Modal damping

When compared to frequencies and mode shapes, damping properties have not been used as extensively as frequencies and mode shapes for damage diagnosis. Crack detection in a structure based on damping, however, has the advantage over other detection schemes based on frequencies and mode shapes. This is due to the fact that the damping changes have the ability to detect the nonlinear, dissipative effects that cracks produce. Modena et al [1999] show that the visually undetectable cracks cause very little change in resonant frequencies and require higher mode shapes to be detected, while the same cracks cause larger changes in the damping. Zonta et al [2000] observe that crack creates a non-viscous dissipative mechanism for making damping more sensitive to damage. Kawiecki [2000] noted that damping can be a useful damage-sensitive feature particularly suitable for SHM of lightweight and micro-structures. The application of arrays of surface-bonded piezo-elements to determine modal damping characteristics for SHM of light weight and micro structure are discussed. Many structural health monitoring techniques rely on the fact that structural damage can be expressed by a reduction in stiffness. Maeck and Roeck [2001] have applied a direct stiffness approach to damage detection, localization and quantification for a bridge structure which uses experimental frequencies and mode shapes in deriving the dynamic stiffness of a structure.

A reduction in stiffness corresponds to an increase in structural flexibility. Pandey and Biswas [1994] have presented a damage detection and damage localization method based on changes in the flexibility of the structure. Bernal [2000] mentions that changes in the flexibility matrix are sometimes more desirable to monitor than changes in the stiffness matrix. Since the flexibility matrix is dominated by the lower modes, good approximations can be obtained even when only a few lower modes are employed. Reich and Park [2000] focus on the use of localized flexibility properties for structural damage detection. The authors choose flexibility over stiffness for several reasons, including the facts that

1. flexibility matrices are directly attainable through the modes and mode shapes determined by the system identification process,
   
2. iterative algorithms usually converge fast to high eigen values,
   
3. in flexibility-based methods, these eigen values correspond to the dominant low frequency components in structural vibrations.

A structural flexibility partitioning technique is used because when the global flexibility matrix is used, there is an inability to uniquely model elemental changes in flexibility. The strain based substructural flexibility matrices measured before and after a damage event, are compared to identify the location and relative degree of damage.