater number of anti-resonance frequencies than natural frequencies since every FRF between an actuator and a sensor pair contains a set of anti-resonance frequencies.

Doebling and Farrar [1997] have examined changes in the frequencies and mode shapes of a bridge as a function of damage. This study focuses on estimating the statistics of the modal parameters using Monte Carlo procedures to determine if damage has produced a statistically significant change in the mode shapes. Stanbridge et al [1997] have also used mode shape changes to detect saw-cut and fatigue crack damage in flat plates. Methods of extracting those mode shapes using Laser Doppler Vibrometer have been discussed.